Benefits of sparse population sampling in multi-objective evolutionary computing for large-Scale sparse optimization problems

Abstract

• Sparse population sampling is a simple population initialization routine with a linear run time and one to two parameters for large-scale sparse multi-objective optimization problems. • For large-scale sparse multi-objective optimization problems, sparse population sampling improves hyper-volume across all studied population based algorithms with minimal side effects. • NSGA-II combined with sparse population sampling outperforms SparseEA in high-dimension problems (i.e., greater than 2,500 decision variables). Sparse optimization problems involving sparse non-zero variables are common among large-scale single or multi-objective real-world problems. However, generic optimization algorithms are inefficient at solving most of these large scale problems. Moreover, algorithms to solve these problems are currently under-researched. This paper proposes a novel approach to improve large-scale sparse multi-objective algorithms using a sparse population sampling (SPS) method. SPS is an optimization subroutine that replaces uniform sampling for population initialization, and can be applied to any population-based algorithm, including evolutionary or particle swarm algorithms. Through rigorous testing, we have found that SPS leads to near-universal improvements in hyper-volume for common population-based algorithms in large-scale (i.e. over 8000 decision variable) and sparse multi-objective optimization problems. Additionally, the elitist non-dominated sorting genetic algorithm (NSGA-II) with SPS is found to outperform a selection of other existing multi-objective optimization algorithms with SPS for handling sparse high-dimensional decision spaces. Considering these benefits and its simplicity, the proposed SPS method is an evidently promising method for boosting performance in large-scale sparse multi-objective optimization algorithms.