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14th International Conference on Swarm Intelligence (ICSI)

作者： Liu, Yue Cheng, Shi Wang, Xueping Shan, Yuyuan Lu, Hui Shaanxi Normal Univ Sch Comp Sci Xian 710119 Shaanxi Peoples R China Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

ISBN: (纸本)9783031366215;9783031366222

Finding more solutions from different Pareto-optimal sets (PSs) in the decision space and maintaining the diversity of solutions at the Pareto front (PF) in the objective space are the two objectives of multimodal multiobjective optimization (MMO). This paper proposes a brain storm optimization algorithm with a non-dominated special crowding distance sorting strategy (BSO-SCD) to ensure a sufficient number of good enough solutions and diversity in both the decision and objective spaces. Based on the brain storm optimization (BSO) algorithm, the BSO-SCD algorithm enhances the ability of diversity maintenance and has three steps. Firstly, k-means clustering divides the population into multiple subpopulations in the decision space to help locate various optimal solutions. Secondly, the non-dominated special crowding distance sorting (SCD) strategy, considering the diversity of decision space and objective space simultaneously, is used to find each subpopulation cluster center and stored in an archive. Finally, the solutions in the archive are selected after the iteration. The performance of the BSO-SCD algorithm and the other five algorithms is verified on 12 MMO benchmark functions. Experimental results show that the BSO-SCD algorithm could find as many equivalent PSs as possible in the decision space and guarantee a good PF distribution in the objective space.

关键词： Brain storm optimization multimodal multiobjective optimization multiobjective optimization multimodal optimization

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Aggregated Partial Hypervolumes - An Overall Indicator for Performance Evaluation of multimodal multiobjective optimization Methods 18th

Aggregated Partial Hypervolumes - An Overall Indicator for P...

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18th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Ahrari, Ali Sarker, Ruhul Coello Coello, Carlos A. Univ New South Wales Sch Syst & Comp Canberra ACT Australia CINVESTAV IPN Dept Computac Mexico City DF Mexico

ISBN: (纸本)9783031700675;9783031700682

multimodal multiobjective optimization (MMMOO) can be perceived as the combination of multiobjective optimization (MOO) and multimodal optimization (MMO). The performance of an MMMOO method should be thus assessed from both perspectives, leading to the prevalence of dual-metric indicators in the existing literature. This study first analyzes the ideal outcome of MMMOO for informed decision-making to determine the prerequisites of a theoretically and practically sound performance indicator. Then, it critically evaluates existing indicators, especially those that intend to measure success from the MMO perspective. Subsequently, it introduces Aggregated Partial Hypervolumes (APHVs) as a novel overall parametric performance indicator that not only addresses the drawbacks of existing ones but can also reflect the relative importance of MMO for the decision-maker. Finally, a few descriptive MMMOO examples are studied to verify that the optimal population according to APHVs matches our understanding of the ideal outcome of MMMOO, taking into account the relative importance of both the MMO and the MOO perspectives.

关键词： Performance indicator multimodal multiobjective optimization Hypervolume

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MMOGA for Solving multimodal multiobjective optimization Problems with Local Pareto Sets

MMOGA for Solving Multimodal Multiobjective Optimization Pro...

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IEEE Congress on Evolutionary Computation (CEC) as part of the IEEE World Congress on Computational Intelligence (IEEE WCCI)

作者： Yue, C. T. Liang, J. J. Suganthan, P. N. Qu, B. Y. Yu, K. J. Liu, S. Zhengzhou Univ Sch Elect Engn Zhengzhou Peoples R China Nanyang Technol Univ Sch Elect Elect Engn Singapore Singapore Zhongyuan Univ Technol Sch Elect & Informat Engn Zhengzhou Peoples R China Henan Prov Peoples Hosp Med Equipment Dept Zhengzhou Peoples R China

ISBN: (纸本)9781728169293

multiobjective optimization problems with multiple equivalent global Pareto solutions or with at least one local Pareto solution are called multimodal multiobjective optimization problems (MMOP). Most of the existing multimodal multiobjective algorithms can only find global Pareto solutions. However, the local Pareto solutions are of great significance when the global ones are impracticable. This paper proposes a multimodal multiobjective Genetic Algorithm (MMOGA) to find both global and local Pareto solutions. In MMOGA, only individuals in the same niche can mate and compete with each other, thus enabling the population to evolve in local areas. Experimental results show that the proposed algorithm can find both global and local Pareto sets of MMOPs.

关键词： multimodal multiobjective optimization local Pareto solution genetic algorithm

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A grid self-adaptive exploration-based algorithm for multimodal multiobjective optimization

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APPLIED SOFT COMPUTING 2024年 166卷

作者： Zou, Juan Yang, Xinjie Deng, Qi Liu, N. Xia, Yizhang Wu, Zeping Xiangtan Univ Hunan Engn Res Ctr Intelligent Syst Optimizat & Se Xiangtan 411105 Peoples R China Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Peoples R China

In multimodal multiobjective optimization, the key is to find as many equivalent Pareto optimal solutions as possible through broad exploration in the decision space. The grid search strategy can achieve quick convergence by guiding the evolution with historical information in each grid while enabling broad exploration. However, inaccurate utilization of information in grids may lead to losing numerous potential solutions, especially on imbalanced problems. In order to resolve this issue, a grid self-adaptive exploration-based algorithm (GSEA) is proposed in this paper. In GSEA, the historical information in the grid is accurately utilized through grid-based self-adaptive exploration and niche clearing methods, which retain a large number of solutions with potential and effectively handle multimodal multiobjective optimization problems (MMOPs). Experimental results show that the proposed algorithm outperforms seven other state-of-the-art multimodal multiobjective evolutionary algorithms (MMEAs) on two types of MMOPs, and the approach can effectively deal with the MMOPs with middle-scale decision variables as memory allows.

关键词： multimodal multiobjective optimization Grid self-adaptive exploration Niching Evolutionary optimization Swarm intelligence

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Differential evolution using improved crowding distance for multimodal multiobjective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2021年 62卷 100849-100849页

作者： Yue, Caitong Suganthan, P. N. Liang, Jing Qu, Boyang Yu, Kunjie Zhu, Yongsheng Yan, Li Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Zhongyuan Univ Technol Sch Elect & Informat Engn Zhengzhou 450007 Peoples R China

In multiobjective optimization, the relationship between decision space and objective space is generally assumed to be a one-to-one mapping, but it is not always the case. In some problems, different variables have the same or similar objective value, which means a many-to-one mapping. In this situation, there is more than one Pareto Set (PS) mapping to the same Pareto Front (PF) and these problems are called multimodal multiobjective problems. This paper proposes a multimodal multiobjective differential evolution algorithm to solve these problems. In the proposed method, the difference vector is generated taking the diversity in both decision and objective space into account. The way to calculate crowding distance is quite different from the others. In the crowding distance calculation process, all the selected individuals are taken into account instead of considering each Pareto rank separately. The crowding distance in decision space is replaced with the weighted sum of Euclidean distances to its neighbors. In the environmental selection process, not all the individuals in top ranks are selected, because some of them may be very crowded. Instead, the potential solutions in the bottom rank are given a chance to evolve. With these operations, the proposed algorithm can maintain multiple PSs of multimodal multiobjective optimization problems and improve the diversity in both decision and objective space. Experimental results show that the proposed method can achieve high comprehensive performance.

关键词： multimodal multiobjective optimization Differential evolution Crowding distance

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A novel grey prediction evolution algorithm for multimodal multiobjective optimization

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2021年 100卷 104173-104173页

作者： Zhou, Ting Hu, Zhongbo Zhou, Quan Yuan, Shixiong Yangtze Univ Sch Informat & Math Jingzhou Hubei Peoples R China

ABSTR A C T In practical applications, solving multimodal multiobjective optimization problems (MMOPs), which have multiple Pareto optimal sets (PSs) in the decision space mapping to the same Pareto front (PF) in the objective space, has great significance for decision makers. The issue of how to maintain diversity in both decision space and objective space remains a key problem for existing multimodal multiobjective evolutionary algorithms. To address this issue, a novel grey prediction evolution algorithm for multimodal multiobjective optimization, termed MMGPE, is proposed in this paper. This is the first time that the grey prediction evolution algorithm (GPE), which is a recently proposed competitive optimization algorithm with strong exploration capability, is improved for MMOPs. These improvements are conducted in the following four aspects: (1) an initialization operator based on particle swarm optimization, (2) an adaptive parameter setting strategy depending on the domain of decision variables of MMOPs, (3) an accelerating convergence mechanism inspired by the niche principle, and (4) an environmental selection operator based on a nondominated sorting mechanism and a special crowding distance approach. The performance of MMGPE is compared with two state-of-the-art multiobjective evolutionary algorithms and four multimodal multiobjective evolutionary algorithms on 11 multimodal multiobjective test functions. MMGPE is also applied to solve a practical problem. The results show the MMGPE?s effectiveness and superiority in achieving the goal of finding multiple PSs while obtaining a well-distributed PF.

关键词： Grey prediction evolution algorithm multimodal multiobjective evolutionary algorithms multimodal multiobjective optimization problems

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A clustering differential evolution algorithm with neighborhood-based dual mutation operator for multimodal multiobjective optimization

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EXPERT SYSTEMS WITH APPLICATIONS 2023年第1期216卷

作者： Zhou, Ting Hu, Zhongbo Su, Qinghua Xiong, Wentao Yangtze Univ Sch Informat & Math Jingzhou Hubei Peoples R China Hubei Engn Univ Sch Math & Stat Xiaogan Hubei Peoples R China

multimodal multiobjective optimization problems (MMOPs) possess multiple equivalent Pareto optimal sets (PSs) corresponding to the same Pareto front (PF). Numerous multimodal multiobjective evolutionary al-gorithms (MMEAs) have been developed to solve MMOPs. However, how to locate multiple high quality equivalent PSs and obtain a uniformly distributed PF simultaneously remains a challenging task. This paper explores a novel multimodal multiobjective differential evolution algorithm, termed MMOcDE, for solving MMOPs. In MMOcDE, a neighborhood-based dual mutation strategy is proposed by developing two novel mutation operators. The two novel mutation operators provide a better tradeoff between exploration and exploitation in locating multiple equivalent PSs. In addition, a clustering-based environmental selection mechanism is designed by integrating an affinity propagation method. The affinity propagation method improves the distribution of solutions in decision and objective spaces, and a harmonic averaged distance is adopted to promote the diversity of a population. The proposed MMO_CDE is compared against state-of-the-art MMEAs on a test suite of CEC 2019 benchmark functions and a map-based practical application. Empirical results validate the superiority of the proposed MMOcDE regarding locating multiple equivalent PSs and obtaining a well-distributed PF.

关键词： Differential evolution multimodal multiobjective optimization problems multimodal multiobjective evolutionary algorithms

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Incorporation of multimodal multiobjective optimization in designing a filter based feature selection technique

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APPLIED SOFT COMPUTING 2021年 98卷 106823-106823页

作者： Jha, Kanchan Saha, Sriparna Indian Inst Technol Dept Comp Sci & Engn Patna Bihar India

Current work reports about the development of a new feature selection technique fusing two concepts, multimodal multiobjective optimization and filter-based feature selection. Use of the concept of multimodality in multiobjective based feature selection helps in generating diverse set of feature subsets on final Pareto front. This approach evaluates the quality of the reduced feature set by utilizing different quality measures. This process of feature selection focuses on achieving two discrete objectives: (1) identification of a large number of Pareto-optimal solutions along with achieving a good distribution in both objective and decision spaces;(2) making a selection of feature subset with minimal redundancy and high correlation with classes. To achieve the second objective, a variety of objective functions based on information-theoretic measures like normalized mutual information and correlation with class attributes are utilized. A multiobjective ring-based Particle swarm optimization (PSO) and non-dominated sorting with special crowding distance are employed to cover the aspects corresponding to the first objective. An evaluation is carried out on seven publicly available datasets concerning different classifiers. The results of these experiments illustrate that the multimodal PSO based feature selection approach finds more feature subsets than its simple PSO counterpart in multiobjective environment. And, the results are also compared with those of existing wrapper based multimodal multiobjective feature selection methods. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Feature selection multimodal multiobjective optimization Particle swarm optimization Normalized mutual information Correlation

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Differential evolution with nearest better clustering for multimodal multiobjective optimization

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APPLIED SOFT COMPUTING 2023年 148卷

作者： Agrawal, Suchitra Tiwari, Aruna Yaduvanshi, Bhaskar Rajak, Prashant Indian Inst Technol Dept Comp Sci & Engn Indore 453552 India

The main aim of multimodal multiobjective optimization algorithms is to find multiple optimal solutions for multiple objectives. The problem with multiple objectives is to maintain the diversity and convergence balance in both decision and objective space. Better performance in one space can lead to deterioration of performance in another space. To effectively perform exploration and exploitation in the decision space, we have proposed a niching technique in our proposed algorithm based on differential evolution to form groups of the population. The niching technique also incorporates a balancing strategy to average the size of niches and a generation strategy to add new elements by finding promising areas. We have also proposed an archive strategy to store the possible optimal solutions that help to explore the decision space and ensure diversity as well as the convergence of the solutions. To show the efficiency of our proposed algorithm, we have performed exhaustive experimentation on the benchmark test suite and compared the results with state-of-the-art algorithms. The experimental results obtained using the proposed algorithm highlight the efficiency and effectiveness of our proposed algorithm in both decision and objective space.

关键词： multimodal multiobjective optimization Differential evolution Balanced nearest better clustering Adaptive generation strategy Archival strategy

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BiOM: A framework for multimodal multiobjective optimization

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INFORMATION SCIENCES 2024年 653卷

作者： Wei, Zhifang Gao, Weifeng Xu, Jingwei Yen, Gary G. Xidian Univ Sch Math & Stat Xian 710126 Peoples R China Xidian Univ Natl Lab Radar Signal Proc Xian 710126 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

multimodal multiobjective evolutionary algorithms are expected to search for not only Pareto optimal front but also the corresponding multiple equivalent Pareto optimal sets. To this end, this paper designs a framework to ameliorate the performance of the existing multiobjective evolutionary algorithms (MOEAs) for solving multimodal multiobjective optimization problems (MMOPs). In this framework, an MMOP is transformed into a bi-objective optimization problem. The first objective is built by either decomposition-based method or indicator-based method in MOEAs to ensure the population convergence. A diversity indicator is another objective used to preserve the population diversity. Based on these two objectives, two diversity selection strategies are developed, which are responsible for balancing the diversity and the convergence in the decision and objective spaces, respectively, at the same time. According to the feedback information in the evolution, our framework adaptively selects one of them to pick out the promising individuals. Four variants based on our framework are built and are evaluated on 22 MMOPs benchmark functions. Six feature selection problems are also employed to test the performance of our framework. The experimental results confirm that our proposed framework performs well in all criteria.

关键词： multimodal multiobjective optimization multiobjective optimization Feature selection Pareto optimal set Pareto front

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