A fitness assignment strategy based on the grey and entropy parallel analysis and its application to MOEA

In this paper, grey and entropy parallel analysis (GEPA) is presented as a new fitness-assignment strategy for solving multi-objective optimization problems. An evolutionary algorithm based on GEPA is proposed, and the grey and entropy parallel relational grade (GEPRG) is used as the fitness value to guide the development of the evolutionary algorithm. Under the analysis of the existing research work, the multi-objective flow shop scheduling problem is chosen as the application object and a flow shop scheduling model with five objectives is established. GEPA_GA, the GA based on GEPA, is described. To verify the performance of the proposed algorithm, GEPA_GA, together with the GA based on the random weighting method (RW_GA), NSGA-II and the GA based on g-dominance (g_GA), are used to optimize the multi-objective flow shop scheduling problem. The experimental data are analyzed by the statistical analysis method, the Kruskal-Wallis test, and three evaluation metrics. The influences of the five grey relational operators and the distinguishing coefficient on the algorithm performance are also studied. Experiments shows that the results obtained by GEPA_GA are better than those of RW_GA, NSGA-II and g_GA even under the situation that the combination of operator and distinguishing coefficient is not the best. It is proven that GEPA_GA works well in solving the multi-objective flow shop scheduling optimization problem, and GEPA is a promising strategy for solving multi-objective optimization problems.