A Comprehensive Review Analysis on PSO and GA Techniques for Mathematical Programming Problems

Abstract

AbstractMathematical programming problems (MPPs) having unique mathematical format usually treated as hard problems are important optimization problems. On the other hand, particle swarm optimization (PSO) and genetic algorithm (GA) are important optimization approaches used in solving complex optimization problems. PSO and GA are nature-inspired techniques based on the social behavior of species and operations of human chromosomes, respectively. During past decades, PSO, GA, and their hybrid techniques were extensively used in solving different types of mathematical programming problems. But there is a lack of comprehensive review analysis on PSO, GA, and associated hybrid techniques for solving various types of mathematical programming problems. In this article, we present a systematic detailed review on these techniques in context of solving mathematical programming problems along with comprehensive review analysis. A systematic review procedure has been used for analysis of sixty-eight articles of reputed databases like Thomson Reuters, Web of Science, Scopus, and IEEE. The research gaps and future research scope for the researcher who inclines to solve different types of mathematical programming problems with these techniques are also identified. Relevance of the work: Mathematical programming problems (e.g., linear programming problem (LPP), NLPP, MOPP, etc.) are important optimization problems in which many types of real-world problems are formulated. On other hand, PSO and GA are prominent natured-inspired techniques used to solve complex optimization problems. This article presents comprehensive review analysis on PSO and GA in context of solving different types of mathematical programming problems. This review work also narrates the unique linkage between GA–PSO techniques and mathematical programming problems. This systematic and in-depth review analysis will be useful to the researchers and scientists working in the related areas of mathematical programming and natured-inspired optimization techniques to pursue carrying out further research in these areas.KeywordsParticle swarm optimization (PSO)Genetic algorithm (GA)Hybrid of PSO and GALinear and nonlinear programming problem