A Many-Objective Optimization Algorithm Based on Weight Vector Adjustment.

Yanjiao Wang,Xiaonan Sun

doi:10.1155/2018/4527968

Abstract

In order to improve the convergence and distribution of a many-objective evolutionary algorithm, this paper proposes an improved NSGA-III algorithm based on weight vector adjustment (called NSGA-III-WA). First, an adaptive weight vector adjustment strategy is proposed to decompose the objective space into several subspaces. According to different subspace densities, the weight vector is sparse or densely adjusted to ensure the uniformity of the weight vector distribution on the Pareto front surface. Secondly, the evolutionary model that combines the new differential evolution strategy and genetic evolution strategy is proposed to generate new individuals and enhance the exploration ability of the weight vector in each subspace. The proposed algorithm is tested on the optimization problem of 3–15 objectives on the DTLZ standard test set and WFG test instances, and it is compared with the five algorithms with better effect. In this paper, the Whitney–Wilcoxon rank-sum test is used to test the significance of the algorithm. The experimental results show that NSGA-III-WA has a good effect in terms of convergence and distribution.

Highlights

Many-objective optimization problems (MAOPs) [1] refer to optimization problems whose number of objectives is over three and need to be processed simultaneously
In 2014, Deb and Jain proposed a nondominated sorting evolution many-objective optimization algorithm based on reference points [20] (NSGA-III), and its reference point is uniformly distributed throughout the objective space; in the same year, Liu et al proposed the many-objective evolutionary algorithms (MOEAs)/D-M2M method; the entire Pareto optimal front surface (PFs) can be divided into multiple segments and solved separately by dividing the entire objective space into multiple subspaces
E NSGA-III-WA algorithm divides the objective space into several subspaces and adjusts the weight vectors according to the individual density of the objective space. is method can better ensure the uniformity of the weight vectors on the objective surface, ensuring the uniformity of the solution set

Summary

A Many-Objective Optimization Algorithm Based on Weight Vector Adjustment

In order to improve the convergence and distribution of a many-objective evolutionary algorithm, this paper proposes an improved NSGA-III algorithm based on weight vector adjustment (called NSGA-III-WA). An adaptive weight vector adjustment strategy is proposed to decompose the objective space into several subspaces. According to different subspace densities, the weight vector is sparse or densely adjusted to ensure the uniformity of the weight vector distribution on the Pareto front surface. The evolutionary model that combines the new differential evolution strategy and genetic evolution strategy is proposed to generate new individuals and enhance the exploration ability of the weight vector in each subspace. E proposed algorithm is tested on the optimization problem of 3–15 objectives on the DTLZ standard test set and WFG test instances, and it is compared with the five algorithms with better effect.

Introduction

The Proposed Algorithm

Simulation Results