Adaptive Strategies Based on Differential Evolutionary Algorithm for Many-Objective Optimization

Yifei Sun,Ruoxia Yao,Zhuo Liu,Kun Bian,Xin Sun,Rui Wang

doi:10.1155/2021/2491796

Abstract

The decomposition-based algorithm, for example, multiobjective evolutionary algorithm based on decomposition (MOEA/D), has been proved effective and useful in a variety of multiobjective optimization problems (MOPs). On the basis of MOEA/D, the MOEA/D-DE replaces the simulated binary crossover (SBX) operator with differential evolution (DE) operator, which is used to enhance the diversity of the solutions more effectively. However, the amplification factor and the crossover probability are fixed in MOEA/D-DE, which would lead to a low convergence rate and be more likely to fall into local optimum. To overcome such a prematurity problem, this paper proposes three different adaptive operators in DE with crossover probability and amplification factors to adjust the parameter settings adaptively. We incorporate these three adaptive operators in MOEA/D-DE and MOEA/D-PaS to solve MOPs and many-objective optimization problems (MaOPs), respectively. This paper also designs a sensitive experiment for the changeable parameter η in the proposed adaptive operators to explore how η would affect the convergence of the proposed algorithms. These adaptive algorithms are tested on many benchmark problems, including ZDT, DTLZ, WFG, and MaF test suites. The experimental results illustrate that the three proposed adaptive algorithms have better performance on most benchmark problems.

Highlights

In fields like industrial production and scientific research, the solutions for many practical problems are considered as a type of multiobjective optimization according to many researches
The amplification factor and the crossover probability are fixed in multiobjective evolutionary algorithm based on decomposition (MOEA/D)-differential evolution (DE), which would lead to a low convergence rate and be more likely to fall into local optimum
We firstly set different values of η to see how IGD and HV would change, and we run these proposed algorithms on more test functions with probable η compared with multiobjective evolutionary algorithms (MOEAs)/D-DE to see which one performs better on these test functions. e probable value of η was decided by the IGD and HV values that most algorithms get best on these test functions

Summary

Introduction

In fields like industrial production and scientific research, the solutions for many practical problems are considered as a type of multiobjective optimization according to many researches. MOEA/D, a representative decomposition-based algorithm, uses a scalarizing approach to divide an MOP into many subproblems with different weights It uses the coefficient method based on population search to solve these subproblems [14]. As for indicator-based algorithms, they usually need a lot of computational resources To handle these problems, a lot of many-objective evolutionary algorithms (MaOEAs) were proposed for solving MaOPs in the few decades. Ma et al [38] designed an adaptive localized decision variable analysis approach to solve MaOPs. A bottleneck objective learning strategy was proposed by Liu et al to balance the diversity and convergence [39].

Background

Proposed Algorithms

Experimental Study and Results Analysis

Conclusion