As the search space and hence the optimum vary through time, dynamic optimization problems (DOPs) bring tremendous difficulties. Changes in DOPs often manifest as diverse dynamics. Consequently, regulating individuals’ search to adapt to diverse dynamics is crucial to tackle DOPs. Besides, due to the inherent population nature in dynamic optimization algorithms (DOAs), loss of global and local diversities is a critical issue deteriorating the performance of DOAs. Faced with these difficulties, this article proposes a neural network-aided differential evolution with double Q-learning (NNDE-DQ), in which an evolutionary regulation network (ERN) is designed to maintain high global and local diversities over time and regulate individuals’ search that can adapt to diverse dynamics. NNDE-DQ first partitions the search space into multiple subspaces and in each subspace distant individuals are selected as the centers of ERN’s hidden nodes activated by radial basis function. Every input individual is mutated with two randomly selected hidden node centers from different subspaces as differential individuals, facilitating the maintenance of a high global diversity due to very distinct differential terms of the population. Moreover, each mutated individual selects a hidden node center from the subspace located by the mutated individual to undergo crossover. Due to distant hidden node centers in each subspace, a high local diversity can be maintained by individuals’ crossover. Besides, DQ is introduced to acquire ERN’s desired output by interactively estimating individuals’ state-action information, enabling ERN to learn the regulation of individuals’ search in dynamic environments and hence adapt to diverse dynamics. The experimental results demonstrate that NNDE-DQ significantly improves the performance in solving various DOPs comparing to seven state-of-the-art DOAs.

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.

Flexible job shop co-scheduling problems (FJSCSPs) normally adopt single-load automated guided vehicles (AGVs) for transportation, possibly causing the waste of load capacity. To enhance the transportation efficiency, a multiload AGVs (MAGVs) that carry more than one job simultaneously within its load capacity come into use in flexible manufacturing systems (FMSs). In this scenario, transit throughput can achieve the obvious improvement without increasing the vehicle fleet size, having become more prevalent gradually. However, co-scheduling machines and MAGVs is seldom investigated, which is crucial for maximizing production efficiency due to the inherent interdependence between transporting and processing. Considering constraints on load capacity, task assignment, and transportation sequence, this co-scheduling problem is formulated by minimizing the makespan as an optimization objective. Subsequently, a collaboration–competition estimation of distribution algorithm (CCEDA) is put forward to solve the difficulties caused by the flexible sequence for pickup and delivery tasks of MAGVs. In particular, two problem-related heuristic rules for selecting AGVs and machines are designed, and then a hybrid initialization strategy is developed to produce high-quality initial individuals. To comprehensively describe the landscape of the problem, multiple probability models are established by learning the elite solutions, and then a collaboration–competition mechanism adaptively samples using different models to maintain the high-efficiency exploration. Furthermore, a local search based on variable neighborhood is introduced to enhance the exploitation in promising regions. The experimental results on 30 instances expose that the proposed algorithm outperforms the other state-of-the-art algorithms significantly. Also, the analysis on the impact of AGV load capacity on production confirms that its increase effectively reduces the makespan, thereby demonstrating the practical value of MAGVs.

Collaborative search by air-ground unmanned swarm, as a pivotal and efficient approach for intelligence gathering and disaster relief, highlights the critical role of search path planning in enhancing overall performance. Addressing the inefficiency resulting from insufficient collaboration between air and ground unmanned platforms in current research, this paper delves into the fundamental characteristics and challenges of collaborative search by air-ground unmanned swarm. This paper clarifies the objectives and constraints of path planning and introduces a method for collaborative search path planning based on the Learning Wolf Pack Algorithm (LWPA). This method initially constructs an optimization model that comprehensively considers area coverage, target detection probability, and search uncertainty. It integrates Distributed Model Predictive Control (DMPC) with the Distributed Constraint Optimization Problem (DCOP) framework, forming an architecture for real-time search path planning. To overcome the limitation of existing DCOP solution methods, which tend to get stuck in local optimal solutions, the LWPA employs a Q-learning mechanism for hierarchical learning and dynamically adjusts parameters to balance local refinement and global exploration. Experimental results demonstrate that this method offers significant advantages in improving search efficiency, coverage, and target detection rates, with an average area coverage of 99.28% and uncertainty as low as 0.86%. These results fully validate its effectiveness and superiority in search tasks in complex urban environments. Furthermore, tests on dynamic adaptability and scalability further verify the potential and value of this method in practical applications.

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.

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.

Data stream clustering can be performed to discover the patterns underlying continuously arriving sequences of data. A number of data stream clustering algorithms for finding clusters in arbitrary shapes and handling outliers, such as density-based clustering algorithms, have been proposed. However, these algorithms are often limited in their ability to construct and merge microclusters by measuring the Euclidean distances between high-dimensional data objects, e.g., transferring valuable knowledge from historical landmark windows to the current landmark window, and exploiting evolving subspace structures adaptively. We propose an online sparse representation clustering (OSRC) method to learn an affinity matrix for evaluating the relationships among high-dimensional data objects in evolving data streams. We first introduce a low-dimensional projection (LDP) into sparse representation to adaptively reduce the potential negative influence associated with the noise and redundancy contained in high-dimensional data. Then, we take advantage of the -norm optimization technique to choose the appropriate number of representative data objects and form a specific dictionary for sparse representation. The specific dictionary is integrated into sparse representation to adaptively exploit the evolving subspace structures of the high-dimensional data objects. Moreover, the data object representatives from the current landmark window can transfer valuable knowledge to the next landmark window. The experimental results based on a synthetic dataset and six benchmark datasets validate the effectiveness of the proposed method compared to that of state-of-the-art methods for data stream clustering.

Dynamic multiobjective optimization problems (DMOPs) are characterized by multiple objectives that change over time in varying environments. More specifically, environmental changes can be described as various dynamics. However, it is difficult for existing dynamic multiobjective algorithms (DMOAs) to handle DMOPs due to their inability to learn in different environments to guide the search. Besides, solving DMOPs is typically an online task, requiring low computational cost of a DMOA. To address the above challenges, we propose a particle search guidance network (PSGN), capable of directing individuals' search actions, including learning target selection and acceleration coefficient control. PSGN can learn the actions that should be taken in each environment through rewarding or punishing the network by reinforcement learning. Thus, PSGN is capable of tackling DMOPs of various dynamics. Additionally, we efficiently adjust PSGN hidden nodes and update the output weights in an incremental learning way, enabling PSGN to direct particle search at a low computational cost. We compare the proposed PSGN with seven state-of-the-art algorithms, and the excellent performance of PSGN verifies that it can handle DMOPs of various dynamics in a computationally very efficient way.

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.

Location-routing problems (LRPs) widely exist in logistics activities. For the biomass waste collection, there is a recognized need for novel models to locate the collection facilities and plan the vehicle routes. So far most location-routing models fall into the cost-driven-only category. However, comprehensive objectives are required in the specific context, such as time-dependent pollution and speed- and load-related emission. Furthermore, LRPs are hierarchical by nature, containing the facility location problems (strategic level) and the vehicle routing problems (VRPs) (tactical level). Existing studies in this field usually adopt computational intelligence methods directly without decomposing the problem. This can be inefficient especially when multiple objectives are applied. Motivated by these, we develop a novel multiobjective optimization model for the LRP for biomass waste collection. To solve this model, we explore the way to tailor evolutionary algorithms to the hierarchical structure. We develop adapted versions of two commonly used evolutionary algorithms: 1) the genetic algorithm and 2) the ant colony optimization algorithm. For the genetic algorithm, we divide the population by the strategic level decisions, so that each subpopulation has a fixed location plan, breaking the LRP down into many multidepot VRPs. For the ant colony optimization, we use an additional pheromone vector to track the good decisions on the location level, and segregate the pheromones related to different satellite depots to avoid misleading information. Thus, the problem degenerates into VRP. Experimental results show that our proposed methods have better performances on the LRP for biomass waste collection.

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.

In dynamic optimization problems (DOPs), environmental changes can be characterized as various dynamics. Faced with different dynamics, existing dynamic optimization algorithms (DOAs) are difficult to tackle, because they are incapable of learning in each environment to control the search. Besides, diversity loss is a critical issue in solving DOPs. Maintaining a high-diversity over dynamic environments is reasonable as it can address such an issue automatically. In this article, we propose a particle search control network (PSCN) to maintain a high-diversity over time and control two key search actions of each input individual, i.e., locating the local learning target and adjusting the local acceleration coefficient. Specifically, PSCN adequately considers the diversity to generate subpopulations located by hidden node centers, where each center is assessed by significance-based criteria and distance-based criteria. The former enable a small intrasubpopulation distance and a big search scope (subpopulation width) for each subpopulation, while the latter make each center distant from other existing centers. In each subpopulation, the best-found position is selected as the local learning target. In the output layer, PSCN determines the action of adjusting the local acceleration coefficient of each individual. Reinforcement learning is introduced to obtain the desired output of PSCN, enabling the network to control the search by learning in different iterations of each environment. The experimental results especially performance comparisons with eight state-of-the-art DOAs demonstrate that PSCN brings significant improvements in performance of solving DOPs.

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.

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.

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.

Previous class imbalance learning methods are mostly grounded on the assumption that all training data have been labeled, however, is impractical in many real-world applications. The limited amount of labeled instances may produce a classifier with poor generalization. To address the issue, a transfer weighted extreme learning machine (TWELM) classifier is proposed, with the purpose of extracting knowledge from other domains to improve the classification performance of a classifier in a limited labeled target domain. To be specific, a well-tuned weighted extreme learning machine classifier is first learned from source data that has been completely labeled. Subsequently, another extreme learning machine classifier is obtained from the limited labeled target domain data to preserve the target domain structural knowledge and the decision boundary information. Finally, the target classifier is optimized by minimizing the outputs of the two classifiers on unlabeled target data. Experimental results on real-world data sets show that TWELM outperforms existing algorithms on classification accuracy and computation cost.

Many existing works represent signals by covariance matrices and then develop learning methods on the Riemannian symmetric positive-definite (SPD) manifold to deal with such data. However, they summarize each instance with a single covariance matrix, omitting some potential important information, such as the time evolution of the correlation in signals. In this paper, we represent each instance by a sequence of covariance matrices and develop a novel dynamic generalized learning Riemannian space quantization (DGLRSQ) method to deal with such data representations. The proposed DGLRSQ method incorporates short-term memory mechanism in generalized learning Riemannian space quantization (GLRSQ), which is an extension of Euclidean generalized learning vector quantization to deal with SPD matrix-valued data. The proposed method can capture the temporal evolution of the correlation in signals and thus provides better performance to its the counterpart – GLRSQ, which treats each instance as a signal covariance matrix. Empirical investigations on synthetic data and motor imagery EEG data show the superior performance of the proposed method.

The performance of decomposition-based algorithms is sensitive to the Pareto front shapes since their reference vectors preset in advance are not always adaptable to various problem characteristics with no a priori knowledge. For this issue, this article proposes an adaptive reference vector reinforcement learning (RVRL) approach to decomposition-based algorithms for industrial copper burdening optimization. The proposed approach involves two main operations, that is: 1) a reinforcement learning (RL) operation and 2) a reference point sampling operation. Given the fact that the states of reference vectors interact with the landscape environment (quite often), the RL operation treats the reference vector adaption process as an RL task, where each reference vector learns from the environmental feedback and selects optimal actions for gradually fitting the problem characteristics. Accordingly, the reference point sampling operation uses estimation-of-distribution learning models to sample new reference points. Finally, the resultant algorithm is applied to handle the proposed industrial copper burdening problem. For this problem, an adaptive penalty function and a soft constraint-based relaxing approach are used to handle complex constraints. Experimental results on both benchmark problems and real-world instances verify the competitiveness and effectiveness of the proposed algorithm.

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.

Evolutionary feature selection (FS) methods face the challenge of “curse of dimensionality” when dealing with high-dimensional data. Focusing on this challenge, this article studies a variable-size cooperative coevolutionary particle swarm optimization algorithm (VS-CCPSO) for FS. The proposed algorithm employs the idea of “divide and conquer” in cooperative coevolutionary approach, but several new developed problem-guided operators/strategies make it more suitable for FS problems. First, a space division strategy based on the feature importance is presented, which can classify relevant features into the same subspace with a low computational cost. Following that, an adaptive adjustment mechanism of subswarm size is developed to maintain an appropriate size for each subswarm, with the purpose of saving computational cost on evaluating particles. Moreover, a particle deletion strategy based on fitness-guided binary clustering, and a particle generation strategy based on feature importance and crossover both are designed to ensure the quality of particles in the subswarms. We apply VS-CCPSO to 12 typical datasets and compare it with six state-of-the-art methods. The experimental results show that VS-CCPSO has the capability of obtaining good feature subsets, suggesting its competitiveness for tackling FS problems with high dimensionality.

Over-sampling technology for handling the class imbalanced problem generates more minority samples to balance the dataset size of different classes. However, sampling in original data space is ineffective as the data in different classes is overlapped or disjunct. Based on this, a new minority sample is presented in terms of the manifold distance rather than Euclidean distance. The overlapped majority and minority samples apt to distribute in fully disjunct subspaces from the view of manifold learning. Moreover, it can avoid generating samples between the minority data locating far away in manifold space. Experiments on 23 UCI datasets show that the proposed method has the better classification accuracy.

The benchmark problems have played a fundamental role in verifying the algorithm's search ability. A dynamic multimodal optimization (DMO) problem is defined as an optimization problem with multiple global optima and characteristics of global optima which are changed during the search process. Two cases are used to illustrate the application scenario of DMO. A set of benchmark functions on DMO, which contains eight problems, are proposed to show the difficulty of DMO. The properties of the proposed benchmark problems, such as the distribution of solutions, the scalability, the number of global/local optima, are discussed.

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.

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.

In practical engineering optimization problems, the parameters of the objective functions may be interval. Existing interval multi-objective optimization methods mostly adopted interval dominant relationships and corresponding crowded operators to find the better solutions. They were complex and time-consuming. So a novel knowledge-inducing interval MOEA/D is put forward. It decomposes interval multi-objective optimization problem to many interval single-objective optimization sub-problems in terms of the weight so as to realize the parallel exploration and avoid the complex dominant comparison. Especially, the improved Chebyshev aggregate function is defined to calculate the distance between the midpoint of the interval objective values and the reference point. Moreover, the reference point depends on the upper limit of the interval objective values. In order to keep the diversity of population and avoid the premature convergence, three kinds of knowledge including situational knowledge, neighborhood knowledge and association knowledge are defined and the differential evolution guided by above knowledge are illustrated in detail. The simulation results for five benchmark functions indicate that the proposed algorithm keeps the diversity of population better and obtains the Pareto-optimal solutions more close to the true Pareto front by comparing with other interval multi-objective optimization algorithms.

This paper investigates the problem of fuzzy controller design for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. By using the average dwell time approach together with the piecewise Lyapunov function technique, a set of well-conditioned sufficient conditions for the existence of controller is proposed, under which the overall switched closed-loop system is asymptotically stable. A state feedback controller depending on the singular perturbation parameter ε, which is shown to work well for all ε ∈ (0, ε0), where ε0is the stability bound of singularly perturbed systems, is developed. In addition, when ε is sufficiently small, the ε-dependent controller can be reduced to an ε-independent one. Then, an ε-independent state feedback stabilization controller design method is proposed in terms of linear matrix inequalities. Furthermore, under the controller, the stability bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to show the feasibility and effectiveness of the obtained results.

The sensor nodes' sensing models directly determine the energy-efficient coverage of wireless sensor networks. Existing uncertain sensing models are all constructed based on stochastic programming or fuzzy programming. Though they consider some uncertain factors in a real environment, the accurate probability distribution and fuzzy membership function are difficult to know in advance. Moreover, the uncertainties of environmental factors are usually irregular and discontinuous. Considering the simplicity of getting an interval, a novel interval sensing mode integrating with the sensing direction is constructed to reflect the possible influence from environmental factors and avoid the obstacles. Experimental results indicate that three key parameters including sensing radius, reliable sensing radius and detection degree have a direct influence on interval sensing ability. Smaller sensing radius, larger reliable sensing radius or less detection degree makes the uncertainty less. Compared with other sensing models, the interval sensing model is more rational and meets the real situation. Consequently, it is more suitable to apply in various uncertain environments and directional sensors.

Robust optimization over time is a practical dynamic optimization method, which provides two detailed computable metrics to get the possible robust solutions for dynamic scalar optimization problems. However, the robust solutions fit for more time-varying moments or approximate the optimum more because only one metric is considered as the optimization objective. To find the true robust solution set satisfying maximum both survival time and average fitness simultaneously during all dynamic environments, a novel two-layer multi-objective optimization method is proposed. In the first layer, considering both metrics, the acceptable optimal solutions for each changing environment is found. Subsequently, they are composed of the practical robust solution set in the second layer. Taking the average fitness and the length of the robust solution set as two objectives, the optimal combinations for the whole time-varying environments are explored. The experimental results for the modified moving peaks benchmark shows that the robust solution sets considering both metrics are superior to the robust solutions gotten by ROOT. As the key parameters, the fitness threshold has the more obvious impact on the performances of MROOT than the time window, whereas ROOT is more sensitive to both of them.

Harmonious color design, as a necessary part in product design, is to find the color combinations matching one's preference. Since visual effect is hard to be described by mathematic model, each color combination shall be evaluated by the designers. Moreover, it has been proved that the knowledge derived from the evolution or gotten in advance can effectively improve the algorithm's performances. Consequently, adaptive interactive cultural algorithm is proposed to help the designer finding the preferred color combination. The algorithm is good at balancing the exploitation and the exploration because the parameters of crossover and mutation operations are adaptively adjusted according to the evolutionary degree. In addition, the detailed evolutionary strategies are adjusted for various persons who have different professional background and design experience. Taking shopping cards' color design as a typical application, the statistical experimental results show that adaptive interactive cultural algorithm has faster convergence speed and better stability. Fewer individuals evaluated by participants mean that human fatigue can be effectively alleviated and they can put more attention to other valuable works.