Adaptive dropout for high-dimensional expensive multiobjective optimization

Jianqing Lin,Cheng He,Ran Cheng

doi:10.1007/s40747-021-00362-5

Abstract

Various works have been proposed to solve expensive multiobjective optimization problems (EMOPs) using surrogate-assisted evolutionary algorithms (SAEAs) in recent decades. However, most existing methods focus on EMOPs with less than 30 decision variables, since a large number of training samples are required to build an accurate surrogate model for high-dimensional EMOPs, which is unrealistic for expensive multiobjective optimization. To address this issue, we propose an SAEA with an adaptive dropout mechanism. Specifically, this mechanism takes advantage of the statistical differences between different solution sets in the decision space to guide the selection of some crucial decision variables. A new infill criterion is then proposed to optimize the selected decision variables with the assistance of surrogate models. Moreover, the optimized decision variables are extended to new full-length solutions, and then the new candidate solutions are evaluated using expensive functions to update the archive. The proposed algorithm is tested on different benchmark problems with up to 200 decision variables compared to some state-of-the-art SAEAs. The experimental results have demonstrated the promising performance and computational efficiency of the proposed algorithm in high-dimensional expensive multiobjective optimization.

Highlights

Multiobjective optimization problems (MOPs) refer to the optimization of multiple conflicting objectives simultaneously, i.e., improvement in one objective may lead to the degeneration of at least one of the other objectives [1]
The radial basis function (RBF)-based search in the proposed ADSAPSO aims to conduct the local search in a low-dimensional space to quickly obtain better-converged solutions, which is naturally suitable for high-dimensional expensive multiobjective optimization problems (EMOPs)
We have proposed an surrogateassisted evolutionary algorithms (SAEAs) with adaptive dropout mechanism, called ADSAPSO, for solving highdimensional EMOPs with up to 200 decision variables

Summary

Introduction

Multiobjective optimization problems (MOPs) refer to the optimization of multiple conflicting objectives simultaneously, i.e., improvement in one objective may lead to the degeneration of at least one of the other objectives [1]. EDN-ARMOEA, a new method was proposed for solving high-dimensional EMOPs, which used a dropout neural network instead of the Gaussian process [27]. A surrogate-assisted particle swarm optimization algorithm with an adaptive dropout mechanism, called ADSAPSO, is proposed to handle high-dimensional EMOPs. We mainly focus on selecting a small number of crucial decision variables for convergence enhancement and diversity maintenance, aiming to reduce the cost for building and training surrogate model(s). (i) EDN-ARMOEA uses the dropout strategy for improving the computational efficiency of the surrogate model; by contrast, the dropout strategy in ADSAPSO is adopted to reduce the dimension of the optimization problem. We use the RBF-based search to optimize the selected d decision variables, and the Replacement operation is used to extend the low-dimensional decision vectors to full-length candidate solutions.

Background

Experimental study

Conclusion