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A directed batch growing self-organizing map based niching differential evolution for multimodal optimization problems

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APPLIED SOFT COMPUTING 2025年 172卷

作者： Shankar, Mahesh Ramu, Palaniappan Deb, Kalyanmoy Indian Inst Technol Madras Dept Engn Design Chennai 600036 India Michigan State Univ Dept Elect & Comp Engn E Lansing MI USA

Many real-world optimization problems naturally result in multiple optimal solutions, thereby falling in the class of multimodal optimization problems (MMOPs). A task of finding a plurality of optimal solutions for MMOPs comes under the scope of multimodal optimization algorithms (MMOAs). To solve MMOPs, niching techniques are usually employed by proactively modifying standard evolutionary algorithms (EAs) to form stable subpopulations around multiple niches within their evolving populations. This way, each optimum can germinate and eventually help forma cloud of solutions around each optimum parallely, thereby finding multiple (but a finite number of) optima simultaneously. However, several existing niching techniques suffer from common drawbacks, such as sensitivity with niching parameters or poor performance on high-dimensional problems. An efficient niching technique needs an effective population partitioning method around distinct leading solutions representing each optimum. In this paper, we propose a directed batch growing self- organizing map based niching differential evolution (DBGSOM-NDE). For this purpose, a standard differential evolution (DE) method is divided into two overlapping phases: (i) population-wide search (PS) and (ii) niche- wide search (NS). PS executes neighborhood search around each individual, promoting exploration, while NS explores only the leaders, thus reducing the effect of exploration for a better search intensification around the leaders using a Cauchy-distribution based local search to improve them. We evaluate the role of each operator of the proposed approach DBGSOM-NDE and compare its performance with a number of state-of-the-art niching techniques demonstrating its competitiveness and superiority, especially on high-dimensional and nonlinear problems taken from the existing literature. Finally, a hyper-parametric study is provided demonstrating weak dependence of them to the algorithm's performance.

关键词： multimodal optimization Niching techniques Differential evolution Directed batch growing self-organizing maps

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Memetic Differential Evolution With Adaptive Niching Selection and Diversity-Driven Strategies for multimodal optimization

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2025年第2期9卷 1322-1339页

作者： Feng, Yufeng Sheng, Weiguo Wang, Zidong Xiao, Gang Li, Qi Li, Li Wang, Zuling Hangzhou Normal Univ Dept Comp Sci Hangzhou 311121 Peoples R China Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH England Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Peoples R China Guilin Univ Elect Technol Guangxi Key Lab Trusted Software Guilin 541004 Peoples R China Chongqing Vocat Inst Safety & Technol Dept Network & Informat Secur Chongqing 404121 Peoples R China

Simultaneously identifying a set of optimal solutions within the landscape of multimodal optimization problem presents a significant challenge. In this work, a differential evolution algorithm with adaptive niching selection, diversity-driven exploration and adaptive local search strategies is proposed to tackle the challenge. In the proposed method, an adaptive niching selection strategy is devised to dynamically select appropriate niching methods from a diverse pool to evolve the population. The pool encompasses niching methods with varying search properties and is dynamically updated during evolution. Further, to enhance exploration, a diversity-driven exploration strategy, which leverages redundant individuals from convergence regions to explore the solution space, is introduced. Additionally, an adaptive local search operation, in which the probability of applying local search and corresponding sampling area are dynamically determined based on the potential of solutions as well as the stage of evolution, is developed to fine-tune promising solutions. The effectiveness of proposed method has been demonstrated on 20 test functions from CEC2013 benchmark suite. Experimental results confirm the effectiveness of our method, demonstrating its superiority compared to related algorithms.

关键词： Vectors Space exploration Search problems optimization Genetic algorithms Topology Indexes Hands Convergence Safety Differential evolution multimodal optimization niching method adaptive selection local search diversity

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Adaptive niching differential evolution algorithm with landscape for multimodal optimization

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INFORMATION SCIENCES 2025年 700卷

作者： Zhou, Xinyu Li, Ningzhi Fan, Long Li, Hongwei Cheng, Bailiang Wang, Mingwen Jiangxi Normal Univ Sch Comp & Informat Engn Nanchang 330022 Jiangxi Peoples R China Nanchang Vocat Univ Coll Informat Technol Nanchang 330007 Jiangxi Peoples R China

To solve multimodal optimization problems (MMOPs), niching techniques play an important role by enabling the optimization algorithm to locate as many solutions as possible. Speciation and crowding, as two representative niching techniques, have been widely adopted and exhibit distinct features. Speciation offers the advantage of a rapid convergence speed, while crowding is characterized by strong diversity. To fully leverage the advantages of both techniques, this paper combines speciation and crowding by designing a novel adaptive niching strategy. In this strategy, the population is divided into two parts based on the individuals' fitness values. The part with superior fitness values is assigned speciation, while the one with inferior fitness values is assigned crowding. More importantly, the proportion of the two parts is dynamically set using the fitness landscape analysis technique, allowing problem features to be considered when setting the proportion. To test the performance of our approach, the CEC2013 benchmark functions are used, and 11 related algorithms are included in the performance comparison, including two competition-winning algorithms. Extensive experimental results demonstrate that our approach provides highly competitive performance.

关键词： multimodal optimization Niching technique Fitness distance correlation Differential evolution

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Multiple global peaks big bang-big crunch algorithm for multimodal optimization

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EVOLUTIONARY INTELLIGENCE 2025年第2期18卷 1-22页

作者： Stroppa, Fabio Astar, Ahmet Kadir Has Univ Comp Engn Dept TR-34083 Istanbul Turkiye

The main challenge of multimodal optimization problems is identifying multiple peaks with high accuracy in multidimensional search spaces with irregular landscapes. This work proposes the Multiple Global Peaks Big Bang-Big Crunch (MGP-BBBC) algorithm, which addresses the challenge of multimodal optimization problems by introducing a specialized mechanism for each operator. The algorithm expands the Big Bang-Big Crunch algorithm, a state-of-the-art metaheuristic inspired by the universe's evolution. Specifically, MGP-BBBC groups the best individuals of the population into cluster-based centers of mass and then expands them with a progressively lower disturbance to guarantee convergence. During this process, it (i) applies a distance-based filtering to remove unnecessary elites such that the ones on smaller peaks are not lost, (ii) promotes isolated individuals based on their niche count after clustering, and (iii) balances exploration and exploitation during offspring generation to target specific accuracy levels. Experimental results on twenty multimodal benchmark test functions show that MGP-BBBC generally performs better or competitively with respect to other state-of-the-art multimodal optimizers.

关键词： Big bang-big crunch algorithm (BBBC) Multiple global peaks big bang-big crunch algorithm (MGP-BBBC) Clustering multimodal optimization

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Multi-level particle swarm optimizer for multimodal optimization problems

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INFORMATION SCIENCES 2025年 702卷

作者： Pan, Hao Yuan, Hui Yue, Qiang Ouyang, Haibin Gu, Fangqing Li, Fei Anhui Univ Technol Sch Elect & Informat Engn Maanshan 243002 Peoples R China Anhui Univ Technol Sch Mech Engn Maanshan 243032 Peoples R China Anhui Univ Technol Anhui Prov Key Lab Special Heavy Load Robot Maanshan 243032 Peoples R China Anhui Univ Technol Power Elect & Mot Control Anhui Higher Educ Inst Maanshan 243032 Peoples R China Anhui Univ Technol Key Lab Met Emiss Reduct & Comprehens Utilizat Res Minist Educ Maanshan 243032 Peoples R China Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Peoples R China Guangdong Univ Technol Guangzhou 510006 Guangdong Peoples R China

multimodal optimization problems (MMOPs) involve finding multiple optimal solutions, which is essential in many real-world applications. Key challenges in solving MMOPs include identifying more global optima and improving solution accuracy. To tackle these issues, we propose a multilevel particle swarm optimizer (MLPSO) that utilizes fast density-peak clustering along with three innovative mechanisms. Firstly, a new niching technique based on fast density-peak clustering is introduced to form multiple sub-populations, aiming to discover as many optimal solutions as possible. Secondly, we implement an equilibrium point setting strategy that adjusts based on the current evolutionary state to balance exploration and exploitation. Different sub-populations will use varying parameters during the learning process. Additionally, an exclusion mechanism is designed to prevent multiple sub-populations from converging on the same peak. Lastly, a hierarchical iterative local search is proposed to refine the accuracy of the identified optima. Experimental results on 20 benchmark functions demonstrate that MLPSO performs competitively with leading multimodal optimization algorithms.

关键词： multimodal optimization Multi-level particle swarm optimizer Fast density-peak clustering Hierarchical iterative local search Equilibrium point setting strategy

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Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

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ENGINEERING COMPUTATIONS 2024年第2期41卷 413-437页

作者： Hong, Fangqi Wei, Pengfei Beer, Michael Northwestern Polytech Univ Sch Power & Energy Xian Peoples R China Leibniz Univ Hannover Inst Risk & Reliabil Hannover Germany Univ Liverpool Inst Risk & Uncertainty Liverpool England Tongji Univ Int Joint Res Ctr Engn Reliabil & Stochast Mech Shanghai Peoples R China Tongji Univ Int Joint Res Ctr Resilient Infrastruct Shanghai Peoples R China

PurposeBayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational ***/methodology/approachBy theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive *** superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering ***/valuemultimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.

关键词： Bayesian cubature Adaptive experiment design Acquisition function Parallel computation multimodal optimization

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multimodal optimization Using a Biobjective Differential Evolution Algorithm Enhanced With Mean Distance-Based Selection

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2013年第5期17卷 666-685页

作者： Basak, Aniruddha Das, Swagatam Tan, Kay Chen Carnegie Mellon Univ Dept Elect & Comp Engn Moffett Field CA 94035 USA Indian Stat Inst Elect & Commun Sci Unit Kolkata 700108 India Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore

In contrast to the numerous research works that integrate a niching scheme with an existing single-objective evolutionary algorithm to perform multimodal optimization, a few approaches have recently been taken to recast multimodal optimization as a multiobjective optimization problem to be solved by modified multiobjective evolutionary algorithms. Following this promising avenue of research, we propose a novel biobjective formulation of the multimodal optimization problem and use differential evolution (DE) with nondominated sorting followed by hypervolume measure-based sorting to finally detect a set of solutions corresponding to multiple global and local optima of the function under test. Unlike the two earlier multiobjective approaches (biobjective multipopulation genetic algorithm and niching-based nondominated sorting genetic algorithm II), the proposed multimodal optimization with biobjective DE (MOBiDE) algorithm does not require the actual or estimated gradient of the multimodal function to form its second objective. Performance of MOBiDE is compared with eight state-of-the-art single-objective niching algorithms and two recently developed biobjective niching algorithms using a test suite of 14 basic and 15 composite multimodal problems. Experimental results supported by nonparametric statistical tests suggest that MOBiDE is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.

关键词： Crowding differential evolution (DE) multimodal optimization multiobjective optimization niching nondominated sorting

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multimodal optimization: An effective framework for model calibration

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INFORMATION SCIENCES 2017年 375卷 79-97页

作者： Chica, Manuel Barranquero, Jose Kajdanowicz, Tomasz Damas, Sergio Cordon, Oscar Open Univ Catalonia IN3 Dept Comp Sci Rambla del Poblenou 156 Barcelona 08018 Spain Novelti Novelti Io Madrid 28050 Spain Wroclaw Univ Technol Fac Comp Syst & Management PL-50370 Wroclaw Poland Univ Granada Dept Software Engn E-18071 Granada Spain Univ Granada DECSAI E-18071 Granada Spain Univ Granada CITIC UGR E-18071 Granada Spain

Automated calibration is a crucial stage when validating non-linear dynamic systems. The modeler must control the calibration results and analyze parameter values in an iterative way. In many non-linear models, it is usual to find sets of configuration parameters that may obtain the same model fitting. In these cases, the modeler needs to understand the results' implications and run a sensitivity analysis to check the model validity. This paper presents a framework based on niching genetic algorithms to provide modeler with a set of alternative calibration solutions which also ease the analysis of their parameters, model's response, and sensitivity analysis. The framework is called MOMCA, an integral and interactive solution for model validation which facilitates the implication of decision makers. The core component of MOMCA is its niching genetic algorithm, able to reach various optima in mtiltimodal optimization problems by keeping the necessary diversity. The proposed framework is applied to two different case studies. The first case study is a biological growth model and the second one is a managerial model to improve brand equity. Both applications show the benefits of the framework when providing a set of calibrated models and a way to analyze and perform sensitivity analysis based on the set of solutions. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Model calibration multimodal optimization Genetic algorithms Sensitivity analysis

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multimodal optimization of Edge Server Placement Considering System Response Time

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ACM TRANSACTIONS ON SENSOR NETWORKS 2023年第1期19卷 1-20页

作者： Zhang, Xinglin Zhang, Jinyi Peng, Chaoqun Wang, Xiumin South China Univ Technol Sch Comp Sci & Engn 382 Huandong Rd Guangzhou Guangdong Peoples R China

Mobile edge computing (MEC) deploys computing and storage resources close to mobile devices, enabling resource demanding applications to run on mobile devices with short network latency. In the past few years, large numbers of research works focused on the research hotspots in MEC, such as computation offloading and energy efficiency. However, few researchers have investigated the deployment of edge servers. On the one hand, blindly deploying numerous edge servers will result in a large amount of capital expenditure. On the other hand, the deployment of edge servers is a multimodal problem that should provide decision makers with multiple deployment options to deal with the impact of unmeasured real-world factors. Considering these factors, we study the multimodal optimization problem of edge server placement (MESP) with the goal of minimizing the average system response time in this work. Regarding the difficulty of the MESP problem, we propose a heuristic algorithm that combines particle swarm optimization and niching technology to obtain a set of competitive placement solutions. Extensive experiments over a real-world dataset show that the proposed algorithm can significantly reduce the system response time.

关键词： Mobile edge computing multimodal optimization particle swarm algorithm server placement problem

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multimodal optimization by Means of a Topological Species Conservation Algorithm

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2010年第6期14卷 842-864页

作者： Stoean, Catalin Preuss, Mike Stoean, Ruxandra Dumitrescu, D. Univ Craiova Fac Math & Comp Sci Dept Comp Sci Craiova 200585 Romania Univ Babes Bolyai Dept Comp Sci Cluj Napoca 400084 Romania TU Dortmund Dept Comp Sci D-44221 Dortmund Germany

Any evolutionary technique for multimodal optimization must answer two crucial questions in order to guarantee some success on a given task: How to most unboundedly distinguish between the different attraction basins and how to most accurately safeguard the consequently discovered solutions. This paper thus aims to present a novel technique that integrates the conservation of the best successive local individuals (as in the species conserving genetic algorithm) with a topological subpopulations separation (as in the multinational genetic algorithm) instead of the common but problematic radius-triggered manner. A special treatment for offspring integration, a more rigorous control on the allowed number and uniqueness of the resulting seeds, and a more efficient fitness evaluations budget management further augment a previously suggested naiive combination of the two algorithms. Experiments have been performed on a series of benchmark test functions, including a problem from engineering design. Comparison is primarily conducted to show the significant performance difference to the naiive combination;also the related radius-dependent conserving algorithm is subsequently addressed. Additionally, three more multimodal evolutionary methods, being either conceptually close, competitive as radius-based strategies, or recent state-of-the-art are also taken into account. We detect a clear advantage of three of the six algorithms that, in the case of our method, probably comes from the proper topological separation into subpopulations according to the existing attraction basins, independent of their locations in the function landscape. Additionally, an investigation of the parameter independence of the method as compared to the radius-compelled algorithms is systematically accomplished.

关键词： Evolutionary algorithms function optimization landscape detection multimodal optimization species conservation

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