Entropy-Based Evolutionary Diversity Optimisation for the Traveling Salesperson Problem

TL;DR

This paper introduces an entropy-based evolutionary algorithm to generate diverse, high-quality solutions for the Traveling Salesperson Problem, focusing on segment diversification and demonstrating significant improvements over previous methods.

Contribution

It presents a novel high-order entropy measure for diversifying segments of TSP solutions within an evolutionary framework, enhancing diversity and solution quality.

Findings

Significant diversity improvements over previous edge-based methods.

Effective diversification of long segments in solutions.

Robust performance with large populations.

Abstract

Computing diverse sets of high-quality solutions has gained increasing attention among the evolutionary computation community in recent years. It allows practitioners to choose from a set of high-quality alternatives. In this paper, we employ a population diversity measure, called the high-order entropy measure, in an evolutionary algorithm to compute a diverse set of high-quality solutions for the Traveling Salesperson Problem. In contrast to previous studies, our approach allows diversifying segments of tours containing several edges based on the entropy measure. We examine the resulting evolutionary diversity optimisation approach precisely in terms of the final set of solutions and theoretical properties. Experimental results show significant improvements compared to a recently proposed edge-based diversity optimisation approach when working with a large population of solutions or long segments.