The increasing labor costs in agriculture have accelerated the adoption of multirobot systems for orchard harvesting. However, efficiently coordinating these systems is challenging due to the complex interplay between makespan and energy consumption, particularly under practical constraints like load-dependent speed variations and battery limitations. This article defines the multiobjective agricultural multielectrical-robot task allocation (AMERTA) problem, which systematically incorporates these often-overlooked real-world constraints. To address this problem, we propose a hybrid hierarchical route reconstruction algorithm (HRRA) that integrates several innovative mechanisms, including a hierarchical encoding structure, a dual-phase initialization method, task-sequence optimizers, and specialized route reconstruction operators. Extensive experiments on 45 test instances demonstrate HRRA's superior performance against seven state-of-the-art algorithms. Statistical analysis, including the Wilcoxon signed-rank and Friedman tests, empirically validates HRRA's competitiveness and its unique ability to explore previously inaccessible regions of the solution space. In general, this research contributes to the theoretical understanding of multirobot coordination by offering a novel problem formulation and an effective algorithm, thereby also providing practical insights for agricultural automation.

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.

Dynamic constrained multiobjective optimization problems (DCMOPs) are widely existed in real-world applications and emerged as a prominent research focus in the evolutionary computation community. Current studies on DCMOPs face two main challenges: limited accuracy in population prediction, and a lack of effective strategies to improve static optimizer performance. To tackle these challenges, this paper proposes a dynamic constrained multiobjective evolutionary algorithm based on multipopulation prediction and dynamic fusion ranking. Specifically, an efficient computer-vision-inspired point set registration method, named coherent point drift, is introduced to align individuals across successive environments. With the correspondences between two environments, the solution trajectory tracking problem is transformed as a point set registration problem. Based on the observed trajectory of solutions, the Pareto-optimal set or Pareto-optimal front in the new environment can be predicted. Additionally, this paper highlights the importance of task-specific multipopulation prediction. After analysis the specific tasks of each population, different initial populations tailored to the tasks are predicted by the proposed prediction method. Finally, a dynamic fusion based two-ranking environmental selection strategy is proposed for the auxiliary task. This strategy dynamically integrates experience-based and constraint-based approaches, improving the auxiliary population evolutionary efficiency and its alignment with the main task. The superiority of proposed algorithm is validated through extensive experiments on a series of benchmark problems and a real-world raw ore allocation problem.

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

Identifying the biomarkers from the personalized gene interaction network of individual patients is important for disease diagnosis. However, existing methods not only ignore the prior biomarkers for practical use but also ignore the observability of the entire system. Therefore, this paper proposes a new constrained multi-objective optimization-based temporal network observability model (CMTNO) to identify biomarkers, which not only requires minimizing the number of selected nodes including ordinary nodes and prior nodes (the first optimization objective) but also maximizing the number of selected prior nodes (the second optimization objective) on the premise of ensuring network observability (the constraint condition). Considering the temporal feature of cancer (patients belong to different stages and each patient contains one task), an experience learning-based constrained multi-objective evolutionary algorithm is designed to solve the CMTNO problems. The selected probabilities of ordinary nodes and prior nodes are treated as experience, stored in two separate archives and updated by the optimal solutions on each task. Experience utilization refers to using two archives to generate new initial populations for new patients, in order to improve the optimization efficiency of the algorithm. Besides, a two-step neighbor-based connectivity method is proposed to distinguish different nodes with similar connectivity to further improve the effectiveness of archives. The proposed model and algorithm are evaluated on three kinds of cancer patients' data under two kinds of network models, and results show their effectiveness in identifying effective biomarkers.

Large-scale constrained multiobjective optimization problems (LSCMOPs) exist widely in science and technology. LSCMOPs pose great challenges to algorithms due to the need to optimize multiple conflicting objectives and satisfy multiple constraints in a large search space. To better address such problems, this article proposes a dynamic subspace search-based evolutionary algorithm for solving LSCMOPs. The main idea is to initially allow the population to search in a low-dimensional subspace to increase convergence, then the searched subspace is gradually expanded to encourage the population to further search the full decision space. Specifically, the contribution of each decision variable to the evolution is first calculated using the proposed decision variable analysis method. Then, a probability-based offspring generation strategy is developed to encourage the population to preferentially search in a low-dimensional subspace composed of decision variables with high contribution degrees, thus speeding up the early convergence. With the continuous progress of evolution, the subspace is gradually expanded to ensure that the population can better explore the entire space. The performance of the proposed algorithm is evaluated on a variety of test problems with 100-1000 decision variables. Experimental results on four test suits and three real-world instances show that the proposed algorithm is efficient in solving LSCMOPs.

Dynamic constrained multiobjective optimization problems (DCMOPs) are widely encountered in real-world applications and have attracted increasing attention in the evolutionary computation community. Existing studies primarily focus on the population initialization, but disregard to improve the evolution process. In DCMOPs, the knowledge is undoubtedly more abundant as the existence of historical environments. Therefore, extracting and utilizing useful knowledge from historical environments can further improve the evolution process. In this article, a history-assisted two-state auxiliary task collaboration approach is proposed to solve DCMOPs by conducting a more effective auxiliary task. Specifically, the algorithm indicates that constrained Pareto-optimal front (CPF) in similar historical environments is more suitable as an auxiliary task for current evolution, as it is closer to the current CPF. To identify the most suitable environment from extensive historical environments, a novel prediction-based similar environment identification method is proposed for the auxiliary task. To fully utilize the novel auxiliary task, an experience-driven two-state environmental selection strategy is proposed, which conditionally considers both historical and current information. In this strategy, individuals in state A are inclined to promote toward the historical CPF while disregarding the dominance relationship or constraints, to help cross infeasible region and approach CPF rapidly. For those individuals in state B, dominance relationship is taken into consideration, further bringing auxiliary task closer to the main task. The superiority of the proposed algorithm has been comprehensively demonstrated by experimental comparison results on a variety of benchmark test problems and a real-world problem with raw ore allocation in mineral processing.

With the rapid advancement of artificial intelligence, autonomous multi-robot systems have been successfully applied to various domains. Therefore, developing intelligent routing and scheduling systems to efficiently coordinate multi-robot movements in transportation networks emerges as a critical challenge. To address this issue, this study constructs an optimization model for cooperative robot operations, aiming to minimize total energy consumption and the completion time of most time-consuming robot. These objectives contain conflicts, thus requiring a multi-objective optimization approach to resolve them. We propose a reinforced neighborhood search method combined with genetic algorithm (RNSGA), which combines single solution search ideas and population-based techniques. RNSGA consists of two crucial steps: route construction to determine the composition and visiting sequence of task points within each route, as well as route allocation to assign routes to individual robots. The route construction phase incorporates several key components, including solution initialization, route balance mechanism, proximity-based optimization mechanism, and intro-route sequence adjustment method. For the route allocation phase, a population-based allocation mechanism is employed to determine the optimal assignment of routes. Comprehensive experiments on 24 classic transportation test instances demonstrate that RNSGA significantly outperforms six state-of-the-art algorithms.

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

In constrained multimodal multiobjective optimization problems (CMMOPs), the existence of discrete and confined feasible regions bring great challenges to current multiobjective optimization evolutionary algorithms (MOEAs). To address these challenges, this article proposes a constrained multimodal multiobjective differential evolution algorithm, which incorporates a similar-niching-based reproduction operator and a novel environmental selection mechanism. The proposed algorithm initiates by segregating the population into distinct niches, thereby promoting independent evolution within each niche. This segmentation enhances the exploration of multiple discrete feasible regions, thus improving the capacity to find diverse Pareto optimal solutions. Moreover, the algorithm selects the most similar niche to collaboratively generate solutions, further enhancing its ability to generate effective feasible solutions. To improve the diversity within the population, the proposed environmental selection mechanism gives preference to solutions that enhance the distribution of the next-generation population. By considering the diversity in both two spaces, the population retains more pareto optimal solutions. Based on the Friedman test results of the comparison experiment with other representative algorithms and the champion algorithm of the CEC2023 CMMOPs competition, the proposed algorithm attained the top ranking, thereby reinforcing its demonstrated superiority. Meanwhile, the proposed algorithm is used to solve the constrained multimodal multiobjective location selection problem and results show its superiority.

In the field of evolutionary multi-objective optimization, the approximation of the Pareto front (PF) is achieved by utilizing a collection of representative candidate solutions that exhibit desirable convergence and diversity. Although several multi-objective evolutionary algorithms (MOEAs) have been designed, they still have difficulties in keeping balance between convergence and diversity of population. To better solve multi-objective optimization problems (MOPs), this paper proposes a Two-stage Evolutionary Framework For Multi-objective Opti-mization (TEMOF). Literally, algorithms are divided into two stages to enhance the search capability of the population. During the initial half of evolutions, parental selection is exclusively conducted from the primary population. Additionally, we not only perform environmental selection on the current population, but we also establish an external archive to store individuals situated on the first PF. Subsequently, in the second stage, parents are randomly chosen either from the population or the archive. In the experiments, one classic MOEA and two state-of-the-art MOEAs are integrated into the framework to form three new algorithms. The experimental results demonstrate the superior and robust performance of the proposed framework across a wide range of MOPs. Besides, the winner among three new algorithms is compared with several existing MOEAs and shows better results. Meanwhile, we conclude the reasons that why the two-stage framework is effect for the existing benchmark functions.

It is a big challenge to develop efficient models for identifying personalized drug targets (PDTs) from high-dimensional personalized genomic profile of individual patients. Recent structural network control principles have introduced a new approach to discover PDTs by selecting an optimal set of driver genes in personalized gene interaction network (PGIN). However, most of current methods only focus on controlling the system through a minimum driver-node set and ignore the existence of multiple candidate driver-node sets for therapeutic drug target identification in PGIN. Therefore, this paper proposed multi-objective optimization-based structural network control principles (MONCP) by considering minimum driver nodes and maximum prior-known drug-target information. To solve MONCP, a discrete multi-objective optimization problem is formulated with many constrained variables, and a novel evolutionary optimization model called LSCV-MCEA was developed by adapting a multi-tasking framework and a rankings-based fitness function method. With genomics data of patients with breast or lung cancer from The Cancer Genome Atlas database, the effectiveness of LSCV-MCEA was validated. The experimental results indicated that compared with other advanced methods, LSCV-MCEA can more effectively identify PDTs with the highest Area Under the Curve score for predicting clinically annotated combinatorial drugs. Meanwhile, LSCV-MCEA can more effectively solve MONCP than other evolutionary optimization methods in terms of algorithm convergence and diversity. Particularly, LSCV-MCEA can efficiently detect disease signals for individual patients with BRCA cancer. The study results show that multi-objective optimization can solve structural network control principles effectively and offer a new perspective for understanding tumor heterogeneity in cancer precision medicine. The source code of our LSCV-MCEA and supplementary files can be freely downloaded from https://github.com/WilfongGuo/MONCP, with all data in this study.

Evolutionary constrained multiobjective optimization has received extensive attention and research in the past two decades, and a lot of benchmarks have been proposed to test the effect of the constrained multiobjective evolutionary algorithms (CMOEAs). Specially, the constraint functions are highly correlated with the objective values, which makes the features of constraints too monotonic and differ from the properties of the real-world problems. Accordingly, previous CMOEAs cannot solve real-world problems well, which generally involve decision space constraints with multi-modal/non-linear features. Therefore, we propose a new benchmark framework and design a suite of new test functions with scalable high-dimensional decision space constraints. To be specific, different high-dimensional constraint functions and mixed linkages in variables are considered to be close to realistic features. In this framework, several parameter interfaces are provided, so that users can easily adjust the parameters to obtain the variant functions and test the generalization performance of the algorithms. Different types of existing CMOEAs are employed to test the use of the proposed test functions, and the results show that they are easy to fall into local feasible regions. Therefore, we improve one evolutionary multitasking-based CMOEA to better handle these problems, in which a new search algorithm is designed to enhance the search abilities of populations. Compared with the existing CMOEAs, the proposed CMOEA presents better performance.

Constrained multiobjective optimization problems with deceptive constraints (DCMOPs) are a kind of complex optimization problems and have received some attention. For DCMOPs, the closer a solution is to the feasible region, the larger its constraint value. Moreover, multiple local infeasible regions will have different minimal constraint values according to their distances to feasible regions. Therefore, most of the existing algorithms are easy to fall into local regions, and even cannot find any feasible solution. To address DCMOPs, this article proposes a new evolutionary multitasking algorithm with a cooperative multistep mutation strategy. In this algorithm, the DCMOP is transformed into a multitasking optimization problem, in which the main task is the original DCMOP and the created auxiliary task aims to provide effective help for solving the main task. Specially, the designed cooperative multistep mutation strategy contains two contributions to solve deceptive constraints. First, a multistep mechanism is proposed, in which the individuals will use multiple different steps to generate the multiple offspring solutions along one direction, so as to expand search range to find feasible regions. Second, a cooperative mechanism between the two tasks is proposed, in which the main purpose is to provide effective and stable search directions. To be specific, an opposite solution generation method is utilized to generate the opposite solution of auxiliary population in the search space, and the direction from the auxiliary population to the main population will be formed. Combined with these two mechanisms, the proposed cooperative multistep mutation strategy can effectively improve the population diversity along the promising and stable search directions. In the experiments, the proposed algorithm is tested on the two benchmark DCMOPs, which contain objective space constraints and decision space constraints respectively. The results show the effectiveness and superiority of the proposed algorithm over the latest compared algorithms.

Constrained multiobjective optimization problems (CMOPs) involve multiple objectives to be optimized and various constraints to be satisfied, which challenges the evolutionary algorithms in balancing the objectives and constraints. This article attempts to explore and utilize the relationship between constrained Pareto front (CPF) and unconstrained Pareto front (UPF) to solve CMOPs. Especially, for a given CMOP, the evolutionary process is divided into the learning stage and the evolving stage. The purpose of the learning stage is to measure the relationship between CPF and UPF. To this end, we first create two populations and evolve them by specific learning strategies to approach the CPF and UPF, respectively. Then, the feasibility information and dominance relationship of the two populations are used to determine the relationship. Based on the learned relationship, specific evolving strategies are designed in the evolving stage to improve the utilization efficiency of objective information, so as to better solve this CMOP. By the above process, a new constrained multiobjective evolutionary algorithm (CMOEA) is presented. Comprehensive experimental results on 65 benchmark functions and ten real-world CMOPs show that the proposed method has a better or very competitive performance in comparison with several state-of-the-art CMOEAs. Moreover, this article demonstrates that using the relationship between CPF and UPF to guide the utilization of objective information is promising in solving CMOPs.

This article proposes a novel differential evolution algorithm for solving constrained multimodal multiobjective optimization problems (CMMOPs), which may have multiple feasible Pareto-optimal solutions with identical objective vectors. In CMMOPs, due to the coexistence of multimodality and constraints, it is difficult for current algorithms to perform well in both objective and decision spaces. The proposed algorithm uses the speciation mechanism to induce niches preserving more feasible Pareto-optimal solutions and adopts an improved environment selection criterion to enhance diversity. The algorithm can not only obtain feasible solutions but also retain more well-distributed feasible Pareto-optimal solutions. Moreover, a set of constrained multimodal multiobjective test functions is developed. All these test functions have multimodal characteristics and contain multiple constraints. Meanwhile, this article proposes a new indicator, which comprehensively considers the feasibility, convergence, and diversity of a solution set. The effectiveness of the proposed method is verified by comparing with the state-of-the-art algorithms on both test functions and real-world location-selection problem.

Handling constrained multiobjective optimization problems (CMOPs) is extremely challenging, since multiple conflicting objectives subject to various constraints require to be simultaneously optimized. To deal with CMOPs, numerous constrained multiobjective evolutionary algorithms (CMOEAs) have been proposed in recent years, and they have achieved promising performance. However, there has been few literature on the systematic review of the related studies currently. This article provides a comprehensive survey for evolutionary constrained multiobjective optimization. We first review a large number of CMOEAs through categorization and analyze their advantages and drawbacks in each category. Then, we summarize the benchmark test problems and investigate the performance of different constraint handling techniques (CHTs) and different algorithms, followed by some emerging and representative applications of CMOEAs. Finally, we discuss some new challenges and point out some directions of the future research in the field of evolutionary constrained multiobjective optimization.

When solving constrained multiobjective optimization problems (CMOPs), the utilization of infeasible solutions significantly affects algorithm’s performance because they not only maintain diversity but also provide promising search directions. In light of this situation, this article proposes a new multitasking-constrained multiobjective optimization (MTCMO) framework, in which a dynamic auxiliary task is created to assist in solving a complex CMOP (the main task) via the knowledge transfer. Moreover, the constraint boundary of the auxiliary task reduces dynamically, so that it keeps a high relatedness with the main task to continuously provide supplementary evolutionary directions. Furthermore, an improved$\epsilon $method is designed for the auxiliary task to utilize diverse high-quality infeasible solutions for breaking through infeasible obstacles in the early stage and approaching the feasible boundary from infeasible regions in the later stage. Besides, a new test function with decision space constraints is designed, where one parameter can be adjusted to control the overlap degree between the constrained Pareto front and the unconstrained Pareto front. This function and the other two modified existing functions are used to analyze the characteristics of MTCMO. Finally, compared with 11 state-of-the-art peer methods, the superior or competitive performance of MTCMO is demonstrated on 54 benchmark functions and two real-world applications.

The evolutionary algorithm recommendation is catching increasing attention when solving practical application problems since different algorithms often perform differently on different problems. To achieve the algorithm recommendation, extracting effective features to accurately characterize the problems is necessary, which is related to the feature extraction problem. So far, most feature extraction methods focus on single-objective optimization problems, and only a few studies are conducted on multiobjective optimization problems and constrained optimization problems, let alone constrained multiobjective optimization problems (CMOPs) that are widely encountered in the real world. To fill the gap, this article proposes an evolution-based constrained multiobjective feature extraction method (ECMOFE), in which the information generated in the evolutionary process is leveraged to form the feature matrix. To be specific, we create two populations to, respectively, optimize constraints and objectives for some generations. Furthermore, two complementary evolutionary operators are used to generate offspring for each population. In the environmental selection, the successful rate of offspring individuals generated by each operator of each population is recorded to form the feature matrix. Then, a dimension reduction method is designed to compress the size of the feature matrix. By the above process, the feature vector that can reflect the global relationship between constraints and objectives and the difficulty of the CMOP is formed. Based on the formed features, several algorithm recommendation methods are built on the basis of classifiers. The results based on multiple metrics show the effectiveness of the proposed ECMOFE.

When solving dynamic multiobjective optimization problems (DMOPs) by evolutionary algorithms, the historical moving directions of some special points along the Pareto front, such as the center and knee points, are widely employed to predict the Pareto-optimal solutions (POSs). However, special points may be impacted by certain individuals with a large direction deviation, and thus, mislead the tracking of dynamic POS. To solve this issue, a correlation-guided layered prediction approach for solving DMOPs is proposed in this article, where multiple prediction models are integrated by considering the correlation of individuals’ moving directions. To be specific, the population is clustered into three subpopulations (i.e., high, mid, and low correlation) by correlation analysis to perform different prediction behaviors. The high correlation subpopulation aims to predict the moving direction via a linear prediction model. The mid correlation subpopulation is devoted to predicting the manifold change of POS by self-adaptively using the direction and length correction models. The diversity preservation is considered by the low correlation subpopulation. While the three subpopulations focus on different optimization tasks, they also cooperate to track the dynamic POS. The comprehensive experimental results on a variety of benchmark test problems demonstrate the superiority of the proposed approach, as compared with some state-of-the-art prediction-based dynamic multiobjective algorithms.

When addressing constrained multiobjective optimization problems (CMOPs) via evolutionary algorithms, various constraints and multiple objectives need to be satisfied and optimized simultaneously, which causes difficulties for the solver. In this article, an evolutionary multitasking (EMT)-based constrained multiobjective optimization (EMCMO) framework is developed to solve CMOPs. In EMCMO, the optimization of a CMOP is transformed into two related tasks: one task is for the original CMOP, and the other task is only for the objectives by ignoring all constraints. The main purpose of the second task is to continuously provide useful knowledge of objectives to the first task, thus facilitating solving the CMOP. Specially, the genes carried by parent individuals or offspring individuals are dynamically regarded as useful knowledge due to the different complementarities of the two tasks. Moreover, the useful knowledge is found by the designed tentative method and transferred to improve the performance of the two tasks. To the best of our knowledge, this is the first attempt to use EMT to solve CMOPs. To verify the performance of EMCMO, an instance of EMCMO is obtained by employing a genetic algorithm as the optimizer. Comprehensive experiments are conducted on four benchmark test suites to verify the effectiveness of knowledge transfer. Furthermore, compared with other state-of-the-art constrained multiobjective optimization algorithms, EMCMO can produce better or at least comparable performance.