A partition-based convergence framework for population-based optimization algorithms

• Published in: Information sciences Vol. 627; pp. 169 - 188
• Main Authors: Li, Xinxin, Hua, Shuai, Liu, Qunfeng, Li, Yun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2023
• Subjects: Global convergence; Global optimization; Partition-based optimization; Population-based optimization; Global optimization; Global convergence; Population-based optimization; Partition-based optimization
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2023.01.085

[Display omitted] •A framework is proposed for population-based optimization algorithms’ convergence.•DIRECT’s partition and population evolutions are repeated in this framework.•The global convergence of the framework is proved.•Framework is applied successfully on three population-based optimization algorithms. Population-based optimization algorithms, such as genetic algorithm and particle swarm optimization, have become a class of important algorithms for solving global optimization problems. However, there is an issue that the global convergence is often absent for most of them. This paper proposes a partition-based convergence framework for population-based optimization algorithms to solve this troubling problem. In this framework, regular partitions and evolutions of populations are implemented alternatively. Specifically, the initial population is generated from a regular partition on the search space; after several generations of evolution of the population, the evolution result is returned to join in the regular partition again, and a new population is generated. Repeat such progress until some stop condition is satisfied. Global convergence is guaranteed for the framework. Then this convergence framework is applied to particle swarm optimization, differential evolution, and genetic algorithm. The modified algorithms are globally convergent and perform better than the original version.