Feature-based Evolutionary Diversity Optimization of Discriminating Instances for Chance-constrained Optimization Problems

TL;DR

This paper presents a method to evolve diverse benchmarking instances for chance-constrained optimization problems, enabling better algorithm selection by highlighting performance differences.

Contribution

It introduces a feature-based evolutionary algorithm to generate instances that differentiate algorithm performance in chance-constrained optimization.

Findings

Successfully generates diverse instances based on features

Effectively distinguishes performance between two algorithms

Demonstrates applicability on chance-constrained maximum coverage problem

Abstract

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a detailed analysis of the problem's features. To do so, it is important to have a diverse set of benchmarking instances highlighting the difference in algorithms' performance. In this paper, we evolve diverse benchmarking instances for chance-constrained optimization problems that contain stochastic components characterized by their expected values and variances. These instances clearly differentiate the performance of two given algorithms, meaning they are easy to solve by one algorithm and hard to solve by the other. We introduce a $(\mu+1)~EA$ for feature-based diversity optimization to evolve such differentiating instances. We study the chance-constrained maximum coverage problem with stochastic weights on the vertices as an example of chance-constrained optimization problems. The experimental results demonstrate that our method successfully generates diverse instances based on different features while effectively distinguishing the performance between a pair of algorithms.