Research On Multi-objective Optimization With Co-evolutionary Algorithms

Multi-objective Optimization Problem(MOP) has been a difficult prob1em and focus for research in field of decision science, There already were a lot of classical methods for solving MOPs before Genetic Algorithms(GAs) were applied to solve MOPs. Classical multi-objective optimization methods have been thoroughly developed,but there are still lots of shortcomings. GAs could hand1e large space of problem and get a couple of solutions in one evolution, and GAs do not need much information about the problem before starting the optimization process. However, there is a irreconcilable conflict between premature convergence and low convergence speed in GAs, so GAs have limits in solving high dimension,multimodal MOPs. Co-evolutionary Algorithm (CEA), a new kind Evolutionary Algorithm which arose in 1990's , can solve the conflict mentioned above perfectly, so using CEA to solve MOPs is the trend in the future.Based on extensive and deep review of literature,a thorough analysis and research on CEAs and MOPs is presented, the main contents are as follows:The development of MOPs and the classical methods for solving MOPs is summarized, and the limits of the classical methods are pointed out. The development of GAs is reviewed, and the basic theories and knowledge of GAs are detailed. Evaluation and comparison of the traditional methods for solving MOPs with the GAs are made, and their inspiration to other algorithms is revealed.The development of the CEAs is summarized, and the thinking of cooperative and competitive CEAs is analyzed. Two CEAs (cooperative and competitive) to solve MOPs are presented, and several improvement strategies are proposed to avoid some problems. These two methods and MOGA are used to solve 6 test functions, and we compare their performance from two indices. It is proved that CEAs have more search ability than traditional GAs.