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Fuzzy clustering-based large-scale multimodal multi-objective differential evolution algorithm

SWARM AND evolutionary computation 2025年 93卷

作者： Wu, Lingyu Zhao, Xinchao Ye, Lingjuan Qiao, Zenglin Zuo, Xingquan Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun Key Lab Math & Informat Networks Minist Educ Beijing Peoples R China Beijing Univ Posts & Telecommun Sch Comp Sci Beijing 100876 Peoples R China

Traditional multi-modal multi-objective problems often have multiple local optima in the decision space, and each local optimum is of great importance. However, real-world multi-modal problems are often largescale problems, and there are few algorithms specifically designed for large-scale multi-modal multi-objective problems. Some proposed algorithms have been tested only on specific problems and are not applicable to solve other specific problems. Based on this problem, this paper proposes a large-scale multi-modal multi- objective differential evolution algorithm called LMMODE, based on fuzzy clustering. The Fuzzy C-means(FCM) algorithm, suitable for high-dimensional data, is employed to divide the search space into multiple subspaces. The multi-stage optimization approach is then utilized to balance the algorithm's performance in the objective space and decision space through different strategies, thereby solving large-scale multi-modal multi-objective problems. Experimental results demonstrate that, compared to state-of-the-art multi-modal and large-scale algorithms, LMMODE is competitive in solving large-scale multi-modal problems.

关键词： Multimodal multi-objective optimization Differential evolution Large-scale optimization Fuzzy C-means evolutionary computation

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Two-Stage Cooperation Multiobjective evolutionary Algorithm Guided by Constraint-Sensitive Variables

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第3期55卷 1450-1463页

作者： Ma, Jun Zhang, Yong Gong, Dun-Wei Gao, Xiao-Zhi Peng, Chao China Univ Min & Technol Artificial Intelligence Res Inst Xuzhou 221008 Peoples R China China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221008 Peoples R China Qingdao Univ Sci & Technol Coll Automat & Elect Engn Qingdao 266061 Shandong Peoples R China Univ Eastern Finland Sch Comp Kuopio 70210 Finland

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.

关键词： Optimization evolutionary computation Convergence Approximation algorithms Search problems Electronic mail Switches Space exploration Cybernetics Chaos Constraints constraint-sensitive variables evolutionary algorithm multiobjective optimization

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Machine Learning-Enabled evolutionary Two-Stage Stochastic Programming

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IEEE TRANSACTIONS ON EMERGING TOPICS IN computationAL INTELLIGENCE 2025年

作者： Pan, Jeng-Shyang Song, Pei-Cheng Chu, Shu-Chuan Snasel, Vaclav Watada, Junzo Nanjing Univ Informat Sci & Technol Sch Artificial Intelligence Nanjing Peoples R China Chaoyang Univ Technol Dept Informat Management Taichung Taiwan Hong Kong Polytech Univ Dept Ind & Syst Engn Hong Kong Peoples R China Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao Peoples R China VSB Tech Univ Ostrava Dept Comp Sci Ostrava Czech Republic Waseda Univ Grad Sch Informat Prod & Syst Kitakyushu Japan

Two-stage Stochastic Programming (2SP) is an effective framework for decision-making and modeling under uncertainty. Some 2SP problems are challenging due to their high dimensionality and nonlinearity. Machine learning can assist in solving 2SP problems by providing data-driven insights and approximations. evolutionary algorithms are more general and effective methods for handling various 2SP problems by exploiting their structures and features. However, there is still a research gap in combining machine learning and evolutionary algorithms for solving 2SP problems. Therefore, this paper proposes for the first time a Machine Learning-enabled evolutionary 2SP framework (MLE2SP), which uses machine learning to construct surrogate-assisted evolutionary optimization frameworks for 2SP. It constructs a novel multi-output 2SP surrogate model that considers scenarios and decision variables of both stages for the first time and proposes a data conversion method to handle the high-dimensional decision variables and scenarios. It also proposes a Machine Learning-enabled Differential Evolution Sampling (MLDES) method to update candidate solutions, which extracts knowledge from dominant candidate solutions to guide the evolutionary direction. Moreover, this work provides open sources of linear and nonlinear two-stage stochastic mixed-integer programming problem instances as benchmark test functions. The effectiveness and generality of the proposed algorithm and framework are verified by the test results on the benchmark test functions and a disaster relief logistics problem, which provide a new research direction for designing general and effective two-stage stochastic programming solving frameworks.

关键词： Stochastic processes Programming Machine learning evolutionary computation Machine learning algorithms Linear programming Random variables Metaheuristics Heuristic algorithms Decision making Stochastic programming machine learning evolutionary computation surrogate model uncertainty

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Finding the Set of Nearly Optimal Solutions of a Multiobjective Optimization Problem

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IEEE TRANSACTIONS ON evolutionary computation 2025年第1期29卷 145-157页

作者： Schutze, Oliver Rodriguez-Fernandez, Angel E. Segura, Carlos Hernandez, Carlos CINVESTAV IPN Comp Sci Dept Mexico City 07360 Mexico Ctr Res Math Comp Sci Dept Guanajuato 36240 Mexico IIMAS UNAM Comp Sci Dept Mexico City 04510 Mexico

evolutionary multiobjective optimization (EMO) is a highly active research field that has attracted many researchers and practitioners over the past three decades. Surprisingly, until now, the goal of almost all EMO algorithms is to compute a suitable finite size representation of the Pareto set/front of a given multiobjective optimization problem or at least a part of it. In other words, the quest is restricted to optimal solutions. In this work, we argue that the entire set of nearly optimal solutions- which includes all optimal ones-is of potential interest for the decision maker as they contain in addition to the optimal solutions alternative realizations or backup solutions. We further make a first effort to reliably compute the set of nearly optimal solutions via EMO algorithms. To this end, we first propose a new set of interest, NQ,E, and analyze its topology. In a next step, we propose an unbounded archiver that aims to capture NQ,E and analyze it with respect to monotonicity and limit behavior. After this, we discuss the related subset selection problem which comes with unbounded archivers leading to four different algorithms. Finally, we numerically investigate the behavior of the archiver and the selection strategies, and present some results when using the archiver as external archiver to three widely used multiobjective evolutionary algorithms indicating the benefit of the new approach.

关键词： evolutionary computation Archiving multiobjective optimization nearly optimal solutions nearly optimal solutions multiobjective optimization nearly optimal solutions

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From Direct to Directional Variable Dependencies-Nonsymmetrical Dependencies Discovery in Real-World and Theoretical Problems

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IEEE TRANSACTIONS ON evolutionary computation 2025年第2期29卷 490-504页

作者： Przewozniczek, Michal Witold Frej, Bartosz Komarnicki, Marcin Michal Wroclaw Univ Sci & Technol Dept Syst & Comp Networks Wroclaw Poland Wroclaw Univ Sci & Technol Fac Pure & Appl Math PL-50370 Wroclaw Poland

The knowledge about variable interactions is frequently employed in state-of-the-art research concerning genetic algorithms (GAs). Whether these interactions are known a priori (gray-box optimization) or are discovered by the optimizer (black-box optimization), they are used for many purposes, including proposing more effective mixing operators. Frequently, the quality of the problem structure decomposition is decisive to the optimizers' effectiveness. However, in gray- and black-box optimization, the dependency between the variables is assumed to be symmetric. This work identifies and defines the nonsymmetrical (directional) variable dependencies. We show that these dependencies may exist (together with symmetrical) in the considered real-world problem, in which we must optimize subsequent variable groups (one after the other) in the appropriate optimization order that is not known by the optimizer. To improve GA's effectiveness in solving the problem of such features, we propose a new linkage learning (LL) technique that can discover symmetrical and nonsymmetrical dependencies (in binary and nonbinary discrete domains) and distinguish them from each other. We show that telling these two types of dependencies from each other may significantly increase the optimizer's effectiveness in solving real-world and theoretical problems with nonsymmetrical dependencies. Finally, we show that using the proposed LL technique does not deteriorate the effectiveness of the state-of-the-art optimizer in solving typical benchmarks containing only symmetrical dependencies.

关键词： Couplings Optimization evolutionary computation Closed box Bayes methods Search problems Benchmark testing Additives Symmetric matrices Standards Empirical linkage learning (ELL) linkage learning (LL) real-world problem optimization

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DANCE: Distributed co-evolutionary design of velocity controllers for swarm intelligence robots in flocking and entrapping tasks

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SWARM AND evolutionary computation 2025年 94卷

作者： Wang, Chen Zhu, Cheng Zhu, Xianqiang Lei, Hongtao Zhang, Weiming Wu, Meng Natl Univ Def Technol Deya Rd Changsha 410073 Hunan Peoples R China Natl Key Lab informat Syst Engn Deya Rd Changsha 410073 Hunan Peoples R China

This study combined evolutionary algorithm and reinforcement learning to propose anew automated design method for generating swarm robots velocity controller model. It alternately evolves heterogeneous swarm and homogeneous swarm through a gene expression programming method that introduces reinforcement learning, and assembles function nodes and leaf nodes into new mathematical formulas during the evolution process. The method enable to realize the effect of swarm robots emerging to perform swarm tasks such as flocking and entrapping. What is more, anew swarm rule was discovered during the evolution process, which is used to realize the flocking of swarm robots at any angle. The experimental results show that the swarm motion controller automatically generated by the model has high task completion efficiency and strong generalization.

关键词： Swarm intelligence Multi-agent systems Robots evolutionary computation Reinforcement learning Gene expression programming

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Text clustering with a hybrid multi-objective optimization approach: The multi-objective firefly differential Jaya Algorithm

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SWARM AND evolutionary computation 2025年 93卷

作者： Naderi, Muhammad Amiri, Maryam Arak Univ Fac Engn Dept Comp Engn Arak *** Iran

The exponential growth of unstructured text data generated by internet users has created an urgent need for efficient organization methods to uncover valuable insights. Text clustering, a widely used data mining approach, often relies on single-objective optimization, which can struggle to deliver optimal results for datasets with diverse clustering criteria. To address these challenges, we propose the Multi-objective Firefly Differential Jaya (MFDJ) algorithm, a novel nature-inspired optimization method designed to enhance text clustering. MFDJ integrates the strengths of NSGA-II, a well-established multi-objective optimization framework, with three complementary algorithms: the Firefly algorithm for swarm intelligence-based optimization, Differential Evolution for robust exploration through mutation, and the Jaya algorithm for parameter-free improvement leveraging both the best and worst solutions. This synergy significantly enhances the algorithm's ability to balance exploration and exploitation, yielding superior clustering performance. We evaluated MFDJ on eight benchmark text datasets, where it demonstrated consistent superiority over state-of-the-art methods, including NSGA-II and MOMDE. On average, MFDJ achieved a 67.89% improvement in F-measure over NSGA-II and a 5.87% improvement over MOMDE, while also exhibiting better convergence properties for the majority of datasets. These results underscore the capability of MFDJ to generate high-quality clusters, making it a versatile tool for tackling complex text clustering and broader optimization challenges.

关键词： evolutionary computation Text clustering Multi-objective optimization Optimization algorithms

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Leveraging Grammarware for Active Video Game Development

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APPLIED SCIENCES-BASEL 2025年第8期15卷 4253-4253页

作者： Crepinsek, Matej Kosar, Tomaz Moravec, Matej Ravber, Miha Mernik, Marjan Univ Maribor Fac Elect Engn & Comp Sci Koroska Cesta 46 Maribor 2000 Slovenia

This paper presents a grammarware-based approach to developing active video games (AVGs) for sensor-driven training systems. The GCGame domain-specific language (DSL) is introduced to define game logic, sensor interactions, and timing behavior formally. This approach ensures cross-platform consistency, supports real-time configurability, and simplifies the integration of optimization and visualization tools. The presented system, called GCBLE, serves as a case study, demonstrating how grammarware enhances modularity, maintainability, and adaptability in real-world physical interaction applications. The results highlight the potential of a DSL-driven design to bridge the gap between developers and domain experts in embedded interactive systems.

关键词： active video games grammarware internet of things DSL procedural level generation evolutionary computation game controllers

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Micro Many-Objective evolutionary Algorithm With Knowledge Transfer

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IEEE TRANSACTIONS ON EMERGING TOPICS IN computationAL INTELLIGENCE 2025年第1期9卷 43-56页

作者： Peng, Hu Luo, Zhongtian Fang, Tian Zhang, Qingfu Jiujiang Univ Sch Comp & Big Data Sci Jiujiang 332005 Peoples R China Jiujiang Key Lab Digital Technol Jiujiang 332005 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong 999077 Peoples R China

computational effectiveness and limited resources in evolutionary algorithms are interdependently handled during the working of low-power microprocessors for real-world problems, particularly in many-objective evolutionary algorithms (MaOEAs). In this respect, the balance between them will be broken by evolutionary algorithms with a normal-sized population, but which doesn't include a micro population. To tackle this issue, this paper proposes a micro many-objective evolutionary algorithm with knowledge transfer (mu MaOEA). To address the oversight that knowledge is often not considered enough between niches, the knowledge-transfer strategy is proposed to bolster each unoptimized niche through optimizing adjacent niches, which enables niches to generate better individuals. Meanwhile, a two-stage mechanism based on fuzzy logic is designed to settle the conflict between convergence and diversity in many-objective optimization problems. Through efficient fuzzy logic decision-making, the mechanism maintains different properties of the population at different stages. Different MaOEAs and micro multi-objective evolutionary algorithms were compared on benchmark test problems DTLZ, MaF, and WFG, and the results showed that mu MaOEA has an excellent performance. In addition, it also conducted simulation on two real-world problems, MPDMP and MLDMP, based on a low-power microprocessor. The results indicated the applicability of mu MaOEA for low-power microprocessor optimization.

关键词： Optimization evolutionary computation Knowledge transfer Vectors Convergence Microprocessors Fuzzy logic Micro many-objective evolutionary algorithm many-objective optimization problems knowledge transfer low-power microprocessors

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Multi-objective genetic programming based on decomposition for feature learning in image classification

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SWARM AND evolutionary computation 2025年 94卷

作者： Zhang, Tuo Bi, Ying Liang, Jing Xue, Bing Zhang, Mengjie Zhengzhou Univ Sch Elect & Informat Engn 100 KeXue Rd Zhengzhou 450001 Henan Peoples R China State Key Lab Intelligent Agr Power Equipment 39 Xiyuan Rd Luoyang 471039 Henan Peoples R China Henan Inst Technol Sch Elect Engn & Automat 699 Pingyuan Rd Xinxiang 453003 Henan Peoples R China Victoria Univ Wellington Ctr Data Sci & Artificial Intelligence Sch Engn & Comp Sci POB 600 Wellington 6140 New Zealand

Image classification presents a challenge due to its high dimensionality and extensive variations. Feature learning is a powerful method in addressing this challenge, constituting a multi-objective problem aimed at maximizing classification accuracy and minimizing the number of learned features. A few multi-objective genetic programming (MOGP) methods have been proposed to optimize these two objectives, simultaneously. However, existing MOGP methods ignore the characteristics of feature learning tasks. Therefore, this work proposes a decomposition-based MOGP approach with a global replacement strategy for feature learning in data-efficient image classification. To handle the different value ranges of the two objectives, a transformation function is designed to uniform the range of the number of learned features. In addition, a preference-based decomposition strategy is proposed to address the preference for the objective of classification accuracy. The proposed approach is compared with existing MOGP methods for feature learning on five different image classification datasets with different numbers of training images. The experimental results demonstrate the effectiveness of the proposed approach by achieving better HVs than or comparable to the existing MOGP methods in at least 13 out of 20 cases and classification accuracy significantly better than a popular neural architecture search method in all cases.

关键词： Genetic programming Multi-objective optimization Feature learning Image classification evolutionary computation

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