Large-scale multi-objective optimization problems (LSMOPs) remain challenging for existingenhanced-search evolutionary algorithms in high-dimensional decision spaces. In this line ofresearch, two recurring limitations remain insufficiently addressed: directional concentration in early-stage direction-guided sampling, where highly correlated search directions narrow decision-space overage; and fixed-structure bias in later-stage search, where fixed population structures cannot adapt exploration–exploitation allocation across evolutionary stages, resulting in inefficient search coordination. To address these issues, this paper proposes LMOEA-BD, a two-stage evolutionary framework for large-scale multi-objective optimization. In the first stage, a distribution-aware boundary–directional hybrid sampling strategy is developed to mitigate directional concentration by complementing conventional directional sampling with distribution-aware boundary-guided search. A fuzzy search mechanism is further incorporated to enrich candidate diversity and strengthen early exploration. In the second stage, an adaptive dual-population search strategy is introduced to alleviate fixed-structure bias. The population is dynamically partitioned into exploration and exploitation subpopulations according to the current population state, and an asymmetric interaction mechanism is designed to coordinate information exchange between them. In this mechanism, the exploitation subpopulation provides convergence guidance to exploration, while the exploration subpopulation supplies diverse high-quality candidates to exploitation. By coupling early-stage coverage expansion with late-stage coordinated search, LMOEA-BD improves the balance between preserving diversity and enhancing convergence. Experimental studies on the LSMOP benchmark suite show that the proposed framework is competitive with several state-of-the-art algorithms in terms of both convergence and diversity.

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 article 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 article 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.

The multimodal multi-objective path planning problem aims to identify a set of equivalent Pareto-optimal routes between a given start and end points that simultaneously minimize traffic congestion, the number of intersections, and path length. This problem is particularly important for handling emergency traffic incidents and disaster relief scenarios. However, existing algorithms generally struggle to maintain the complete set of equivalent optimal paths. To overcome this challenge, a path similarity driven multimodal multi-objective evolutionary algorithm (MMOEA) is proposed for path planning. The algorithm measures the dissimilarity among candidate paths in the decision space to effectively identify and preserve promising multimodal solutions. Extensive comparisons with four representative approaches on the IEEE CEC 2021 multimodal path planning benchmark verify that the proposed method exhibits superior performance in both detecting and maintaining multiple equivalent solutions.

As the continuous deepening of low-carbon emission reduction policies, the manufacturing industries urgently need sensible energy-saving scheduling schemes to achieve the balance between improving production efficiency and reducing energy consumption. In energy-saving scheduling, reasonable machine states-switching is a key point to achieve expected goals, i.e., whether the machines need to switch speed between different operations, and whether the machines need to add extra setup time between different jobs. Regarding this matter, this work proposes a novel machine multi states-based energy saving flexible job scheduling problem (EFJSP-M), which simultaneously takes into account machine multi speeds and setup time. To address the proposed EFJSP-M, a kind of discrete differential evolution particle swarm optimization algorithm (D-DEPSO) is designed. In specific, D-DEPSO includes a hybrid initialization strategy to improve the initial population performance, an updating mechanism embedded with differential evolution operators to enhance population diversity, and a critical path variable neighborhood search strategy to expand the solution space. At last, based on datasets DPs and MKs, the experiment results compared with five state-of-the-art algorithms demonstrate the feasible of EFJSP-M and the superior of D-DEPSO.

A novel knee solution-based membrane-inspired evolutionary algorithm (Knee-MOMTMIEA) is proposed to solve multi-objective multi-task optimization problems. The algorithm integrates hierarchical membrane structures with a knee solution-based information transfer mechanism to enable efficient and adaptive knowledge sharing among tasks. By utilizing knee solutions as representative individuals, the approach enhances convergence and solution quality. Comprehensive experiments on the classical MOMTO test suite validate the algorithms effectiveness, demonstrating that Knee-MOMTMIEA consistently outperforms state-of-the-art multi-task optimization algorithms. This work represents a significant advancement in integrating membrane computing with evolutionary multitasking, offering an efficient framework for solving MOMTO problems.

RNA secondary structure plays a crucial role in regulating the biological functions of non-coding RNAs, particularly when pseudoknots are involved. However, accurate prediction of RNA secondary structures with pseudoknots remains a computationally challenging problem due to its NP-complete nature and the limitations of existing deterministic and heuristic algorithms. In this study, we propose NSGA-II4RNA, a multi-objective evolutionary algorithm that formulates the prediction task as a bi-objective optimization problem. The algorithm simultaneously maximizes the number of base pairs and minimizes the number of stems to balance structural stability and compactness. A candidate stem pool is constructed under minimal thermodynamic constraints, and non-dominated sorting with crowding distance selection is applied to evolve diverse RNA structures toward the Pareto front. Extensive experiments conducted on benchmark sequences from the PseudoBase database demonstrate that the proposed method outperforms widely used tools, including RNAfold, RNAstructure, and IPknot, particularly in sensitivity and F-measure. Notably, NSGA-II4RNA produces valid predictions for all test cases, including complex pseudoknotted structures that baseline methods fail to process. These results confirm the algorithm’s robustness, applicability, and effectiveness in handling diverse RNA sequences.

Due to their exceptional programmability, DNA molecules are widely employed in the design of molecular circuits for applications such as DNA computing, DNA storage and cancer diagnosis and treatment. The quality of DNA sequences directly determines the reliability of these molecular circuits. However, existing DNA encoding algorithms suffer from limitations such as reliance on Hamming distance and conflicts among multiple objectives, resulting in insufficient stability of the generated sequences. To address these issues, this paper proposes a thermodynamics-based multi-objective evolutionary optimisation algorithm (TEMOA). The core innovations of the proposed algorithm are as follows: First, a thermodynamics-based DNA encoding modelling strategy (TDEMS) is introduced, which simplifies the encoding process and significantly improves the sequence quality by incorporating thermodynamic stability constraints. Second, two diversity optimisation strategies-the diversity assessment strategy (DAS) and the front equalisation nondominated sorting (FENS) strategy-are designed to enhance the algorithm's global search capability. Finally, a flexible fitness function design is incorporated to accommodate diverse user requirements. Experimental results demonstrate that TEMOA is more effective than state-of-the-art methods on challenging multi-objective optimisation problems, whereas the DNA sequences generated by TEMOA exhibit greater reliability compared to those produced by traditional DNA encoding algorithms.

When using evolutionary algorithms to handle constrained multi-objective optimization problems (CMOPs), it is of significance to balance objective optimization and constraints satisfaction, which poses a severe challenge for solvers. As a remedy for this issue, this paper proposes a multi-population evolutionary algorithm based on strong coevolution for CMOPs. Specifically, the proposed method consists of one main population and two auxiliary populations. The main population takes constraints into account to find feasible Pareto optimal solutions to guarantee the feasibility. The first auxiliary population is used to preserve solutions with superior objective function values, which is beneficial to break through infeasible barriers. Meanwhile, a mating selection strategy is designed to coordinate the interaction between main population and the first auxiliary population. Furthermore, the second auxiliary population evolve towards CPF from the infeasible sides by employing the improved method, aiming to provide some promising search directions. Similarly, another mating selection strategy is designed to coordinate the information exchange between the main population and the second auxiliary one. The effectiveness of proposed algorithm is demonstrated on 47 benchmark CMOPs compared with four state-of-the-art methods.

Space manipulator is regarded as one of the technologies with the greatest potential in various on-orbit service missions. By leveraging the fully actuated system approach (FASA) and neural network (NN), this paper explores the trajectory tracking control problem of space manipulator with the dynamical model error and external disturbance. The designed controller consists of three parts: the FASA-based part and two radial basis function NN (RBFNN) auxiliary inputs, the FASA-based part provides the desired eigenstructure and the global asymptotic stability for the nominal error system. It solves the problem that the trajectory tracking effect of space manipulator is poor under the working conditions of model error and external disturbance. This paper adopts a combination of offline training and online learning to comprehensively deal with uncertainties. By leveraging particle swarm optimization (PSO) method, we utilize abundant offline data to train the first RBFNN so as to approximate the inherent model error, and adopt an online adaptive learning strategy to update the weight of the second RBFNN. Based on Lyapunov's direct method, stability analysis validates that the tracking error and the estimation error of RBFNN weight would finally converge to a small neighborhoods about the origin. Finally, simulation results with a planar free-flying space manipulator show that the proposed controller demonstrates more rapid convergence and more accurate tracking precision in contrast to the classical adaptive RBFNN controller.

DNA computing is an emerging computational model that has garnered significant attention due to its distinctive advantages at the molecular biological level. Since it was introduced by Adelman in 1994, this field has made remarkable progress in solving NP-complete problems, enhancing information security, encrypting images, controlling diseases, and advancing nanotechnology. A key challenge in DNA computing is the design of DNA coding, which aims to minimize nonspecific hybridization and enhance computational reliability. The DNA coding design is a classical combinatorial optimization problem focused on generating high-quality DNA sequences that meet specific constraints, including distance, thermodynamics, secondary structure, and sequence requirements. This paper comprehensively examines the advances in DNA coding design, highlighting mathematical models, counting theory, and commonly used DNA coding methods. These methods include the template method, multi-objective evolutionary methods, and implicit enumeration techniques.

DNA sequence design aims to design a set of high-quality DNA molecules, which need to satisfy the thermodynamic constraint, similarity constraint, H-Measure constraint and other conflicting objective functions. Therefore DNA sequence design is a typical multi-objective optimization problem. High-quality DNA molecules can effectively prevent non-specific hybridization, undesired secondary structures, and unstable chemical properties during DNA computing, ensuring the reliability and validity of DNA computing. The main deficiency of the existing algorithms is that they may frequently fall into the local optimum. To address this problem, a dual-sorting based constrained multi-objective evolutionary algorithm (DS-CMOEA) is proposed in this paper. DS-CMOEA presents an evaluation index Balance to guide the algorithm to select the solution with similarity and H-Measure equilibrium, and proposes a new fitness function to dynamically adjust the direction of population evolution to avoid the algorithm getting trapped in local optimum. The experimental results indicate that DS-CMOEA exhibits strong global search capability and produces high-quality DNA sequences that outperform those generated by other comparative algorithms.

When solving dynamic multimodal optimization problems (DMMOPs) with evolutionary algorithms, researchers often respond to environment change by designing dynamic response mechanisms, and the use of information from the historical environment greatly affects the performance of the mechanisms. However, existing research tends to find connections between environments only from the perspective of decision space or objective space, which leads to underutilization of historical information. To solve these issues, a dual-space history information-driven dynamic multimodal evolutionary algorithm is proposed in this paper. Specifically, the algorithm identifies the similar historical environments for the new environment based on the similarity between the decision space and the objective space simultaneously, and migrates the approximate global optimal solutions found in these similar environments to the new environment. These individuals are utilized to generate a partial initial population, which is focused on convergence. Furthermore, the algorithm improves the performance of the random reinitialization strategy based on the information in the most neighboring environment. The excellent individuals from that environment are utilized to assist in generating the remaining initial individuals, which balances the diversity and convergence of the population. The effectiveness of proposed algorithm is demonstrated on 24 benchmark DMMOPs compared with five state-of-the-art methods.

This article investigates the vehicle routing problem with time windows (VRPTW) in logistics route optimization. The VRPTW is modeled as a multi-objective optimization problem with preference relationships. To solve this problem, a hybrid neighborhood operation-based artificial bee colony (ABC-RI) algorithm is proposed. To enhance the efficiency of the algorithm, a preprocessing method based on customer information is introduced to refine the initial population. Furthermore, a path reconstruction strategy is proposed to improve the accuracy of the solution. This strategy generates better replacement solution by retaining part of the original paths from discarded solutions. In addition, the algorithm incorporates a hybrid neighborhood operation based on removal and insertion operators to strengthen the exploration capability of the decision space. Finally, the proposed algorithm is tested on the Solomon benchmark instances and compared with five state-of-the-art algorithms. The experimental results demonstrate the effectiveness of the ABC-RI algorithm.

Multi-objective multi-point shortest path planning problems are commonly encountered in real-world applications. Numerous path planning algorithms have been proposed to accommodate different model assumptions. However, most existing algorithms can only identify a subset of the Pareto optimal paths and overlook equivalent Pareto optimal paths. Relying solely on a subset of Pareto optimal solutions is insufficient to effectively respond to unforeseeable road eventualities in the real-world traffic environment. In this paper, multi-objective multi-point shortest path planning problem is modeled as a multimodal multi-objective optimization problem with necessary points constrains. A multimodal multi-objective evolutionary algorithm using constraint dominance principle-based path comparison strategy and path similarity-based multimodal solutions selection strategy is proposed to address this problem. The proposed constraint dominance principle-based path comparison strategy can effectively navigate through large infeasible regions by relaxing necessary point constraints, thereby obtaining a true constrained Pareto front. The proposed path similarity-based multimodal solutions selection strategy can effectively balance the distribution of solutions in the decision space, thereby preserving multiple equivalent optimal solutions. The proposed algorithm is compared with five state-of-the-art path planning algorithms from the benchmark test suite derived from the 2021 IEEE CEC path planning competition, where city maps are adapted from real transportation networks in Chinese cities, in our experiments. The exceptional performance is demonstrated through thirty independent runs, yielding experimental results that showcase the superiority of the proposed algorithm on the test problem set. This superior performance highlights the potential for designing more resilient path planners suitable for scenarios affected by unpredictable road eventualities.

Multi-task multi-objective optimization problems need to consider the algorithm's convergence and the population's diversity. The information transfer of decision variables with different characteristics may harm the effect of knowledge reuse. This paper proposes a novel hybrid multi-objective multifactorial memetic algorithm to address this issue. The proposed variable classification method will classify decision variables into convergence-related and diversity-related decision variables. Only the same type of decision variables in the source and target tasks can transfer information to avoid negative transfer. Different evolutionary operators are adopted according to the characteristics of decision variables during individual recombination. In addition, the proposed algorithm hybridizes the immune algorithm as the global evolutionary operator and the evolutionary gradient search algorithm as the local search operator into the multifactorial framework to enhance the searching ability. Finally, the proposed algorithm is compared with the state-of-the-art multi-objective evolutionary multitasking algorithms. The results of the experiments show that the proposed algorithm can achieve promising performance on the classical and complex multi-task multi-objective benchmark test suites.

The crux of solving constrained multi-objective optimization problems (CMOPs) lies in balancing the interplay between constraints, convergence, and diversity. However, the relationship among these three elements is intricately complex, altering one can inadvertently lead the other two towards undesirable outcomes, making the constrained multi-objective problem very challenging. To address this, this paper proposes a novel two-stage multi-objective evolutionary algorithm based on decomposition (MOEA/D), TCBCMO, designed for addressing constrained multi-objective optimization problems (CMOPs) through constraint classification. The algorithm employs MOEA/D in the first stage to identify the unconstrained Pareto front (UPF), followed by a new constraint handling technique (CHT) in the second stage that classifies constraints and dominance relations, facilitating the transition to the constrained Pareto front (CPF). In addition, an adaptive stage-switching method is proposed to retain more genetically good individuals during population iterations and improve algorithmic stability. Lastly, we validate the effectiveness of TCBCMO in benchmark tests of CMOPs, where the evaluated performance demonstrates superior results on most of the test problems compared to the other six related algorithms.

In recent years, numerous efficient and effective multimodal multiobjective evolutionary algorithms (MMOEAs) have been developed to search for multiple equivalent sets of Pareto optimal solutions simultaneously. However, some of the MMOEAs prefer convergent individuals over diversified individuals to construct the mating pool, and the individuals with slightly better decision space distribution may be replaced by significantly better objective space distribution. Therefore, the diversity in the decision space may become deteriorated, in spite of the decision and objective diversities have been taken into account simultaneously in most MMOEAs. Because the Pareto optimal subsets may have various shapes and locations in the decision space, it is very difficult to drive the individuals converged to every Pareto subregion with a uniform density. Some of the Pareto subregions may be overly crowded, while others are rather sparsely distributed. Consequently, many existing MMOEAs obtain Pareto subregions with imbalanced density. In this article, we present a two-stage double niched evolution strategy, namely DN-MMOES, to search for the equivalent global Pareto optimal solutions which can address the above challenges effectively and efficiently. The proposed DN-MMOES solves the multimodal multiobjective optimization problem (MMOP) in two stages. The first stage adopts the niching strategy in the decision space, while the second stage adapts double niching strategy in both spaces. Moreover, an effective decision density self-adaptive strategy is designed for improving the imbalanced decision space density. The proposed algorithm is compared against eight state-of-the-art MMOEAs. The inverted generational distance union (IGDunion) performance indicator is proposed to fairly compare two competing MMOEAs as a whole. The experimental results show that DN-MMOES provides a better performance to search for the complete Pareto Subsets and Pareto Front on IDMP and CEC 2019 MMOPs test suite.

In recent years, numerous efficient many-objective optimization evolutionary algorithms have been proposed to find well-converged and well-distributed nondominated optimal solutions. However, their scalability performance may deteriorate drastically to solve large-scale many-objective optimization problems (LSMaOPs). Encountering high-dimensional solution space with more than 100 decision variables, some of them may lose diversity and trap into local optima, while others may achieve poor convergence performance. This article proposes a multipopulation-based differential evolution algorithm, called LSMaODE, which can solve LSMaOPs efficiently and effectively. In order to exploit and explore the exponential decision space, the proposed algorithm divides the population into two groups of subpopulations, which are optimized with different strategies. First, the randomized coordinate descent technique is applied to 10% of individuals to exploit the decision variables independently. This subpopulation maintains diversity in the decision space to avoid premature convergence into local optimum. Second, the remaining 90% of individuals are optimized with the nondominated guided random interpolation strategy, which interpolates individual among three nondominated solutions randomly. The strategy can guide the population convergent toward the nondominated solutions quickly, meanwhile, maintain good distribution in objective space. Finally, the proposed LSMaODE is evaluated on the LSMOP test suites from the scalability in both decision and objective dimensions. The performance is compared against five state-of-the-art large-scale many-objective evolutionary algorithms. The experimental results show that LSMaODE provides highly competitive performance.

A research about the path planning problem has been popular topic nowadays and some effective algorithms have been developed to solve this kind of problem. However, the existing algorithms to solve the path problem can only find a single optimal path, cannot satisfactorily find multiple groups of optimal solutions at the same time, and it is very necessary to propose as many solutions as possible. So this paper carries out a research on the Multi-modal Multi-Objective Path Planning (MMOPP), the objective is to find all sets of Pareto optimal path solutions from the start point to the end point in a grid map. This paper proposes a multi-modal multi-objective ant colony path planning optimization algorithm based on matrix preprocessing technology and Dijkstra algorithm (MD-ACO). Firstly, a new method of storing maps that reduces the size of the map and reduces the size of the decision space has been proposed in this paper. Secondly, using the characteristics of the Dijkstra algorithm that can quickly find the optimal path, generate an initial feasible solution about the problem, and improve the problem that the initial pheromone of ant colony algorithm is insufficient and searching for solutions is slow. Thirdly, a reasonable threshold is set for the pheromone to avoid algorithm getting stuck in local optimal solution. Finally, the algorithm is tested on the MMOPP test sets to evaluate the performance of the algorithm, and the results show that MD-ACO algorithm can solve MMOPP and get the optimal solution set.

Due to the excessive number of objective functions in DNA coding problem, there are dominant impedance between solutions which makes it difficult to evaluate the solutions and the algorithm is hard to converge. And traditional multi-objective evolutionary algorithms tend to fall into premature convergence when dealing with DNA coding problems. We proposed an Improved Nondominated Sorting Genetic Algorithm II with Constraint (ICNSAG-II) to deal with these problem. Firstly, the DNA coding problem and its 6 coding constraints are introduced. Secondly, the constraint function and Block operator are used to reduce the dimensionality of the DNA coding problem, so that the objective function is reduced to two, which make it easy to optimize using multi-objective evolutionary algorithms. Finally, by comparing with the sequences generated by the comparative algorithm, it was verified that the DNA sequences generated by ICNSGA-II have good chemical stability and are able to prevent the of unexpected secondary structures and non-specific hybridization reactions.