Do search and selection operators play important roles in Multi-objective Evolutionary Algorithms: A case study

• Published in: Wuhan University journal of natural sciences 2003, Vol.8 (1), p.195-201
• Main Authors: Zhen-yu, Yan, Li-shan, Kang, Guang-ming, Lin, Mei, He
• Format: Article
• Language: English
• Subjects: Algorithms; Competition; Convergence; Evolutionary algorithms; Genetic algorithms; Markov chains; Multiple objective analysis; Operators; Pareto optimization; Searching; Traveling salesman problem
• ISSN: 1007-1202; 1993-4998
• DOI: 10.1007/BF02899478

Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.