Researches On Strategies To Keep Diversity In Multi Objective Genetic Algorithms

Since a group of Pareto trade-off solutions can be obtained by multi objective genetic algorithm(MOGA)in a single run, many researchers become interested in MOGA. The performance of an MOGA can be measured from three aspects: the convergence to the true Pareto optimal front, the diversity of solutions and the time consuming. A favorable diversity of solutions can give decision makers the opportunities to choose the most adequate solution for the problem from the solution set. Referring to how to maintain the solution diversity, some scholars have done numerous work and suggested several strategies to keep diversity, four of which are the most representative ones: the strategy based on fitness sharing whose performance depends on the selection of the parameter; the method based on crowding distance which can not achieve good diversity on the problem with more than two objectives; the strategy based on the kth distances of the neighbors which has a high time complexity; the grid technique in which the parameter is also hard to determine.Based on the existing researches on the diversity keeping strategies mentioned above, this thesis proposes a strategy based on polar coordinates to keep diversity of solutions without any parameters, whose time complexity is less than O ( N 2). In order to obtain a diverse solution set, by equal division of each polar angle, it separates the searching space into several areas each of which keeps only one solution near its center position ultimately. Furthermore, a new MOGA named PCGA2 is also presented in this thesis, which employs the arena's principle to construct the non-dominated set and the strategy based on polar coordinates to keep diversity of solution set. For testing the performance of PCGA2, we compare it with NSGA2, PESA2 and SPEA2 in our experiments. The experimental results show that PCGA2 can achieve a good performance with respect to both diversity and CPU time; moreover, PCGA2 can arrive at a perfect diversity of solution set in the sense of polar angle distribution.