Research On Multi-objective Optimization Pareto Dominance Prediction Methods And Algorithm

Multi-objective optimization evolutionary algorithms based on Pareto dominance have been applied in various fields successfully and widely. It determines the Pareto dominance relationship of arbitrary candidate solutions by comparing their objective values directly. It simulates the survival of the fittest rule, urges the candidate solution population iteration converge to the Pareto optimal surface. However, when this kind of algorithm is used to solve expensive multi-objective optimization problems, once evaluation of objective functions needs hours or even days, the efficiency is hard to accept. It is urgent to reduce the evaluation cost of objective functions for engineering practice.This paper investigates the Pareto dominance classification method to solve problems of computation cost curse using pattern recognition techniques. To solve Pareto dominance prediction of multi-objective problems without analytical model, reflect the mapping information from decision space to objective space at the same time, this study investigates a nearest neighbor prediction method of Pareto dominance using general regression neural networks. The decision differential value (D-value) vector of two feasible solutions is used as the input of GRNN, and the objective D-value vector is used as the output. Under the supervision of sample candidate solutions, GRNN is used to predict objective D-value vectors between an observed solution and samples. For an observed candidate, the predicted objective D-Value vectors are used to find out the nearest neighbor samples in objective space. Experimental results show that the nearest neighbor prediction of Pareto dominance relationships using GRNN can obtain acceptable prediction accuracy. The proposed algorithm provides an effective method to relieve the curse of computation cost in computationally expensive multi-objective optimization problems, but without requirement for analytical models of objective functions.In order to overcome the defect of low predicting accuracy caused by unbalanced class proportions, the paper improves class proportion distribution by defining d-Pareto dominance. Framework of d-Pareto prediction was put forward and the predicting error rate was also analyzed theoretically. Interactive experiments between d-Pareto predicting model and evolutionary algorithm for different MOPs was conducted, simulation results show that d-Pareto dominance relationship is a valid and feasible method.A novel algorithm evaluating individual quality based on the distance and direction between candidate solutions and optimal non-dominated solutions was investigated from the aspect of saving computation cost. The algorithm combines elitist strategy and crowding distance computation, improves the convergence rate and diversity of solutions. The simulation results show that the algorithm can not only obtain well distance Pareto front, but also can simplify the computation and shorten the running time. This paper contains21figures,13tables and62references.