Diffusion models have achieved remarkable success in image generation, image super-resolution, and text-to-image synthesis. Despite their effectiveness, they face key challenges, notably long inference time and complex architectures that incur high computational costs. While various methods have been proposed to reduce inference steps and accelerate computation, the optimization of diffusion model architectures has received comparatively limited attention. To address this gap, we propose LDMOES (Lightweight Diffusion Models based on Multi-Objective Evolutionary Search), a framework that combines multi-objective evolutionary neural architecture search with knowledge distillation to design efficient UNet-based diffusion models. By adopting a modular search space, LDMOES effectively decouples architecture components for improved search efficiency. We validated our method on multiple datasets, including CIFAR-10, Tiny-ImageNet, CelebA-HQ [Formula: see text], and LSUN-church [Formula: see text]. Experiments show that LDMOES reduces multiply-accumulate operations (MACs) by approximately 40% in pixel space while outperforming the teacher model. When transferred to the larger-scale Tiny-ImageNet dataset, it still generates high-quality images with a competitive FID score of 4.16, demonstrating strong generalization ability. In latent space, MACs are reduced by about 50% with negligible performance loss. After transferring to the more complex LSUN-church dataset, the model surpasses baselines in generation quality while reducing computational cost by nearly 60%, validating the effectiveness and transferability of the multi-objective search strategy. Code and models will be available at https://github.com/GenerativeMind-arch/LDMOES .

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.

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.

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.

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.

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.

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.

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.

The interactive evolutionary multi-task optimization approach assisted by surrogate models has proven successful in enhancing individualized recommendation performance. However, in light of the dynamically changing user preferences, it becomes imperative to further develop more powerful knowledge sharing strategy to improve the interactive multi-task optimization efficiency. A probability model-assisted search space alignment among multiple tasks method is proposed for knowledge transfer across multi-task environment. Additionally, a diversity maintaining mechanism of the transferred population is proposed to improve the quality and diversity of the initial population in a preference varied multi-task environment. The research demonstrates the effectiveness of the proposed approach in achieving effective knowledge transfer across multi-task environmen. Furthermore, the utilization of a high-quality initial population not only enhances the evolutionary search efficiency of the algorithm but also significantly improves the accuracy, diversity., and novelty of personalized recommendation.

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.

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.

An important problem in data science, feature selection (FS) consists of finding the optimal subset of features and eliminating irrelevant or redundant features. The FS task on high-dimensional data is challenging for the FS methods currently available in the literature. To overcome this limitation, we propose a novel feature selection method called External Attention-Based Feature Ranker for Large-Scale Feature Selection (EAR-FS) whose function is based on the logic of an attention mechanism and a hybrid metaheuristic. EAR-FS comprises three interdependent modules: (1) in the training module design, a multilayer perceptron network endowed with an attention module is trained to fit the dataset; (2) in feature ranking by attention, the trained attention module is used for attention updating and to rank features according to their importance; 3) in subset generation, a two-stage heuristic approach is applied to determine a small number of features that still guarantee high-accuracy performance. The experimental benchmark comprised 26 datasets of small, large and very large sizes, ranging from 15 to 12,533 features. Experiments performed against the state-of-the-art algorithms of FS show that our algorithm is efficient at selecting a small number of features from large datasets while guaranteeing excellent levels of classification accuracy. For instance, EAR-FS demonstrated its capability to reduce the features of the 11 Tumor dataset by 97% while maintaining a classifier accuracy of over 93%.

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.

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.

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.

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.

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.

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.

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.

The environment after disaster is complicated and it is difficult to rescue the survivors timely and effectively. Robots can complete the rescue work instead of rescuers with high-efficiency and without limits of the disaster area. Based on this, a novel task allocation method for multi-robot in an environment after disaster is presented. Firstly, according to the locations and time constraints of the tasks, a new grouping method of the tasks is proposed to reduce the computational complexity. Following that, a new initial solution generation method is used to speed up the evolution. Finally, an improved particle swarm algorithm with the adaptive inertia weight and velocity update is developed to solve the grouping-based task allocation. The experimental results indicate that the proposed method can increase the success rate of rescue and speed up the rescue effectively.

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.

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.

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.

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 (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.

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.