Probabilistic Multimodal Optimization Algorithm Based on the Buffon Distance in Noisy Environment

被引：0
作者：
Wang X. [1 ,2 ]
Wang Y.-M. [1 ]
Shi X.-L. [1 ]
Gao L. [1 ]
Li P. [1 ]
机构：
[1] School of Information Science and Engineering, Yunnan University, Kunming
[2] School of Electrical and Information Engineering, Yunnan Minzu University, Kunming
来源：
Zidonghua Xuebao/Acta Automatica Sinica | 2021年 / 47卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Buffon distance; Multimodal optimization; Noisy environment; Probabilistic;
D O I：
10.16383/j.aas.c190474
中图分类号：
学科分类号：
摘要：
To solve the problem of multiple extremum points optimization in noisy environment, a probabilistic multimodal optimization algorithm based on the Buffon distance (PMB) is proposed in this paper. Based on the principle of Buffon needles, the concepts of Buffon distance and resolution of extreme value under noisy environment are put forward. The theoretical derivation proves that the relationship between peak detection rate of PMB algorithm and Buffon distance conforms to a probabilistic relation. In global scope, the search space is divided by Buffon distance for diversity maintenance. The improved Fibonacci method is used in local search to reduce the probability of falling into the local optimum caused by noise. Based on 34 test functions, experiments are carried out from four aspects, including probabilistic property verification, analysis of influencing factors of optimization results, multiple extremum points optimization and multidimensional optimization. It is proved that the relationship of Buffon distance and peak detection rate of PMB algorithm is in line with the deduced probabilistic relationship. Compared with the improved bat algorithm and particle swarm optimization (PSO), PMB algorithm can locate extremum points of multimodal function by a steady probability in noise environment, and gain more extremum points accurately. Thus, the correctness of PMB algorithm principle and probabilistic performance of global optimization under noise condition are proved, which has theoretical and practical significance. Copyright © 2021 Acta Automatica Sinica. All rights reserved.
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页码：2691 / 2714
页数：23
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