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Probabilistic Multimodal Optimization

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Metaheuristics for Finding Multiple Solutions

Part of the book series: Natural Computing Series ((NCS))

Abstract

Multimodal optimization, which aims to discover multiple satisfactory solutions simultaneously, has attracted increasing attention from researchers in the evolutionary computation community. With the aid of niching methods, evolutionary algorithms could simultaneously locate multiple satisfactory solutions in a single run. Although many multimodal evolutionary algorithms have been developed, they are confronted with two limitations: (1) in the niching stage, most niching-based multimodal methods need to compute pairwise Euclidean distances between individuals to separate the population into species, which gives rise to a high computational burden; and (2) in the optimization stage, most existing multimodal algorithms may have limitations in exploring the solution space, due to the utilization of traditional individual-based meta-heuristics, which may easily get trapped in local areas. To resolve the above issues, in this chapter, we introduce probabilistic multimodal optimization algorithms by presenting two probability-based frameworks for multimodal optimization. More specifically, we present a probability-based niching framework to accelerate the niching speed and a probability-based optimization framework to promote the optimization efficiency of multimodal algorithms, respectively. In the former, we utilize locality sensitive hashing to project individuals into buckets with probabilities to divide the population into species. Such a framework can be embedded into different niching methods to accelerate the niching speed. In the latter, we take advantage of the probability distribution of individuals to evolve the population along with a novel adaptive local search method. To instantiate these two frameworks, we customize them using two distinct approaches, respectively. More concretely, we embed the former into locally informed particle swarm optimization (LIPS) and neighborhood-based crowding differential evolution (NCDE), and customize the latter utilizing an explicit probability-based algorithm, the estimation of distribution algorithm (EDA), and an implicit probability-based algorithm, the continuous ant colony optimization algorithm (ACO), respectively. The efficiency and effectiveness of these two frameworks are carefully examined on a widely used multimodal benchmark set by means of comparing the associated customized algorithms with state-of-the-art multimodal methods. Lastly, the application of the proposed algorithms on multiple pedestrian detection problems is also presented. Experimentally, our approach is seen to perform competitively with traditional methods in this domain.

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Acknowledgements

This work was supported in part by the Key Project of Science and Technology Innovation 2030 supported by the Ministry of Science and Technology of China (Grant No. 2018AAA0101300), in part by the National Natural Science Foundation of China under Grant 61976093, 62006124, and 61873097, in part by the Science and Technology Plan Project of Guangdong Province 2018B050502006, in part by Guangdong Natural Science Foundation Research Team 2018B030312003, in part by the Natural Science Foundation of Jiangsu Province under Project BK20200811, in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant 20KJB520006 and in part by the Startup Foundation for Introducing Talent of NUIST.

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Authors and Affiliations

  1. School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, China

    Qiang Yang

  2. School of Computer Science and Engineering, South China University of Technology, Guangzhou, China

    Qiang Yang & Wei-Neng Chen

  3. Hanyang University, Seoul, Korea

    Jun Zhang

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  1. Qiang Yang
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  2. Wei-Neng Chen
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Correspondence to Wei-Neng Chen .

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Editors and Affiliations

  1. LIACS, Universiteit Leiden, Leiden, The Netherlands

    Mike Preuss

  2. The Signal Group, Athens, Greece

    Michael G. Epitropakis

  3. Computer Science and Software Engineering, RMIT University, Melbourne, VIC, Australia

    Xiaodong Li

  4. Department of Computer Science, University of Exeter, Exeter, UK

    Jonathan E. Fieldsend

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Yang, Q., Chen, WN., Zhang, J. (2021). Probabilistic Multimodal Optimization. In: Preuss, M., Epitropakis, M.G., Li, X., Fieldsend, J.E. (eds) Metaheuristics for Finding Multiple Solutions. Natural Computing Series. Springer, Cham. https://doi.org/10.1007/978-3-030-79553-5_9

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