Exact algorithms, known for high computational efficiency and stability, are among the mainstream methods for solving practical optimization problems, but their performance deteriorates significantly when tackling complex problems. Intelligent optimization algorithms with self-organizing, adaptability and self-learning characteristics are better suited for complex problems but have longer runtimes, which hinders rapid response. Given this, this paper proposes a data-driven constrained multi-objective dual-layer autonomous intelligent optimization method that utilizes the complementary advantages of exact and intelligent algorithms to solve constrained multi-objective optimization problems with different response time requirements. In the first layer, an evaluation rule based on preference information enables a unified comparison of the performance of exact and intelligent algorithms, thereby identifying algorithm categories suitable for solving problems based on their requirements. In the second layer, the most suitable algorithms are generated based on problem characteristics and response time requirements. The proposed method is applied to six benchmark test problems and the operation optimization problems of integrated coal mine energy systems, and the experimental results verify its effectiveness and feasibility.

The coal mine integrated energy system dispatch problem (CMIES-DP) is a constrained multiobjective optimization problem (CMOP) with the characteristics of multiple objectives, high-dimensional decision variables, and multiple constraints, which makes it challenging for existing methods. On the one hand, existing constrained multiobjective evolutionary algorithms (CMOEAs) are prone to falling into local optima when facing problems with high-dimensional variables. On the other hand, the relationship between objectives and constraints of CMIES-DP has not been fully analyzed to guide the design of targeted solving techniques. Therefore, this article proposes a time-division-based CMOEA (TDCEA), where the characteristics of CMIES-DP are analyzed to design two main strategies. First, by analyzing the temporal relationship of objectives and constraints, CMIES-DP is decomposed into multiple subproblems with fewer variables and constraints, and these subproblems are sequentially solved to obtain better decision variables. Then, a random concatenation method is designed to combine the decision variables output from subproblems into a solution set with complete decision variables, and the new solution set will be further optimized to find feasible Pareto optimal solutions. Second, the relationship between constraints and objectives is analyzed to guide the design of evolving populations, so as to improve the search ability of the algorithm. In the experiments, the proposed algorithm is used to solve a real-world CMIES-DP case, and results demonstrate that compared with other advanced algorithms, the proposed algorithm achieves better performance regarding diversity, convergence, and distribution.

Most existing constrained multi-objective evolutionary algorithms (CMOEAs) experience a dramatic performance degradation when solving large-scale constrained multi-objective optimization problems (LSCMOPs), since they converge very slowly and easily get trapped in local optima due to the loss of diversity. To enhance the efficiency of tackling LSCMOPs, this paper proposes an indicator-based evolutionary algorithm, referred to as ILCMO. In ILCMO, two complementary indicators are proposed to assess the contribution of each individual to feasibility, convergence, and diversity. The first is a feasibility-oriented indicator designed to drive the population towards the feasible regions. The second is an infeasibility-assisted dynamic indicator, which comprises two relaxed constraint boundaries. Theoretical studies demonstrate that this dynamic indicator can effectively guide the population to focus on evenly searching the infeasible regions around feasible solutions to enhance local diversity. In addition, a variable grouping-based differential evolution (VGDE) strategy, which includes a group-based intra-learning operator and a group-based inter-learning operator, is devised to improve the quality of reproduction in large-scale search spaces. The effectiveness of the proposed algorithm is validated through comprehensive experiments on four benchmarks and a microgrid dispatch problem against seven state-of-the-art algorithms.

In the field of message-passing interface (MPI) program path coverage test case generation, evolutionary algorithms (EAs) have been frequently utilized to generate test cases. However, relying solely on EAs will incur excessive computational costs. In this article, we improve the efficiency and quality of MPI program path coverage test cases generated by EAs based on elite individual selection. First, data within the data domain is sampled and fitness is calculated to form a shared set. Then, the population data is initialized using EAs, and the fitness of individuals is predicted using the neighbor value sharing algorithm (NVSA). Subsequently, individuals are ranked using rank-based elite selection (RES). Finally, elite individuals are chosen through ranking to run the program and verify the generation of test cases. In order to reduce computational costs, data dimensionality reduction operations are added to the above process. We demonstrate that the proposed method can effectively generate test data and reduce test costs by comparing it with several excellent methods on seven representative MPI programs. Among them, NVSA has a maximum improvement of 42.2%, RES has a maximum improvement of 31.5%, dimensionality reduction can increase by 20.2%, and the overall method has a maximum improvement of 47.4%.

Cross-Project Defect Prediction (CPDP) utilizes the existing labeled data in the source project to assist with the prediction of unlabeled projects in the target dataset, which effectively improves the prediction performance and has become a research hotspot in software engineering. At present, CPDP can be categorized into homogeneous CPDP and heterogeneous CPDP (HDP), in which HDP doesn’t require that the source project and the target project have the same feature space, thus, it is more widely used in the actual CPDP. Most of current HDP methods map the original features to the latent feature space and reduce the inter-project variation by transferring domain-independent features, but the transferring process ignores the use of domain-related features, which affects the prediction performance of the model. Moreover, the mapped latent features are not conducive to the model’s interpretability. Based on these, this article proposes a Heterogeneous Defect Prediction method based on Feature Disentanglement (FD-HDP). We disentangle the features using domain-related and domain-independent feature extractors, respectively, to improve the interpretability of the model by maximizing the domain adversarial loss during training and guiding the feature extractors to produce accurate domain-related and domain-independent features. The weighted sum of the prediction results from domain-related and domain-independent predictors is used as the final prediction result of the project during the prediction process, which realizes the combination of domain-independent and domain-related features and effectively improves the prediction performance. In this article, we conducted experiments using four publicly available defect datasets to construct heterogeneous scenarios. The results demonstrate that the FD-HDP model shows significant advantages over state-of-the-art methods in six metrics.

A target path of Message Passing Interface (MPI) programs typically consists of several target sub-paths. During solving a test case that cover the target path using an intelligent optimization algorithm, we often find that there are some hard-to-cover target sub-paths, which limit the testing efficiency of the entire target path. Therefore, this paper proposes an approach of low-cost testing for path coverage of MPI programs using surrogate-assisted changeable multi-objective optimization, which is used to further improve the effectiveness and efficiency of test case generation. The proposed approach first establishes a changeable multi-objective optimization model, which is used to guide the generation of test cases. During solving the changeable multi-objective optimization model using an intelligent optimization algorithm, we then determine each hard-to-cover target sub-path and form a corresponding sample set. Finally, we manage the surrogate model corresponding to each hard-to-cover target sub-path based on the formed sample set, and select superior evolutionary individuals to really execute the MPI program under test, thus reducing the cost and times of program execution. The proposed approach has been applied to path coverage testing of several benchmark MPI programs, and compared with several state-of-the-art approaches. The experimental results show that the proposed approach significantly improves the effectiveness and efficiency of generating test cases.

The solving process of constrained multi-objective evolutionary optimization algorithms (CMOEAs) is closely related to the search direction of the population. How to learn promising search directions through population data remains challenging. Therefore, this paper proposes a CMOEA with search direction learning. In this method, principal component analysis (PCA) is first used to learn the mainstream direction of population evolution, then single-constraint domination is used to learn the tributary direction of population evolution, and finally, the search directions are summarized to guide the generation of high-quality offspring populations. The performance comparison with five state-of-the-art algorithms on three standard test problems demonstrates the superiority of the proposed method. Its applicability in the field of simulated integrated circuits proves the scalability of the proposed method.

Given the high complexity and significant uncertainty of the multiple loads in integrated coal mine energy systems, interval prediction provides more comprehensive information for developing dispatch strategies, thus improving the reliability and robustness of the decision-making process. However, traditional interval prediction evaluation metrics fail to adequately reflect the impact of interval prediction results on the optimal dispatch cost. To address this, this paper proposes a day-ahead interval prediction method for the multivariate load of an integrated coal mine energy system, explicitly considering the dispatch cost. First, multi-task learning is combined with quantile regression to explore the coupling characteristics between multiple loads systematically. Next, an optimization model is constructed that simultaneously accounts for interval prediction performance and dispatch cost to determine the optimal upper and lower quantile combinations, adapting to dynamic load changes. Finally, the upper and lower quantile combinations are optimized using genetic algorithms, and the prediction intervals of multiple loads for the day ahead are obtained based on the optimized quantile combinations and the trained model. The proposed method is applied to an integrated coal mine energy system and compared with existing methods. Experimental results demonstrate that the proposed method ensures the prediction accuracy of the day-ahead multivariate load interval and significantly reduces the system’s dispatch cost.

ABSTRACT Crowdsourcing testing has the advantages of efficiency, speed, and reliability, but an excessive number of test reports makes it a challenge for report reviewers to select high‐quality test reports in a limited time. Test reports submitted by crowd workers often tend to be short textual descriptions with a large number of screenshots attached. Most traditional processing methods of test reports target reports that only contain text information, which cannot meet the defect detection requirements of crowdsourced test reports. In view of this, this paper proposes a prioritization method of crowdsourced test reports that integrates text and image information. First, we extract the text and image information from the test reports, based on which the defect detection abilities of the test reports are measured and the similarities between test reports are calculated. Then, a multi‐stage prioritization method of the test reports is presented based on the defect detection levels and similarities of the test reports. In the first stage, based on the defect detection levels and the similarities, the test report set is sorted and clustered to obtain the sorting results of partial reports and the similar set for each sorted report; in the second stage, the similar test report set is sorted with the criteria of minimizing the similarity and maximizing the defect detection level; the sorting results of the two stages are combined to form the final priorities of test reports. To validate our approach, we conducted experiments on five crowdsourced test datasets. The results and the analysis show that our approach can detect all faults faster in a limited time. By comprehensively utilizing text and image information to prioritize test reports, better sorting results can be obtained than state‐of‐the‐art methods.

ABSTRACT A software ecosystem is a complex system that allows developers to cooperate with each other. Community is a universal and important topological property of networks. Detecting the communities of the software ecosystem is of great significance for analyzing its structural characteristics, discovering its hidden patterns, and predicting its behavior. Traditional community detection algorithms of complex networks are mostly for undirected networks. For the social network, the direction of information dissemination between developers cannot be ignored. In addition, the existing algorithms of community detection usually only consider direct influence between individuals while neglecting indirect relationships. To solve these problems, this paper presents a community detection method based on a two‐step information dissemination model for the software ecosystem. First, a two‐step information dissemination model is established to calculate the information gain of nodes. Second, a ranking method of developers' comprehensive influence is given through their influence vectors and information gains. Finally, communities are detected by taking the influential nodes as the cluster centers and the probability of information dissemination as the clustering direction. The proposed method is applied to community detection of typical software ecosystems in GitHub. The experimental results show that our method has good performance in the identification of community structure.

To address the target inaccessibility issue of the Artificial Potential Field (APF) method and the slow convergence of deep reinforcement learning algorithms, we propose a method combining the artificial potential field and an improved twin delayed deep deterministic policy gradient algorithm (PG-ITD3) for UAV path planning in post-disaster scenarios. This approach considers Unmanned Aerial Vehicles (UAV) kinematic constraints and dynamically adjusts the repulsive gain coefficient through deep reinforcement learning to enhance planning efficiency. The introduction of a virtual obstacle strategy, combining the aftershock probability model with prioritized experience replay (PER), and a novel reward function facilitates real-time reward acquisition and accelerates convergence. Simulation results demonstrate that our proposed algorithm outperforms traditional APF method and other advanced deep reinforcement learning methods in success rate, path length, path reward, and global smoothness. This research offers an effective solution for post-disaster UAV rescue path planning, contributing significantly to enhancing rescue efficiency and safety.

Constrained multiobjective optimization problems are widespread in practical engineering fields. Scholars have proposed various effective constrained multiobjective evolutionary algorithms (CMOEAs) for such problems. However, most existing algorithms overlook the differences between different decision variables in influencing the degree of constraint violation and still lack an effective handling mechanism for constraint-sensitive variables. To address this issue, a two-stage cooperation multiobjective evolutionary algorithm guided by constraint-sensitive variables (CV-TCMOEA) is proposed. In the first stage, a relatively simple auxiliary problem with only a few dominant constraints is constructed to approximate the original problem. After obtaining a set of approximate Pareto optimal solutions by dealing with the auxiliary problem, in the second stage, a constraint-sensitive variable-guided multistrategy cooperation search method is developed. In this method, decision variables are divided into two types: 1) constraint-sensitive and 2) constraint-insensitive variables, and a variable-type-guided cooperative individual update strategy is proposed to autonomously select appropriate search strategies for different types of variables. Experimental results on 28 benchmark functions and 10 engineering problems demonstrated the superiority of the CV-TCMOEA over seven state-of-the-art CMOEAs.

Dynamic constrained multiobjective optimization problems (DCMOPs) require algorithms to quickly track the feasible Pareto optima under dynamic environments. The existing dynamic constrained multiobjective evolutionary algorithms (DCMOEAs) normally focus on the convergence speed, but cannot well guarantee distribution. To address this issue, a subspace sparsity driven knowledge transfer strategy based DCMOEA is developed in this article, called SSDKT. First, reference points are introduced to partition objective space into multiple subspaces. Subsequently, the feasibility of each subspace is determined by the distribution of all historical feasible optimal solutions in it, and defined as the sparsity of subspace. A predictor based on the gated recurrent unit (GRU) network is further constructed to estimate the sparsity under the future environment. Once a new environment appears, a subspace transfer strategy is designed to generate an initial population. In each feasible subspace, the GRU-based prediction method is developed and competed with Kalman filter to generate the initial solution under the new environment. Based on the predicted solution of the nearest feasible neighbor, a potential initial individual in each infeasible subspace is produced by transferring the corresponding knowledge. The experimental results on various benchmarks verify that, compared with several state-of-the-art DCMOEAs, the proposed algorithm achieves the most competitive performance in solving DCMOPs.

The dispatch optimization of coal mine integrated energy system is challenging due to high dimensionality, strong coupling constraints, and multiobjective. Existing constrained multiobjective evolutionary algorithms struggle with locating multiple small and irregular feasible regions when solving the dispatch problem. To address this issue, we here develop a multiform EA framework that incorporates the dispatch-correlated domain knowledge to effectively deal with strong constraints and multiobjective optimization. Possible evolutionary multiform construction strategy based on complex constraint relationship analysis and handling, i.e., constraint-coupled spatial decomposition, constraint strength classification, and constraint handling technique, is first explored. Within the multiform evolutionary optimization framework, two strategies, i.e., an elite-guided knowledge transfer by designing a special crowding distance mechanism to select dominant individuals from each task and a neighborhood-driven dual mutation to effectively balance the diversity and convergence of each optimized task for the differential evolution algorithm, are further developed. The performance of the proposed algorithm in feasibility, convergence, and diversity is demonstrated in a case study of a coal mine integrated energy system (IES) by comparing with CPLEX solver and eight state-of-the-art constrained multiobjective EAs.

Dynamic multiobjective evolutionary algorithms (DMOEAs) have gained great popularity in dealing with the dynamic multiobjective optimization problems (DMOPs). However, the existing studies have difficulties in tackling DMOPs subject to (dynamic) constraints. In this article, we propose a prediction and weak coevolutionary multiobjective optimization algorithm (PWDCMO) to handle the dynamic constrained multiobjective optimization problems (DCMOPs), where a prediction strategy is employed to forecast potential optimal regions under the new environment, with a weak coevolutionary constrained multiobjective optimization (CCMO) as the optimizer aiming at balancing exploration and convergence. The proposed method is compared with the four popular dynamic constrained multiobjective evolutionary algorithms (DCMOEAs) on six test instances from two various test suites with their convergence and the overall performance being discussed. Furthermore, the performance of the proposed prediction strategy is also investigated to observe its impact on the final results. Additionally, the PWDCMO is employed in the optimization of an integrated coal mine energy system (ICMES) to validate the proficiency in addressing real world problems. Experimental results demonstrate the superiority of PWDCMO.

Feature selection (FS) is an effective data preprocessing technique. In some practical applications, features may continuously arrive one by one or by groups, and we cannot know the exact number of features before learning. Streaming FS (SFS) aims to remove redundant and irrelevant features from the continuously arriving features. This article proposes a three-stage SFS method based on dynamic feature clustering and particle swarm optimization (SFS-DPSO). In the first stage, an online relevance analysis is utilized to quickly remove irrelevant features, reducing the size of newly arrived feature groups. In the second stage, a dynamic feature clustering technique is employed to divide redundant features into different groups, thereby reducing the search space for subsequent evolutionary algorithms. In the third stage, a historical information-driven integer particle swarm optimization algorithm is exploited to search for optimal feature subset in the clustered feature space. The proposed algorithm is applied in 12 typical datasets with different difficulty levels and a real-word case, experimental results show that it can achieve better-classification results in a reasonable time and is superior to most existing algorithms.

Dynamic interval multiobjective optimization problems, such as those encountered in wireless sensor network scheduling and portfolio selection, are increasingly prevalent. However, they present significant challenges due to the inherent uncertainty and variability of their parameters. This article proposes a dynamic interval multiobjective evolutionary algorithm in terms of multitask learning and inverse mapping. The algorithm employs an interval-based MOEA/D as its foundational framework. Upon encountering environmental changes, prediction models for the midpoints and widths of intervals are developed using multitask learning combined with a self-evolving fuzzy system. These models generate a predicted Pareto front (PF) in the objective space. Subsequently, inverse mappings of the objective functions at the new time are established to identify solutions that correspond to the predicted PF in the decision space. Finally, these solutions are expanded to form an initial population at the new time. Testing on 18 benchmark optimization problems and an uncertain scheduling of underwater wireless sensor networks, the proposed algorithm demonstrates both competitiveness and superiority when compared to five state-of-the-art algorithms.

Design change is an important issue in complex product development projects. In a complex product with numerous parts (also known as components), the change of one key part may spread to other parts associated with it, generating a chain reaction throughout the entire project. Therefore, it is necessary to select a suitable change plan involving only fewer crucial parts in order to enhance the product’s performance, minimize change cost, and reduce change duration/time. Focusing on the case where the correlation strength between parts cannot be accurately obtained, in this paper we study an interval multi-objective evolutionary algorithm for finding excellent design change plans. Firstly, on the basis of the established multi-layer product network with interval correlation weights, an interval multi-objective optimization model of the product design change planning problem is established, where three new objective functions regarding product performance, carbon trading cost and supply risk are defined. Then, a constraint multi-objective evolutionary algorithm based on interval Pareto dominance is proposed to search for optimal change plans. Several novel operators, including the problem characteristic-guided population update strategy, the probability-based interval Pareto dominance, and the interval constraint handling strategy, are developed to enhance the algorithm’s performance. Finally, the proposed algorithm is compared with eight existing algorithms on the two design change cases, experimental results revealed its effectiveness.

Electric vehicle charging station location optimization (EVCSO) often involves multiple stakeholders, each with distinct objectives. This can be formulated as multi-view multi-objective optimization problems (MVMOPs) to provide a systematic and scientific scheme. However, no research has yet been conducted on MVMOPs within the context of EVCSO. To fill this gap, this paper models a tri-view tri-objective optimization problem. It is difficult to find a set of public Pareto-optimal solutions for the modeled MVMOP, therefore, a knowledge-sharing evolutionary algorithm is proposed. This includes a combination strategy to transfer knowledge between views, along with a two-layer decision strategy and weight vector update strategy to balance exploration and exploitation. A series of experiments are conducted to validate the feasibility and efficiency of the proposed model and algorithm. The proposed algorithm outperforms three state-of-the-art peer algorithms on test problems with respect to two indicators, e.g., it obtains 71.4% the best instances on the seven test MVMOPs, positioning itself as a promising tool for tackling MVMOPs. Moreover, compared to five conventional algorithms, the proposed method yields a more balanced and rational layout for electric vehicle charging stations, increasing revenue by 28.57% and reducing queueing time by 1.7% relative to the second-best algorithm.

The purpose of Intrusion Detection Systems (IDS) is to identify security issues in data transmitted by various devices and communication protocols. For domains with sparse data, such as the Internet of Things (IoT), cross-domain models are applied to solve the sparse problem by transfer knowledge from the source domain with rich data to the target domain. However, most of the cross-domain intrusion detection methods map different explicit features in the source and target domains to implicit features in a common implicit space, which weakens the interpretability of these methods. To enhance the interpretability of cross-domain models, we propose a Cross-Domain Intrusion Detection Method Based on Nonlinear Augmented Explicit Features (NAEF). Specifically, we augment the feature space of the source and target domains as the combination of shared features, source domain specific features and target domain specific features. Moreover, we model the nonlinear mapping relationship from shared features to special features in the source and target domains separately. Then, the original features in the source and target domains are mapped to uniform explicit features in the augmented space by migration of the nonlinear mapping relationship. Additionally, a classifier based on ensemble learning and attention mechanism balances the data distribution and selects important features to enhance detection performance. Our experimental results demonstrate the effectiveness of the proposed NAEF method on four public datasets.

Evolutionary multitask optimization (EMTO) can solve multiple tasks simultaneously by leveraging the relevant information between tasks, but existing EMTO algorithms do not take into account the fact that almost all problems in the real world contain constraints. To address this dilemma, this article studies a local knowledge transfer-based evolutionary algorithm for constrained multitask optimization. To be specific, each task population is divided into multiple niches to enhance the diversity and control the intensity of knowledge transfer, thus avoiding excessive transfer of knowledge. Then a new similarity judgment method based on the information feedback of pioneer individuals is developed to judge the similarity between tasks and whether to perform knowledge transfer. Furthermore, two different transfer methods: a direct transfer and a learning transfer, are devised to perform knowledge transfer among niches pertaining to different tasks. In addition, an excellent-information-guided mutation mechanism is proposed to prevent niches from getting trapped in local optima and to promote rapid convergence. The system experiment on 18 constrained multitask test instances and 2 real-world problems demonstrate that the proposed algorithm outperforms or is at least comparable to other EMTO algorithms and constrained single-objective optimization algorithms.

Real-world production scenarios often involve multiobjective optimization problems with intricate constraints. Although there has been a growing interest in multiobjective problems with complex constraints, such as the vehicle routing problem with time windows, existing multiobjective evolutionary optimization techniques still face significant challenges, particularly when addressing the fragmented and narrow feasible regions that arise from these constraints. Our research introduces a refined framework tailored for complex constrained multiobjective evolutionary optimization. The methodology conducts an initial strong-weak analysis to categorize constraints and merges each strong constraint with all weak constraints to form subsets. Each subset, combined with the original objective functions, defines a subproblem. Independent optimization of the original problem and subproblems is carried out by utilizing multiple populations. Information acquired from the subproblems’ populations is transferred into the population of the original issue, thereby expediting the detection of the feasible region and simplifying the resolution of the original problem. The efficacy of our innovative algorithm, when benchmarked against traditional constrained multiobjective evolutionary algorithms across 72 test functions, has demonstrated superior convergence, diversity, and competitiveness.

Various constrained multiobjective evolutionary optimization algorithms (CMOEAs) have been proposed for constrained multiobjective optimization problems (CMOPs). However, their reproduction operators often fail to effectively utilize constraint information, leading to inefficient exploration of feasible regions and premature convergence near boundaries of feasible regions. In light of this, we propose a novel population image convolution (PIC) method to improve information sharing among population individuals. Three column-oriented convolutional kernels are designed to participate in population reproduction, which can quickly locate the feasible region and thoroughly searching within it. Furthermore, our method features adaptive updating of the scope and control parameters for applying convolutional kernels to multiple subpopulations. To validate the effectiveness and superiority, we conducted comparisons against 11 state-of-the-art CMOEAs across five test suites. The results demonstrate the robust performance of our approach in diverse optimization scenarios. In addition, we showcase the practical applicability of our method to the dispatch optimization of integrated coal mine energy systems.

Dynamic constrained multiobjective optimization problems (DCMOPs) abound in real-world applications and gain increasing attention in the evolutionary computation community. To evaluate the capability of an algorithm in solving DCMOPs, artificial test problems play a fundamental role. Nevertheless, some characteristics of real-world scenarios are not fully considered in the previous test suites, such as time-varying size, location and shape of feasible regions, the controllable change severity, as well as small feasible regions. Therefore, we develop the generators of objective functions and constraints to facilitate the systematic design of DCMOPs, and then a novel test suite consisting of nine benchmarks, termed as DCP, is put forward. To solve these problems, a dynamic constrained multiobjective evolutionary algorithm with a two-stage diversity compensation strategy (TDCEA) is proposed. Some initial individuals are randomly generated to replace historical ones in the first stage, improving the global diversity. In the second stage, the increment between center points of Pareto sets in the past two environments is calculated and employed to adaptively disturb solutions, forming an initial population with good diversity for the new environment. Intensive experiments show that the proposed test problems enable a good understanding of strengths and weaknesses of algorithms, and TDCEA outperforms other state-of-the-art comparative ones, achieving promising performance in tackling DCMOPs.

In practice, some optimization problems require expensive calculation and exhibit multimodal characteristics simultaneously. These problems are called high-dimensional expensive multimodal optimization problems. When addressing such problems, existing surrogate-assisted evolutionary algorithms (SAEAs) encounter the “curse of dimensionality," which severely affects their capability to search optimal solutions. Therefore, this study proposed a surrogate and autoencoder-assisted multitask particle swarm optimization algorithm. First, an autoencoder-embedded multitask evolutionary framework was established to transform a high-dimensional multimodal optimization problem into multiple low-dimensional subproblems or subtasks. Further, a multi-level surrogate model management mechanism combining mirror learning was proposed. An appropriate local surrogate model can be rapidly generated for each modality of the problem. Moreover, a dual-mode local exploitation strategy was developed to improve the capability of swarm to exploit each subtask. The proposed algorithm was compared with seven existing SAEAs on 33 benchmark functions and the aeroengine aerodynamic design optimization problem. Experimental results revealed that the proposed algorithm can obtain multiple highly competitive optimal solutions, including global optimal solutions.

Various real-world problems can be attributed to constrained multiobjective optimization problems (CMOPs). Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for CMOPs. Given this, a process knowledge-guided constrained multiobjective autonomous evolutionary optimization method is proposed. First, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving CMOPs.

The operation optimization problem of coal mine integrated energy system (CMIES) is characterized by multiobjective, strong constraints, large scale, and mixed variables. It is difficult for existing multiobjective evolutionary algorithms to obtain a set of nondominated solutions with good convergence and uniform distribution, primarily due to the absence of suitable constraint-handling techniques. This research proposes a multitask multiobjective operation optimization framework combining evolutionary algorithm and mathematical programming (MO-EAMP) to address this issue. Within this framework, the main task employs an evolutionary algorithm with global search capability to solve the multiobjective CMIES operation optimization problem. Meanwhile, auxiliary tasks utilize mathematical programming method with robust linear constraint handling capability to solve multiple weighted single-objective CMIES operation optimization problems. During the iteration process of MO-EAMP, the scale and form of auxiliary tasks are adjusted autonomously based on the current state of population, with the aim of guiding the population search toward more promising regions. Finally, the presented algorithm is applied to a coal mine in Shanxi Province, China, and the experimental results demonstrate that the proposed algorithm can obtain a set of optimal operation plans with better convergence and distribution in a shorter time, compared with 7 other existing algorithms.

Ensemble learning, as a popular method to tackle concept drift in data stream, forms a combination of base classifiers according to their global performances. However, concept drift generally occurs in local data space, causing significantly different performances of a base classifier at different locations. Thus, employing global performance as a criterion to select base classifier is inappropriate. Moreover, data stream is often accompanied by class imbalance problem, which affects the classification accuracy of ensemble learning on minority instances. To drawback these problems, a dynamic ensemble selection for imbalanced data streams with concept drift (DES-ICD) is proposed. For data arrived in chunk-by-chunk, a novel synthetic minority oversampling technique with adaptive nearest neighbors (AnnSMOTE) is developed to generate new minority instances that conform to the new concept. Following that, DES-ICD creates a base classifier on newly arrived data chunk balanced by AnnSMOTE and merges it with historical base classifiers to form a candidate classifier pool. For each query instance, the optimal combination is constructed in terms of the performance of candidate classifiers in its neighborhood. Experimental results for nine synthetic and five real-world datasets show that the proposed method outperforms seven comparative methods on classification accuracy and tracks new concepts in an imbalanced data stream more preciously.

Message passing interface (MPI) is a powerful tool for parallel computing, originally designed for high-performance computing on massively parallel computers. In this paper, we combine FERPSO-IMPR (fitness Euclidean distance ratio particle swarm optimizer with information migration-based penalty and population reshaping) and surrogate-assisted models to generate test cases for MPI program path coverage testing. In our proposed method, FERPSO-IMPR employs a dual population strategy to initialize data and calculate fitness. Then, we create a sample set based on the initial data and its fitness. Subsequently, we train the master-slave surrogate models to predict individual fitness. Finally, a small number of elite individuals are selected to execute the program to decide whether to generate the required test data and guide the subsequent evolution process. We apply the proposed method to seven MPI programs and perform experimental comparisons from five directions. Experimental results show that compared with the comparative method, the time consumption of the proposed method is reduced by 33.2%, the number of evaluations is reduced by 38.8%, and the success rate is increased by 7.6%. These results prove that our method can effectively reduce the test data generation cost of MPI programs.

Mutation testing, a mainstream fault-based software testing technique, can mimic a wide variety of software faults by seeding them into the target program and resulting in the so-called mutants. Test data generated in mutation testing should be able to kill as many mutants as possible, hence guaranteeing a high fault-detection effectiveness of testing. Nevertheless, the test data generation can be very expensive, because mutation testing normally involves an extremely large number of mutants and some mutants are hard to kill. It is thus a critical yet challenging job to find an efficient way to generate a small set of test data that are able to kill multiple mutants at the same time as well as reveal those hard-to-detect faults. In this paper, we propose a new approach for test data generation in mutation testing, through the novel applications of the Markov chain usage model and the estimation of distribution algorithm. We first utilize the Markov chain usage model to reduce the so-called mutant branches in weak mutation testing and generate a minimal set of extended paths. Then, we regard the problem of generating test data as the problem of covering extended paths and use an estimation of distribution algorithm based on probability model to solve the problem. Finally, we develop a framework, TAMMEA, to implement the new approach of generating test data for mutation testing. The empirical studies based on fifteen object programs show that TAMMEA can kill more mutants using fewer test data compared with baseline techniques. In addition, the computation overhead of TAMMEA is lower than that of the baseline technique based on the traditional genetic algorithm, and comparable to that of the random method. It is clear that the new approach improves both the effectiveness and efficiency of mutation testing, thus promoting its practicability.

Solving dynamic multiobjective optimization problems (DMOPs) is very challenging due to the requirements to respond rapidly and precisely to changes in an environment. Many prediction- and memory-based algorithms have been recently proposed for meeting these requirements. However, much useful knowledge has been ignored during the historical search process, and prediction deviations could occur, thus limiting the applicability of these methods to a variety of problems. Facing these concerns, this article proposes an evolutionary algorithm named FGTTMP based on feedback-guided transfer (FGT) and trend manifold prediction (TMP) for solving DMOPs. The FGT employs an information feedback model to extract valuable knowledge using all historical environments and then identifies excellent individuals using cluster-transfer learning. This can both accelerate convergence and introduce diversity for future environments. The TMP applies the probability-based trend prediction method to estimate the mass center of the whole population and the corresponding manifold, relying on the two previous moments. Thus, the FGT and TMP strategies combine historical knowledge with prediction techniques, synergistically leading the population in promising directions. The performance of the proposed algorithm is fully investigated and compared with eight state-of-the-art algorithms. Experimental results demonstrate that the proposed FGTTMP method can achieve better convergence and diversity on 19 various benchmark problems than the state-of-the-art algorithms.

An intelligent optimization algorithm is only valid for solving some problems, which difficultly solves all operation optimization problems of integrated coal mine energy systems with different characteristics. An optimization paradigm usually consists of multiple operators/strategies, each of which is suitable for solving different problems. It is difficult for an operator/strategy to ensure that the population can evolve forward in the evolution process since the state of the population is changing. To this end, a multi-granularity autonomous intelligent optimization method is proposed to optimize the operation of integrated coal mine energy systems with various scenarios. This method automatically determines appropriate optimization paradigms according to problem characteristics and adaptively adjusts optimization operators/strategies based on population states in the evolution process. For the adaptive adjustment of operators/strategies, this paper proposes an adaptive adjustment strategy based on Q-Learning. Taking a coal mine in Shanxi Province, China as the research object, a series of experiments are conducted, and the experimental results show the effectiveness of the proposed algorithm.

Task allocation is a crucial issue of mobile crowdsensing. The existing crowdsensing systems normally select the optimal participants giving no consideration to the sudden departure of mobile users, which significantly affects the sensing quality of tasks with a long sensing period. Furthermore, the ability of a mobile user to collect high-precision data is commonly treated as the same for different types of tasks, causing the unqualified data for some tasks provided by a competitive user. To address the issue, a dynamic task allocation model of crowdsensing is constructed by considering mobile user availability and tasks changing over time. Moreover, a novel indicator for comprehensively evaluating the sensing ability of mobile users collecting high-quality data for different types of tasks at the target area is proposed. A new Q -learning-based hyperheuristic evolutionary algorithm is suggested to deal with the problem in a self-learning way. Specifically, a memory-based initialization strategy is developed to seed a promising population by reusing participants who are capable of completing a particular task with high quality in the historical optima. In addition, taking both sensing ability and cost of a mobile user into account, a novel comprehensive strength-based neighborhood search is introduced as a low-level heuristic (LLH) to select a substitute for a costly participant. Finally, based on a new definition of the state, a Q -learning-based high-level strategy is designed to find a suitable LLH for each state. Empirical results of 30 static and 20 dynamic experiments expose that this hyperheuristic achieves superior performance compared to other state-of-the-art algorithms.

Many real-world applications can be formulated as expensive multimodal optimization problems (EMMOPs). When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face the problem of selecting surrogate models but also need to tackle the problem of discovering and updating multiple modalities. Different optimization problems and different stages of evolutionary algorithms (EAs) generally require different types of surrogate models. To address this issue, in this article, we present a multisurrogate-assisted multitasking particle swarm optimization algorithm to seek multiple optimal solutions of EMMOPs at a low computational cost. The proposed algorithm first transforms an EMMOP into a multitasking optimization problem by integrating various surrogate models, and designs a multitasking niche particle swarm algorithm to solve it. Following that, a surrogate model management strategy based on the skill factor and clustering is developed to effectively balance the number of real function evaluations and the prediction accuracy of candidate optimal solutions. In addition, an adaptive local search strategy based on the trust region is proposed to enhance the capability of swarm in exploiting potential optimal modalities. We compare the proposed algorithm with five state-of-the-art SAEAs and seven multimodal EAs on 19 benchmark functions and the building energy conservation problem and experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.

Expensive constraint multimodal optimization problems (ECMMOPs) have such characteristics as expensive objectives and constraints, and multiple optimal modalities simultaneously, which pose severe challenges to evolutionary optimization methods. This article studies an objective-constraint mutual-guided surrogate-assisted particle swarm optimization algorithm for the kind of problem, aiming to discover multiple competing feasible optimal solutions at a lower calculation cost. The algorithm designs first a new two-layer cooperative surrogate model framework based on heterogeneous database to effectively adjust the prediction accuracies of objective surrogates and constraint surrogates on different search regions. An objective-constraint mutual-guided partial evaluation strategy (O-C-PES) is developed to generate high-quality infilling samples for objective and constraint surrogates, respectively, based on which the number of unnecessary real evaluations can be significantly reduced. Moreover, a position feature-guided hybrid update mechanism (PF-HUM) is proposed to find more optimal solutions by searching excellent infeasible and feasible areas at the same time, and a feasible ratio-driven local search (FR-LS) strategy is proposed to improve the algorithm’s exploitation. Compared with four existing surrogate-assisted evolutionary algorithms (EAs) and one constraint multimodal EAs on 21 benchmark problems and three engineering instances, experiment results show that the proposed algorithm can simultaneously obtain multiple highly-competitive feasible optimal solutions with less computational cost.

In some real-world optimization problems, the parameters of an objective function may be expressed as intervals, such as the benefit of a project and the driving speed of a robot. An optimization problem involving interval parameters and multiple conflicting objectives is termed as a multiobjective optimization problem with interval parameters (IMOP). Few studies have addressed IMOPs compared to deterministic multiobjective optimization at present. In addition, the uncertainty involved in the problems raises higher demands on the diversity and efficiency of an algorithm. Therefore, an adaptive reference vector-based interval multiobjective evolutionary algorithm in the framework of MOEA/D (IMOEA/D) was proposed in this article. First, an IMOP is decomposed into a number of subproblems with interval parameters by setting an interval-valued reference point and constructing interval-valued scalar functions. Following that, an ensemble scheme for evaluating interval individuals is developed via the rank sum ratio method. Finally, reference vectors are adaptively adjusted based on the interval crowding distance to enhance the distribution of a population. The proposed IMOEA/D was tested on 20 benchmark IMOPs as well as a scheduling problem of underwater wireless sensor networks, and compared with four state-of-the-art interval MOEAs. The empirical results demonstrate its superior performance and strong competitiveness.

The key task in dynamic multiobjective optimization problems (DMOPs) is to find Pareto-optima closer to the true one as soon as possible once a new environment occurs. Previous dynamic multiobjective evolutionary algorithms (DMOEAs) normally focus on DMOPs with regular environmental changes, but neglect widespread random one, limiting their applications in real-world fields. To address this issue, a knowledge guided transfer strategy (KTS)-based DMOEA is proposed in this article. First, knowledge described as a two-tuple is extracted under each historical environment and preserved to a knowledge pool. Redundant knowledge is recognized and adaptively removed so as to guarantee the diversity of the pool. Second, a knowledge matching strategy is developed to re-evaluate the representative of each stored knowledge under a new environment, with the purpose of finding the most valuable one to promote positive knowledge transfer. Third, an improved knowledge transfer mechanism based on subspace alignment is introduced. By integrating it with the knowledge reuse mechanism, a hybrid transfer strategy is constructed to adaptively select the most suitable one in terms of the similarity degree of selected knowledge on the current environment, and then generate a new initial population. Experiments on 20 benchmark problems demonstrate that the KTS outperforms five state-of-the-art algorithms, achieving good versatility in solving DMOPs with both regular and random changes.

In traditional data stream mining, classification models are typically trained on labeled samples from a single source. However, in real-world scenarios, obtaining accurate labels is very hard and expensive, especially, when multiple data streams are concurrently sampled from an environment or the same process. To address this issue, multistream classification is proposed, in which a data stream with biased labels (called the source stream) is leveraged to train a suitable model for prediction over another stream with unlabeled samples (called the target stream). Despite the growing research in this field, previous multistream classification methods are mostly designed for single-source stream scenarios. However, various source streams contain diverse data distributions, providing more valuable information for building a more accurate model. In addition, previous works construct classification models in the original shared feature space, ignoring the effect of redundant or low-quality features on the classification performance. This may produce inefficient knowledge transfer across streams. In view of this, a reduced-space multistream classification based on multiobjective evolutionary optimization is proposed in this article. First, a multiobjective evolutionary optimization is employed to seek the most valuable feature subset shared in the source and target domains, with the purpose of narrowing the distribution difference between source and target streams. Following that, a Gaussian mixture model-based weighting mechanism for source samples is presented. More especially, two drift adaptation methods are proposed to address asynchronous drift. Experimental results on benchmark datasets show that the proposed method outperforms other comparative methods on classification accuracy and G-mean.

With the increase of the number of features and the sample size, existing feature selection (FS) methods based on evolutionary optimization still face challenges such as the “curse of dimensionality” and the high computational cost. In view of this, dividing or clustering the sample and feature spaces at the same time, this article proposes a hybrid FS algorithm using surrogate sample-assisted particle swarm optimization (SS-PSO). First, a nonrepetitive uniform sampling strategy is employed to divide the whole sample set into several small-size sample subsets. Regarding each sample subset as a surrogate unit, next, a collaborative feature clustering mechanism is proposed to divide the feature space, with the purpose of reducing both the computational cost of clustering feature and the search space of PSO. Following that, an ensemble surrogate-assisted integer PSO is proposed. To ensure the prediction accuracy of ensemble surrogate when evaluating particles, an ensemble surrogate construction and management strategy is designed. Since the whole sample set is replaced by a small number of surrogate units, SS-PSO significantly reduces the cost of evaluating particles in PSO. Finally, the proposed algorithm is applied to some typical datasets, and compared with six typical evolutionary FS algorithms, as well as its several variant algorithms. The experimental results show that SS-PSO can obtain good feature subsets at the smallest computational cost on most of datasets. All verify that SS-PSO is a highly competitive method for high-dimensional FS.

There are lots of many-objective optimization problems (MaOPs) in real-world applications, which often have many decision variables. Although a variety of methods have been proposed to solve MaOPs, with the increasing number of decision variables or objective functions, the performance of these algorithms deteriorates appreciably. In view of this, this article proposes a method to solve large-scale MaOPs (LSMaOPs) based on dimension reduction and a solving knowledge-guided evolutionary algorithm (KGEA). First, a dimension reduction method of objective functions is proposed. By clustering and aggregating the objective functions based on their correlation, the dimension of the original LSMaOP is effectively reduced. In addition, the correlations between the reduced objective functions are relatively low, so they can better represent different preferences. Then, we propose a solving KGEA to solve the transformed LSMaOP. In order to get a better set of initial solutions, a population initialization method by mirror partitioning the decision space is given, in which we dynamically modify the sampling probability according to the performance of solutions contained in each subdomain. At the same time, the algorithm will continuously supplement new excellent individuals using the solving knowledge obtained in the evolution of the population. To examine the performance of the proposed method, we carried out a number of comparative experiments. The experimental results demonstrated that the proposed algorithm can effectively tackle LSMaOPs.

The decomposition-based multiobjective optimization algorithm (MOEA/D) is an effective method of solving a multiobjective optimization problem (MOP). The main idea of MOEA/D is that the objectives are weighted through different vectors to form different subproblems, and an optimal solution set is obtained by co-evolution in a certain neighborhood. However, with the increase of objectives, the number of nondominated solutions increases exponentially, resulting in the deteriorated capability of searching for optimal solutions. In addition, for an optimization problem with the complex Pareto front (PF), the selection pressure of nondominated solutions is insufficient. To make evolution more efficient, an MOEA/D with adaptively adjusting weight vectors and neighborhoods (MOEA/D-AAWNs) is developed in this article. First, the evolutionary direction of each subproblem is analyzed and the Sparsity function (Spa) is proposed to measure the population density on the PF. By using Spa, a method of generating uniform vectors is presented to improve the diversity of solutions. Besides, a method of adaptively adjusting neighborhoods is given. It adjusts neighborhoods according to the number of iterations and the Spa value of its corresponding subproblem. In this way, the computational resource can be effectively allocated, leading to the improvement in evolutionary efficiency. The proposed algorithm is applied to solve a series of benchmark optimization instances, and the experimental results show that the proposed algorithm outperforms comparison algorithms in runtime, convergence, and diversity.

When a large number of target paths in a sequential program need to be covered, we can divide similar target paths into the same group, and generate a test suite covering the same group of target paths at the same time, so as to reduce the testing cost. However, different communication edges may be run under a same test input when executing a Message-PassingInterface (MPI) program with non-determinism, which cause different code fragments may be traversed, indicating the difficulty of generating a test suite to cover each group of target paths. This paper proposes an approach to evolutionary generation of test suites for multi-path coverage of MPI programs with non-determinism, which can significantly reduce the testing cost and difficulty. We first design an indicator for evaluating each traversal set of communication edges, which is used to form a relation matrix between each target path and each traversal set of communication edges, so as to divide all the target paths into a certain amount of groups. Then, we construct an optimization model for test suite generation associated with each group. Finally, an evolutionary optimization algorithm is extended to solve each model, and used to generate a test suite covering each group of target paths. The proposed approach is utilized and compared with several state-of-the-art approaches to seven benchmark MPI programs, as well as the experimental results illustrate that the proposed approach can efficiently generate a test suite, thus supporting the superiority of the proposed approach.

In this study, we propose an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms (hereinafter, referred to as IGSA) to solve the flexible job shop scheduling problem with crane transportation processes (CFJSP). Two objectives are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumptions during machine processing and crane transportation. Different from the methods in the literature, crane lift operations have been investigated for the first time to consider the processing time and energy consumptions involved during the crane lift process. The IGSA algorithm is then developed to solve the CFJSPs considered. In the proposed IGSA algorithm, first, each solution is represented by a 2-D vector, where one vector represents the scheduling sequence and the other vector shows the assignment of machines. Subsequently, an improved construction heuristic considering the problem features is proposed, which can decrease the number of replicated insertion positions for the destruction operations. Furthermore, to balance the exploration abilities and time complexity of the proposed algorithm, a problem-specific exploration heuristic is developed. Finally, a set of randomly generated instances based on realistic industrial processes is tested. Through comprehensive computational comparisons and statistical analyses, the highly effective performance of the proposed algorithm is favorably compared against several efficient algorithms.Note to Practitioners—The flexible job shop scheduling problem (FJSP) can be extended and applied to many types of practical manufacturing processes. Many realistic production processes should consider the transportation procedures, especially for the limited crane resources and energy consumptions during the transportation operations. This study models a realistic production process as an FJSP with crane transportation, wherein two objectives, namely, the makespan and energy consumptions, are to be simultaneously minimized. This study first considers the height of the processing machines, and therefore, the crane lift operations and lift energy consumptions are investigated. A hybrid iterated greedy algorithm is proposed for solving the problem considered, and several problem-specific heuristics are embedded to balance the exploration and exploitation abilities of the proposed algorithm. In addition, the proposed algorithm can be generalized to solve other types of scheduling problems with crane transportations.

The "curse of dimensionality" and the high computational cost have still limited the application of the evolutionary algorithm in high-dimensional feature selection (FS) problems. This article proposes a new three-phase hybrid FS algorithm based on correlation-guided clustering and particle swarm optimization (PSO) (HFS-C-P) to tackle the above two problems at the same time. To this end, three kinds of FS methods are effectively integrated into the proposed algorithm based on their respective advantages. In the first and second phases, a filter FS method and a feature clustering-based method with low computational cost are designed to reduce the search space used by the third phase. After that, the third phase applies oneself to finding an optimal feature subset by using an evolutionary algorithm with the global searchability. Moreover, a symmetric uncertainty-based feature deletion method, a fast correlation-guided feature clustering strategy, and an improved integer PSO are developed to improve the performance of the three phases, respectively. Finally, the proposed algorithm is validated on 18 publicly available real-world datasets in comparison with nine FS algorithms. Experimental results show that the proposed algorithm can obtain a good feature subset with the lowest computational cost.

Personalized search is essentially a complex qualitative optimization problem, and interactive evolutionary algorithms (EAs) have been extended from EAs to adapt to solving it. However, the multisource user-generated contents (UGCs) in the personalized services have not been concerned on in the adaptation. Accordingly, we here present an enhanced restricted Boltzmann machine (RBM)-driven interactive estimation of distribution algorithms (IEDAs) with multisource heterogeneous data from the viewpoint of effectively extracting users’ preferences and requirements from UGCs to strengthen the performance of IEDA for personalized search. The multisource heterogeneous UGCs, including users’ ratings and reviews, items’ category tags, social networks, and other available information, are sufficiently collected and represented to construct an RBM-based model to extract users’ comprehensive preferences. With this RBM, the probability model for conducting the reproduction operator of estimation of distribution algorithms (EDAs) and the surrogate for quantitatively evaluating an individual (item) fitness are further developed to enhance the EDA-based personalized search. The UGCs-driven IEDA is applied to various publicly released Amazon datasets, e.g., recommendation of Digital Music, Apps for Android, Movies, and TV, to experimentally demonstrate its performance in efficiently improving the IEDA in personalized search with less interactions and higher satisfaction.

Band selection (BS) is a widely used dimensionality reduction technique for hyperspectral images. However, most of existing evolutionary algorithms focus on searching a globally optimal band subset under a fixed size, and their obtained band subsets may still contain a large number of redundant bands. In order to simultaneously obtain multiple optimal band subsets with different sizes, this article proposes an unsupervised multitask artificial bee colony (ABC) BS algorithm based on variable-size clustering (MBBS-VC). First, a variable-size band clustering method based on worst class decomposition is developed, based on which the BS problem can be modeled as a multitask optimization problem. Next, a multitask multimicrogroup bee colony algorithm with variable coding length is proposed to simultaneously search multiple optimal band subsets with different sizes. Moreover, several new strategies, including the intergroup collaboration strategy based on bidirectional neighborhood learning and the multimeasure integration judgment (MIJ) mechanism, are designed to improve the performance of MBBS-VC. In this article, the hyperspectral BS problem is transformed into a multitask optimization problem for the first time. Finally, compared with 15 classical BS algorithms on several commonly used datasets, experimental results verify the superiority of the proposed BS algorithm.

Feature selection (FS) in data with class imbalance or missing values has received much attention from researchers due to their universality in real-world applications. However, for data with both the two characteristics above, there is still a lack of the corresponding FS algorithm. Due to the complex coupling relationship between missing data and class imbalance, the need for better FS method becomes essential. To tackle high-dimensional imbalanced data with missing values, this article studies a new evolutionary FS method. First, an improved$F$-measure based on filling risk (RF-measure) is defined to evaluate the influence of missing data on the performance of FS in the case of class imbalance. Following that taking the RF-measure as an objective function, a particle swarm optimization-based FS method with fuzzy clustering (PSOFS-FC) is proposed. Two new problem-specific operators or strategies, i.e., the swarm initialization strategy guided by fuzzy clustering and the local pruning operator based on feature importance, are developed to improve the performance of PSOFS-FC. Compared with state-of-the-art FS algorithms on several public datasets, experimental results show that PSOFS-FC can achieve excellent classification performance with relatively less running time, indicating its superiority on tackling high-dimensional imbalanced data with missing values.

Mutation testing, a fundamental software testing technique, which is a typical way to evaluate the adequacy of a test suite. In mutation testing, a set of mutants are generated by seeding the different classes of faults into a program under test. Test data shall be generated in the way that as many mutants can be killed as possible. Thanks to numerous tools to implement mutation testing for different languages, a huge amount of mutants are normally generated even for small-sized programs. However, a large number of mutants not only leads to a high cost of mutation testing, but also make the corresponding test data generation a non-trivial task. In this paper, we make use of intelligent technologies to improve the effectiveness and efficiency of mutation testing from two perspectives. A machine learning technique, namely fuzzy clustering, is applied to categorize mutants into different clusters. Then, a multi-population genetic algorithm via individual sharing is employed to generate test data for killing the mutants in different clusters in parallel when the problem of test data generation as an optimization one. A comprehensive framework, termed as$\mathbf {FUZGENMUT}$, is thus developed to implement the proposed techniques. The experiments based on nine programs of various sizes show that fuzzy clustering can help to reduce the cost of mutation testing effectively, and that the multi-population genetic algorithm improves the efficiency of test data generation while delivering the high mutant-killing capability. The results clearly indicate that the huge potential of using intelligent technologies to enhance the efficacy and thus the practicality of mutation testing.

For the path coverage testing of a Message-Passing Interface (MPI) program, test data generation based on an evolutionary optimization algorithm (EOA) has been widely known. However, during the use of the above technique, it is necessary to evaluate the fitness of each evolutionary individual by executing the program, which is generally computationally expensive. In order to reduce the computational cost, this article proposes a method of integrating an ensemble surrogate model’s estimation into the process of generating test data. The proposed method first produces a number of test inputs using an EOA, and forms a training set together with their real fitness. Then, this article trains an ensemble surrogate model (ESM) based on the training set, which is employed to estimate the fitness of each individual. Finally, a small number of individuals with good estimations are selected to further execute the program, so as to have their real fitness for the subsequent evolution. This article applies the proposed method to seven benchmark MPI programs, which is compared with several state-of-the-art approaches. The experimental results show that the proposed method can generate test data with significantly low computational cost.

Compared with traditional structural test criteria, test data generated based on mutation testing are proved more effective at detecting faults. However, not all test data have the same potence in detecting software faults. If test data are prioritized while generating for mutation testing, the defect detectability of the test suite can be further strengthened. In view of this, we propose a method of test data generation for weak mutation testing via sorting mutant branches based on their dominance degrees. First, the problem of weak mutation testing is transformed into that of covering mutant branches for a transformed program. Then, the dominance relation of mutant branches in the transformed program is analyzed to obtain the non-dominated mutant branches and their dominance degrees. Following that, we prioritize all non-dominated mutant branches in descending order by virtue of their dominance degrees. Finally, the test data are generated in an orderly manner by selecting the mutant branches sequentially. The experimental results on 15 programs show that compared with other methods, the proposed test data generation method can not only improve the error detectability of the test suite, but also has higher efficiency.

The two-dimensional principal component analysis (2DPCA) has been one of the basic methods of developing artificial intelligent algorithms. To increase the feasibility, we propose a new general ridge regression model for 2DPCA and variations, with extracting low dimensional features under two projection subspaces. A new relaxed 2DPCA under the quaternion framework is proposed to utilize the label (if known) and color information to compute the essential features of generalization ability with optimization algorithms. The 2DPCA-based approaches for face recognition are also improved by weighting each principle component a scatter measure, which increases efficiently the rate of face recognition. In numerical experiments on well-known standard databases, the R2DPCA approach has high generalization ability and achieves a higher recognition rate than the state-of-the-art 2DPCA-like methods, and has better performance than the basic deep learning methods such as CNNs , DBNs, and DNNs in the small-sample case.

Ensemble learning is an effective approach for improving the generalization ability of base classifiers. To generate a set of accurate and diverse base classifiers, different data perturbation schemes have been proposed. For instance, Bagging perturbs the training data via bootstrap sampling. However, when a stable learning algorithm (e.g., KNN, Naive Bayes) is used to train base classifiers, the sole perturbation on the training data may not produce diverse base classifiers. In this paper, by using the attribute reduction technology in rough sets, a multi-modal perturbation-based algorithm (called ‘E _ EARBS’) is proposed for the ensemble of base classifiers. E _ EARBS simultaneously perturbs the feature space, training data and learning parameters, where the relative decision entropy(RDE)-based approximate reducts are used to perturb the feature space, and bootstrap sampling is used to perturb the training data. Experimental results show that E _ EARBS can provide competitive solutions for ensemble learning.

Feature selection (FS) is an important data processing technique in the field of machine learning. There have been various FS methods, but all assume that the cost associated with a feature is precise, which restricts their real applications. Focusing on the FS problem with fuzzy cost, a fuzzy multiobjective FS method with particle swarm optimization, called PSOMOFS, is studied in this article. The proposed method develops a fuzzy dominance relationship to compare the goodness of candidate particles and defines a fuzzy crowding distance measure to prune the elitist archive and determine the global leader of particles. Also, a tolerance coefficient is introduced into the proposed method to ensure that the Pareto-optimal solutions obtained satisfy decision makers' preferences. The developed method is used to tackle a series of the UCI datasets and is compared with three fuzzy multiobjective evolutionary methods and three typical multiobjective FS methods. Experimental results show that the proposed method can achieve feature sets with superior performances in approximation, diversity, and feature cost.

Various real-world applications can be classified as expensive multimodal optimization problems. When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face a contradiction between the precision of surrogate models and the cost of individual evaluations but also have the difficulty that surrogate models and problem modalities are hard to match. To address this issue, this article studies a dual-surrogate-assisted cooperative particle swarm optimization algorithm to seek multiple optimal solutions. A dual-population cooperative particle swarm optimizer is first developed to simultaneously explore/exploit multiple modalities. Following that, a modal-guided dual-layer cooperative surrogate model, which contains one upper global surrogate model and a group of lower local surrogate models, is constructed with the purpose of reducing the individual evaluation cost. Moreover, a hybrid strategy based on clustering and peak-valley is proposed to detect new modalities. Compared with five existing SAEAs and seven multimodal evolutionary algorithms, the proposed algorithm can simultaneously obtain multiple highly competitive optimal solutions at a low computational cost according to the experimental results of testing both 11 benchmark instances and the building energy conservation problem.

Message-passing interface (MPI) programs, a typical kind of parallel programs, have been commonly used in various applications. However, it generally takes exhaustive computation to run these programs when generating test data to test them. In this article, we propose a method of test data generation for path coverage of MPI programs using surrogate-assisted evolutionary optimization, which can efficiently generate test data with high quality. We first divide a sample set of a program into a number of clusters according to the multi-mode characteristic of the coverage problem, with each cluster training a surrogate model. Then, we estimate the fitness of each individual using one or more surrogate models when generating test data through evolving a population. Finally, a small number of representative individuals are selected to execute the program, with the purpose of obtaining their real fitness, to guide the subsequent evolution of the population. We apply the proposed method to seven benchmark MPI programs and compare it with several state-of-the-art approaches. The experimental results show that the proposed method can generate test data with reduced computation, thus improving the testing efficiency.

Interactive Estimation of Distribution Algorithm (IEDA), by integrating users interactions with Estimation of Distribution Algorithm, is powerful for efficient personalized search when the probability model and fitness function are well designed. We here propose an improved IEDA by using attention mechanism strengthened Restricted Boltzmann Machine (RBM). An attention mechanism assisted RBM model is constructed to approximate the user preferences by inputting item features and user generated contents. Then the attention-enhanced probability model of EDA and the fitness function are developed based on the RBM. In the evolutionary process, the attention-based RBM together with the probability model and fitness function are managed according to new interactions and corresponding information. The proposed algorithm is applied to real-world Amazon data sets usually used in the personalized search or recommendation, and its performance is experimentally demonstrated in better predicting the user preferences to improve the searching efficiency and accuracy.

As a distributed problem-solving model based on human-machine integration, crowdsourcing has attracted wide attention in industry and academia with the development of Internet technology. There are many prominent problems on the crowdsourcing platform, for example, the task can't be noticed by users and the users are not competent for the task, resulting in huge waste of time and economy. If we can make coping recommendations according to the characteristics of the tasks, the operational efficiency of crowdsourcing platforms will be greatly improved. Therefore, this paper proposed a new task oriented recommendation method based on Hungarian algorithm in crowdsourcing platform. Aiming at the problem that the new users and tasks on the crowdsourcing platform have low matching degree, we establish the multi-objective optimization model of task recommendation with the aim of maximizing quality, time and cost efficiency. Then, the model is solved by the Hungarian algorithm through appropriate transformation. The experimental results show that the proposed method can improve the recommendations accuracy of new tasks, and therefor effectively improve the operational efficiency of crowdsourcing platforms.

With the development of the internet technology, a large amount of softwares have emerged to meet users' increasing needs. At the mean time, software systems have been faced with a problem that they must adapt to the dynamic network environment. It is obvious that a variety of software development models have been proposed in the past few decades. However, the majority of these methods are gradually unadaptable to new circumstances. In this paper, we proposed a new software development model integrating collective intelligence, service and ecosystem. On the one hand, we have introduced the model in detail. On the other hand, We took a practical example to demonstrate the effectiveness of the proposed model.

Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.

One of the most important and widely faced optimization problems in real applications is the interval multiobjective optimization problems (IMOPs). The state-of-the-art evolutionary algorithms (EAs) for IMOPs (IMOEAs) need a great deal of objective function evaluations to find a final Pareto front with good convergence and even distribution. Further, the final Pareto front is of great uncertainty. In this paper, we incorporate several local searches into an existing IMOEA, and propose a memetic algorithm (MA) to tackle IMOPs. At the start, the existing IMOEA is utilized to explore the entire decision space; then, the increment of the hypervolume is employed to develop an activation strategy for every local search procedure; finally, the local search procedure is conducted by constituting its initial population, whose center is an individual with a small uncertainty and a big contribution to the hypervolume, taking the contribution of an individual to the hypervolume as its fitness function, and performing the conventional genetic operators. The proposed MA is empirically evaluated on ten benchmark IMOPs as well as an uncertain solar desalination optimization problem and compared with three state-of-the-art algorithms with no local search procedure. The experimental results demonstrate the applicability and effectiveness of the proposed MA.

Dynamic interval multiobjective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms (EAs) that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multiobjective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two subpopulations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances as well as a multiperiod portfolio selection problem and compared with five state-of-the-art EAs. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances.

Previous methods of designing a bolt supporting network, which depend on engineering experiences, seek optimal bolt supporting schemes in terms of supporting quality. The supporting cost and time, however, have not been considered, which restricts their applications in real-world situations. We formulate the problem of designing a bolt supporting network as a three-objective optimization model by simultaneously considering such indicators as quality, economy, and efficiency. Especially, two surrogate models are constructed by support vector regression for roof-to-floor convergence and the two-sided displacement, respectively, so as to rapidly evaluate supporting quality during optimization. To solve the formulated model, a novel interactive preference-based multiobjective evolutionary algorithm is proposed. The highlight of generic methods which interactively articulate preferences is to systematically manage the regions of interest by three steps, that is, “partitioning-updating-tracking” in accordance with the cognition process of human. The preference regions of a decision-maker (DM) are first articulated and employed to narrow down the feasible objective space before the evolution in terms of nadir point, not the commonly used ideal point. Then, the DM’s preferences are tracked by dynamically updating these preference regions based on satisfactory candidates during the evolution. Finally, individuals in the population are evaluated based on the preference regions. We apply the proposed model and algorithm to design the bolt supporting network of a practical roadway. The experimental results show that the proposed method can generate an optimal bolt supporting scheme with a good balance between supporting quality and the other demands, besides speeding up its convergence.

A large number of prediction strategies are specific to a dynamic multiobjective optimization problem (DMOP) with only one type of the Pareto set (PS) change. However, a continuous DMOP with more than one type of the unknown PS change has been seldom investigated. We present a multimodel prediction approach (MMP) realized in the framework of evolutionary algorithms (EAs) to tackle the problem. In this paper, we first detect the type of the PS change, followed by the selection of an appropriate prediction model to provide an initial population for the subsequent evolution. To observe the influence of MMP on EAs, optimal solutions obtained by three classical dynamic multiobjective EAs with and without MMP are investigated. Furthermore, to investigate the performance of MMP, three state-of-the-art prediction strategies are compared on a large number of dynamic test instances under the same particle swarm optimizer. The experimental results demonstrate that the proposed approach outperforms its counterparts under comparison on most optimization problems.

Mutation testing is a fault-oriented software testing technique, and a test suite generated based on the criterion of mutation testing generally has a high capability in detecting faults. A mutant that is hard killed is called a stubborn one. The traditional methods of test data generation often fail to generate test data that kill stubborn mutants. To improve the efficiency of killing stubborn mutants, in this article, we propose a method of generating test data by dynamically reducing the search domain under the criterion of strong mutation testing. To fulfill this task, we first present a method of measuring the stubbornness of a mutant based on the reachability condition of a mutated statement. Then, we formulate the problem of generating test data to kill the mutant as an optimization one with a unique constraint. Finally, we generate test data using a coevolutionary genetic algorithm. Given the fact that the domain of test data that kills a stubborn mutant is generally small, we adopt a method of dynamically reducing the search domain to improve the efficiency of the algorithm. We apply the proposed method to test eight benchmark and industrial programs. The experimental results demonstrate that the proposed method has capabilities in seeking stubborn mutants and efficiently generating test data to kill stubborn mutants.

A surrogate model is normally employed to evaluate an individual instead of time-consuming and expensive simulation. Inaccuracy model learning by the limited samples may mislead the evolution process. Thus, effectively updating the model by learning more typical samples is necessary. In this paper, a preference-based method of updating the surrogate model by broad learning is proposed, with the purpose of improving the accuracy of the model with the least computation complexity. The preferred individuals with the least distances to the Pareto front are chosen as the infilling samples. Following that, the surrogate model is updated based on the infilling samples by broad learning, so as to reduce the learning time. The rationality of the proposed updating method is verified by the instance of constructing a surrogate model for bolt supporting quality. The experimental results show that the preference-based updating method has the best accuracy and the least running time. The obtained optimal solutions meet the actual preference of the decision makers with the best convergence.

In this paper, a modified centralized algorithm based on particle swarm optimization (MCPSO) is presented to solve the task allocation problem in the search and rescue domain. The reason for this paper is to provide a benchmark against distributed algorithms in search and rescue application area. The hypothesis of this paper is that a centralized algorithm should perform better than distributed algorithms because it has all the available information at hand to solve the problem. Therefore, the centralized approach will provide a benchmark for evaluating how well the distributed algorithms are working and how much improvement can still be gained. Among the distributed algorithms, the consensus-based bundle algorithm (CBBA) is a relatively recent method based on the market auction mechanism, which is receiving considerable attention. Other distributed algorithms, such as PI and PI with softmax, have shown to perform better than CBBA. Therefore, in this paper, the three distributed algorithms mentioned earlier are compared against three centralized algorithms. They are particle swarm optimization, MCPSO, described in this paper, and genetic algorithms. Two experiments were conducted. The first involved comparing all the above-mentioned algorithms, both centralized and distributed, using the same set of application scenarios. It is found that MCPSO always outperforms the other five algorithms in time cost. Due to the high failure rate of CBBA and the other two centralized methods, the second experiment focused on carrying out more tests to compare MCPSO against PI and PI with softmax. All the results are shown and analyzed to determine the performance gaps between the distributed algorithms and the MCPSO. Note to Practitioners-This paper was motivated by the limitation of current distributed task allocation algorithms as they cannot achieve performances that are as good as the centralized ones. Therefore, a centralized algorithm is designed to evaluate the performance gap between the state-of-the-art distributed and centralized approaches. In the future research section, a new distributed particle swarm optimization (PSO) algorithm is proposed based on this paper as the research has shown that the proposed centralized PSO algorithm delivers the best results so it is potentially a strong candidate for adaptation.

In various flow shop scheduling problems, it is very common that a machine suffers from breakdowns. Under this situation, a robust and stable suboptimal scheduling solution is of more practical interest than a global optimal solution that is sensitive to environmental changes. However, blocking lot-streaming flow shop (BLSFS) scheduling problems with machine breakdowns have not yet been well studied up to date. This paper presents, for the first time, a multiobjective model of the above problem including robustness and stability criteria. Based on this model, an evolutionary multiobjective robust scheduling algorithm is suggested, in which solutions obtained by a variant of single-objective heuristic are incorporated into population initialization and two novel crossover operators are proposed to take advantage of nondominated solutions. In addition, a rescheduling strategy based on the local search is presented to further reduce the negative influence resulted from machine breakdowns.The proposed algorithm is applied to 22 test sets, and compared with the state-of-the-art algorithms without machine breakdowns. Our empirical results demonstrate that the proposed algorithm can effectively tackle BLSFS scheduling problems in the presence of machine breakdowns by obtaining scheduling strategies that are robust and stable.

Various real-world multiobjective optimization problems are dynamic, requiring evolutionary algorithms (EAs) to be able to rapidly track the moving Pareto front of an optimization problem once an environmental change occurs. To this end, several methods have been developed to predict the new location of the moving Pareto set (PS) so that the population can be reinitialized around the predicted location. In this paper, we present a multidirectional prediction strategy to enhance the performance of EAs in solving a dynamic multiobjective optimization problem (DMOP). To more accurately predict the moving location of the PS, the population is clustered into a number of representative groups by a proposed classification strategy, where the number of clusters is adapted according to the intensity of the environmental change. To examine the performance of the developed algorithm, the proposed prediction strategy is compared with four state-of-the-art prediction methods under the framework of particle swarm optimization as well as five popular EAs for dynamic multiobjective optimization. Our experimental results demonstrate that the proposed algorithm can effectively tackle DMOPs.

There have been few researches on solving multimodal multiobjective optimization problems, whereas they are commonly seen in real-world applications but difficult for the existing evolutionary optimizers. In this paper, we propose a novel multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies. In the proposed algorithm, the properties of decision variables and the relationships among them are analyzed at first to guide the evolutionary search. Then, a general framework using two archives, i.e., the convergence and the diversity archives, is adopted to cooperatively solve these problems. Moreover, the diversity archive simultaneously employs a clustering strategy to guarantee diversity in the objective space and a niche-based clearing strategy to promote the same in the decision space. At the end of evolution process, solutions in the convergence and the diversity archives are recombined to obtain a large number of multiple Pareto optimal solutions. In addition, a set of benchmark test functions and a performance metric are designed for multimodal multiobjective optimization. The proposed algorithm is empirically compared with two state-of-the-art evolutionary algorithms on these test functions. The comparative results demonstrate that the overall performance of the proposed algorithm is significantly superior to the competing algorithms.

For dynamic multi-objective vehicle routing problems, the waiting time of vehicle, the number of serving vehicles, and the total distance of routes were normally considered as the optimization objectives. Except for the above objectives, fuel consumption that leads to the environmental pollution and energy consumption was focused on in this paper. Considering the vehicles' load and the driving distance, a corresponding carbon emission model was built and set as an optimization objective. Dynamic multi-objective vehicle routing problems with hard time windows and randomly appeared dynamic customers, subsequently, were modeled. In existing planning methods, when the new service demand came up, global vehicle routing optimization method was triggered to find the optimal routes for non-served customers, which was time-consuming. Therefore, a robust dynamic multi-objective vehicle routing method with two-phase is proposed . Three highlights of the novel method are: (i) After finding optimal robust virtual routes for all customers by adopting multi-objective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in next phase. (ii) The dynamically appeared customers append to be served according to their service time and the vehicles' statues. Global vehicle routing optimization is triggered only when no suitable locations can be found for dynamic customers. (iii) A metric measuring the algorithms robustness is given. The statistical results indicated that the routes obtained by the proposed method have better stability and robustness, but may be sub-optimum. Moreover, time-consuming global vehicle routing optimization is avoided as dynamic customers appear.

Dynamic multi-objective optimization problems (DMOPs) not only involve multiple conflicting objectives, but these objectives may also vary with time, raising a challenge for researchers to solve them. This paper presents a cooperative co-evolutionary strategy based on environment sensitivities for solving DMOPs. In this strategy, a new method that groups decision variables is first proposed, in which all the decision variables are partitioned into two subcomponents according to their interrelation with environment. Adopting two populations to cooperatively optimize the two subcomponents, two prediction methods, i.e., differential prediction and Cauchy mutation, are then employed respectively to speed up their responses on the change of the environment. Furthermore, two improved dynamic multi-objective optimization algorithms, i.e., DNSGAII-CO and DMOPSO-CO, are proposed by incorporating the above strategy into NSGA-II and multi-objective particle swarm optimization, respectively. The proposed algorithms are compared with three state-of-the-art algorithms by applying to seven benchmark DMOPs. Experimental results reveal that the proposed algorithms significantly outperform the compared algorithms in terms of convergence and distribution on most DMOPs.

Interval many-objective optimization problems (IMaOPs), involving more than three objectives and at least one subjected to interval uncertainty, are ubiquitous in real-world applications. However, there have been very few effective methods for solving these problems. In this paper, we proposed a set-based genetic algorithm to effectively solve them. The original optimization problem was first transformed into a deterministic bi-objective problem, where new objectives are hyper-volume and imprecision. A set-based Pareto dominance relation was then defined to modify the fast nondominated sorting approach in NSGA-II. Additionally, set-based evolutionary schemes were suggested. Finally, our method was empirically evaluated on 39 benchmark IMaOPs as well as a car cab design problem and compared with two typical methods. The numerical results demonstrated the superiority of our method and indicated that a tradeoff approximate front between convergence and uncertainty can be produced.

Feature selection is an important data-preprocessing technique in classification problems such as bioinformatics and signal processing. Generally, there are some situations where a user is interested in not only maximizing the classification performance but also minimizing the cost that may be associated with features. This kind of problem is called cost-based feature selection. However, most existing feature selection approaches treat this task as a single-objective optimization problem. This paper presents the first study of multi-objective particle swarm optimization (PSO) for cost-based feature selection problems. The task of this paper is to generate a Pareto front of nondominated solutions, that is, feature subsets, to meet different requirements of decision-makers in real-world applications. In order to enhance the search capability of the proposed algorithm, a probability-based encoding technology and an effective hybrid operator, together with the ideas of the crowding distance, the external archive, and the Pareto domination relationship, are applied to PSO. The proposed PSO-based multi-objective feature selection algorithm is compared with several multi-objective feature selection algorithms on five benchmark datasets. Experimental results show that the proposed algorithm can automatically evolve a set of nondominated solutions, and it is a highly competitive feature selection method for solving cost-based feature selection problems.

Most existing multiobjective evolutionary algorithms experience difficulties in solving many-objective optimization problems due to their incapability to balance convergence and diversity in the high-dimensional objective space. In this paper, we propose a novel many-objective evolutionary algorithm using a one-by-one selection strategy. The main idea is that in the environmental selection, offspring individuals are selected one by one based on a computationally efficient convergence indicator to increase the selection pressure toward the Pareto optimal front. In the one-by-one selection, once an individual is selected, its neighbors are de-emphasized using a niche technique to guarantee the diversity of the population, in which the similarity between individuals is evaluated by means of a distribution indicator. In addition, different methods for calculating the convergence indicator are examined and an angle-based similarity measure is adopted for effective evaluations of the distribution of solutions in the high-dimensional objective space. Moreover, corner solutions are utilized to enhance the spread of the solutions and to deal with scaled optimization problems. The proposed algorithm is empirically compared with eight state-of-the-art many-objective evolutionary algorithms on 80 instances of 16 benchmark problems. The comparative results demonstrate that the overall performance of the proposed algorithm is superior to the compared algorithms on the optimization problems studied in this paper.

Interactive evolutionary algorithms have been applied to personalized search, in which less user fatigue and efficient search are pursued. Motivated by this, we present a fast interactive estimation of distribution algorithm (IEDA) by using the domain knowledge of personalized search. We first induce a Bayesian model to describe the distribution of the new user's preference on the variables from the social knowledge of personalized search. Then we employ the model to enhance the performance of IEDA in two aspects, that is: 1) dramatically reducing the initial huge space to a preferred subspace and 2) generating the individuals of estimation of distribution algorithm(EDA) by using it as a probabilistic model. The Bayesian model is updated along with the implementation of the EDA. To effectively evaluate individuals, we further present a method to quantitatively express the preference of the user based on the human-computer interactions and train a radial basis function neural network as the fitness surrogate. The proposed algorithm is applied to a laptop search, and its superiorities in alleviating user fatigue and speeding up the search procedure are empirically demonstrated.

Multi-objective optimization problems with interval parameters (IMOPs) are ubiquitous in real-world applications. The existing evolutionary algorithms for IMOPs (IMOEAs) require a large amount of function evaluations to generate an approximate Pareto front which is well converged and evenly distributed, and the generated front has uncertainties to a large extent. In this paper, a local search is embedded into an existing IMOEA, and a memetic algorithm for IMOPs is developed. The existing IMOEA is first employed to search the entire search space, and then the rate of changes of hypervolume is utilized to design an activation mechanism to specify when to conduct the local search. Finally, an initial population of the local search is created by taking the individuals with a large contribution to hypervolume and a small imprecision as the center, and the local search is implemented by taking the contribution to hypervolume as its fitness function. The proposed algorithm is applied to six benchmark IMOPs and an uncertain optimization problem of solar desalination, and compared with a typical IMOEA without the local search. The empirical results indicate the effectiveness of the proposed algorithm.

Interval programming problems are ubiquitous in real-world situations. There exist a variety of theories and methods for handling them; the existing methods, however, have adopted various dominance criteria to distinguish solutions, and these criteria are always subjective. Different dominance criteria will produce different optimal solution(s), and subjective criteria make users, especially for those who are not familiar with interval arithmetic, difficult to choose, which restricts their widespread applications. In this study, the idea of ensemble dominance on intervals for tackling these problems is proposed. Dominance criteria on intervals are first defined, and their correlations are depicted by equivalent, inclusive and non-included relations; then, a reduction scheme is derived by investigating the influence of different criteria on the ordering of solutions, and a novel ensemble dominance relation on intervals is defined to rationally and equally evaluate the quality of a solution; furthermore, the complexity of the proposed method is analyzed; finally, empirical results indicate the effectiveness of the proposed method.

Multi-objective optimization problems with interval (MOPs-I) uncertainties parameters are common in practice. Evolutionary multi-objective (EMO) algorithms are popularly employed to solve these problems due to their powerful explorations. The comparison strategies among interval objectives of MOPs-I are crucially important for obtaining a superior Pareto front when applying EMOs. By effectively combining two different intervals ranking methods together, i.e., μ and P metrics, we present an improved NSGA-II with a synthesized intervals ranking strategy for optimizing MOPs-I. The characteristics of μ and P in ranking intervals are first analyzed, and then the synthesized ranking method termed as μ ⊕ P is developed to compare and select individuals within the NSGA-II framework. The proposed algorithm is experimentally validated by four MOPs-I functions and a practical problem, and the results empirically demonstrate its merits in obtaining Pareto front with outstanding convergence and spread.

In order to solve the problem of path planning in an environment with many terrains, we propose a method based on interval multi-objective Particle Swarm Optimization (PSO). First, the environment is modeled by the line partition method, and then, according to the distribution of the polygonal lines which form the robot path and taking the velocity's disturbance into consideration, robot's passing time is formulated as an interval by combining Local Optimal Criterion (LOC), and the path's danger degree is estimated through the area ratio between the robot path and the danger source. In addition, the path length is also calculated as an optimization objective. As a result, the robot path planning problem is modeled as an optimization problem with three objectives. Finally, the interval multiobjective PSO is employed to solve the problem above. Simulation and experimental results verify the effectiveness of the proposed method.

Surrogate-assisted interactive genetic algorithms (IGAs) are found to be very effective in reducing human fatigue. Different from models used in most surrogate-assisted evolutionary algorithms, surrogates in IGA must be able to handle the inherent uncertainties in fitness assignment by human users, where, e.g., interval-based fitness values are assigned to individuals. This poses another challenge to using surrogates for fitness approximation in evolutionary optimization, in addition to the lack of training data. In this paper, a new surrogate-assisted IGA has been proposed, where the uncertainty in subjective fitness evaluations is exploited both in training the surrogates and in managing surrogates. To enhance the approximation accuracy of the surrogates, an improved cotraining algorithm for semisupervised learning has been suggested, where the uncertainty in interval-based fitness values is taken into account in training and weighting the two cotrained models. Moreover, uncertainty in the interval-based fitness values is also considered in model management so that not only the best individuals but also the most uncertain individuals will be chosen to be re-evaluated by the human user. The effectiveness of the proposed algorithm is verified on two test problems as well as in fashion design, a typical application of IGA. Our results indicate that the new surrogate-assisted IGA can effectively alleviate user fatigue and is more likely to find acceptable solutions in solving complex design problems.

Interactive genetic algorithms (IGAs) are effective methods of solving optimization problems with qualitative indices. The problem of user fatigue resulting from his/her evaluations, however, restricts their applications in complex optimization problems. Employing various surrogate models to evaluate (a part of) individuals instead of a user is a feasible approach to solving the above problem. Previous studies, however, have not fully utilized knowledge provided by users with similar preference when constructing these models. The problem of constructing surrogate models by using knowledge of users with similar preference was focused in this study. First, users with similar preference participating the evolution were identified based on the matrix formed by the relationship between users and the “fitness” of allele meaning units and the users' interests in allele meaning units by using the collaborative filtering algorithm based on nearest-neighbor; and then the individuals evaluated by users with similar preference and chosen according to the users' preference similarities and confidence, along with their fitness, were as a part of samples for training the surrogate model of the current user's cognition. The proposed method was applied to an evolutionary fashion design system, and the experimental results show that the proposed method can improve the capability in exploration on the premise of greatly alleviating user fatigue.

Interactive genetic algorithms (IGAs) have been successfully applied to optimize problems with aesthetic criteria by embedding the intelligent evaluations of a user into the evolutionary process. User fatigue caused by frequent interactions, however, often greatly impairs the potentials of IGAs on solving complicated optimization problems. Taking the benefits of collective intelligence into account, we here present an IGA with collective intelligence which is derived from a mechanism of group decision making. An IGA with interval individual fitness is focused here and it can be separately conducted by multiple users at the same time. The collective intelligence of all participated users, represented with social and individual knowledge, is first collected by using a modified group decision making method. Then the strategy of applying the collective intelligence to initialize and guide the single evolution of the IGA is given. With such a multi-user promoted IGA framework, the performance of a single IGA is expected to be evidently improved. In a local network environment, the algorithm is applied to a fashion design system and the results empirically demonstrate that the algorithm can not only alleviate user fatigue but also increase the opportunities of IGAs on finding most satisfactory solutions.

Traditional methods of generating test data may result in redundancy of test data, which brings many troubles to software testing. In order to solve the redundancy of test data, this study proposed a novel approach of generating test data by reducing target statements based on dominant relations. First, basic concepts and principles concerning dominance are listed. Then, an approach is proposed to reduce target statements according to their dominant relations. Finally, test suite covering the reduced set of target statements is generated by a genetic algorithm. The generated test suite can also cover all original target statements, which is guaranteed by the proposed strategy. We applied the method to nine benchmark programs, and compared with traditional and greedy methods. The experimental results show that our method can not only reduce redundancy, but also improve the efficiency of generating test data.

Odor source localization is very important in real world applications. We studied the problem of odor source localization and presented a modified particle swarm optimization algorithm for odor source localization of multi robot. The algorithm dynamically adjusts two learning factors in the velocity update equation based on the effect of wind on self cognition and social cognition of a particle. In addition, an artificial potential field method is employed to improve the performance of our algorithm. We conducted various experiments in time-varying environments, and the experimental results confirm the superiority of our algorithm.

Optimization problems with intervals and hybrid indices are common in real-world applications. Previous theories and methods suitable for them, however, are few. We present a large population evolutionary algorithm with a user's interval preferences to effectively solve the problems above in this study. In this algorithm, a large population is adopted to improve the performance of the algorithm in exploration. A similarity-based strategy is employed to estimate the implicit indices of the individuals that the user has not evaluated to alleviate the user's fatigue. When Pareto domination is utilized to compare different individuals, the user's preferences to the individuals with the same rank are calculated to further distinguish their performance. In addition, the user's preferences to different indices, expressed with intervals, are quantified by solving another optimization problem. We apply the proposed algorithm to the interior layout problem, a typical optimization one with both interval parameters in the explicit index and interval value of the implicit index, and compare it with other three optimization algorithms. The experimental results validate its superiority.

Multi-objective optimization (MOO) problems with interval parameters are popular and important in real-world applications. Previous evolutionary optimization methods aim to find a set of well-converged and evenly-distributed Pareto-optimal solutions. We present a novel evolutionary algorithm (EA) that interacts with a decision maker (DM) during the optimization process to obtain the DM's most preferred solution. First, the theory of a preference polyhedron for an optimization problem with interval parameters is built up. Then, an interactive evolutionary algorithm (IEA) for MOO problems with interval parameters based on the above preference polyhedron is developed. The algorithm periodically provides a part of non-dominated solutions to the DM, and a preference polyhedron, based on which optimal solutions are ranked, is constructed with the worst solution chosen by the DM as the vertex. Finally, our method is tested on two bi-objective optimization problems with interval parameters using two different value function types to emulate the DM's responses. The experimental results show its simplicity and superiority to the posteriori method.

We propose a robot path planning method based on particle swarm optimization in an uncertain environment. We consider the case that a robot's cognition to its environment is not complete, i.e., the information of these obstacles in the environment is uncertain. We firstly construct a global environment model based on the uncertain information of these obstacles, and then give a globally optimal path by using particle swarm optimization. Finally, we present a local optimal strategy to handle the uncertain information detected by the robot in real-time. Our preliminary simulation results show that the proposed method is feasible and efficient.

In order to alleviate user fatigue of interactive genetic algorithms with an individual's fuzzy and stochastic fitness, we propose a surrogate model-assisted algorithm by using a directed fuzzy graph to extract user cognition. According to cut-set level and interval dominance probability, we present approaches to construct a directed fuzzy graph of an evolutionary population and calculate an individual's precise fitness based on it. By applying the fuzzy entropy, the chance of data sampling is achieved to obtain reliable samples for training the surrogate model. We adopt a support vector regression machine as the surrogate model, train it using the sampled individuals and their precise fitness, and apply a traditional genetic algorithm to optimize the surrogate model for some generations, providing guided individuals to the user to accelerate the evolution. We quantitatively analyze the performance of the presented algorithm in alleviating user fatigue and increasing more opportunities to look for the satisfactory individuals. Finally, we apply our algorithm to a fashion evolutionary design system to demonstrate its efficiency.

Interactive genetic algorithms with individual's fuzzy fitness well portray the fuzzy uncertainties of a user's cognition. In this paper, we propose an efficient surrogate model-assisted one to alleviate user fatigue by building a classifier and a regressor to approximate the user's cognition. Two reliable training data sets are obtained based on the user's evaluation credibility. Then a support vector classification machine and a support vector regression machine are trained as the surrogate models with these samples. Specifically, the input trained samples are the individuals evaluated by the user, and the output training samples of the classifier and the regressor are widths and centers of these individuals' fuzzy fitness assigned by the user, respectively. These two surrogate models are simultaneously applied to the subsequent evolutions with enlarged population size so as to alleviate user fatigue and enhance the search ability of the algorithm. We constantly update the training data sets and the surrogate models in order to guarantee the approximation precision. Furthermore, we quantitatively analyze the algorithm's performance in alleviating user fatigue and increasing more opportunities to find the optimal solutions. We also apply it to a fashion evolutionary design system to show its efficiency.

Interactive genetic algorithms (IGAs) are effective methods to solve an optimization problem with implicit indices. Whereas it requires direct evaluation of user for each individual and the fact limits the population size for user fatigue problem. While, in general to solve many problems with genetic algorithm, it is desirable to maintain the population size as large as possible. To break the restriction of population size and not increasing the number of individuals being evaluated by user we propose an interactive genetic algorithm with large population size in this paper. The algorithm divides the whole population into several clusters, the maximum number of which changes along with the evolution. User only assigns one representative individualpsilas fitness for each cluster and expresses it with an accurate number. The fitness of other individuals are estimated according to the representativepsilas fitness directly, and are expressed with some intervals, which can maintain the large population size with less number of individuals being evaluated by user. In addition we choose appropriate individuals and crossover point to perform crossover operator. This algorithm is applied in a fashion evolutionary design system and compared it with the above interactive genetic algorithm with small population size, the results effectively validate that the proposed algorithm has good performance in alleviating user fatigue and looking for ldquothe most satisfactory suits".