Research On Methods Of Predicting Pareto Dominance In Multi-objective Optimization

Evolutionary algorithms have been successfully applied to solve multi-objectiveoptimization problems (MOPs), however, for expensive multi-objective optimizationproblems (EMOPs), evaluation of objective functions or constraint functions is a hugetime-consuming procedure taking several hours or even days, which referred as curseof computation cost. Although surrogate models have lessen the evaluations ofobjective functions at some extent, lots of prior knowledge is needed to approximationtechniques. In addition, different objective function requires different model, the typeand parameter precision of model influence the accuracy of estimation directly, theconstruction of surrogate models are itself challenging.This paper engages in the study of Pareto dominance classification method,applying pattern recognition techniques to overcome the curse of computational cost,and presents a basic framework of pattern classifers to predict Pareto dominancebetween candidate solutions with unknown objective vector value through learning thesample Pareto dominance of candidate solutions. On the assumption that classcondition probability density function subjects to normal distribution, this paperpreliminarily implements a Bayesian classifier based on statistical learning theory,laying a foundation for further research of Pareto dominance prediction.To improve the accurracy of predicting Pareto dominance, this paper conducts astudy of MOPs’ own characteristics. For MOPs whose domains differ in orders ofmagnitude, two similarity measurements of the weighed sum of binary bit stringand the sum of ranked dimensional sequential number are put forward, which bringabout obvious improvements of prediction accuracy and robustness compared with thenearest neighbor classification using Euclidian distance in decision space. For MOPswhose decision vector has equivalent components, the equivalent components ofdecision vector are defined by analyzing the contribution rate of each decisioncomponent to each objective component. For each objective component, the decisionvector is divided into a group of equivalent sub-vectors, each of which is consisted ofthe equivalent components with the same contribution rate. A similarity measurementmethod, the weighted sum of the minimized cross distance based on the equivalentsub-vector, is proposed. The experiments on testing problems show that the proposed method remarkably improves the prediction performance of nearest neighborclassifiers.In order to overcome the deficiency of nearest neighbor classification inpredicting Pareto dominance of MOPs with severely unbalanced class proportions, thispaper improves class proportions distribution by defining L-Pareto dominance, andrealizes the predicting method of L-Pareto dominance based on qualitatively analyzingthe predicting error rate of L-Pareto dominance and Pareto dominance. Theoreticalanalysis and simulation results for various typical MOPs indicate that the L-Paretodominance prediction is feasible and effective method to solve EMOPs.