A Hybrid Simplex Multi-Objective Evolutionary Algorithm Based on A New Fitness Assignment Strategy

In multi-objective evolutionary algorithms (MOEAs), the traditional fitness assignment strategy based on Pareto dominance is ineffective in sorting out the high-quality solutions when the number of the objective is large. Recently, many scholars have used preference order (PO) ranking approach as an optimality criterion in the ranking stage of MOEAs. The experiment shows that the algorithms equipped with the PO ranking procedures can have a better convergence to the true Pareto surface, but are ineffective to maintain a set of well-distributed solutions over the Pareto surface. In order to overcome above shortcomings, a new algorithm is proposed which adopts a new fitness assignment strategy using the information of the individual preference order ranking and the individual density. In this way,  it is helpful to guide the individuals to more sparse areas in the Pareto Front. At the same time, the proposed algorithm effectively combines multi-objective evolutionary algorithm with the Nelder-Mead simplex search to get a balance between the exploration and exploitation abilities. In each generation, the algorithm adopts a parallel hybrid way to evolve two subsets simultaneously, and the population will be improved by both evolution algorithm and simplex search. The proposed algorithm has been compared with other MOEAs on some many-objective problems by experiments. The experimental results indicate that the proposed algorithm achieves a better performance in convergence and diversity.