Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation

TL;DR

This paper introduces EAX-EDO, an evolutionary algorithm that efficiently finds diverse, high-quality solutions for the TSP, outperforming existing methods whether the optimal solution is known or unknown.

Contribution

It presents a novel EAX-based evolutionary diversity optimization approach for the TSP that maximizes diversity alongside solution quality, regardless of knowledge of the optimal tour.

Findings

EAX-EDO outperforms existing approaches in generating diverse high-quality TSP solutions.

The method is effective both when the optimal solution is known and unknown.

EAX-EDO achieves a better balance of diversity and quality than previous algorithms.

Abstract

Evolutionary algorithms based on edge assembly crossover (EAX) constitute some of the best performing incomplete solvers for the well-known traveling salesperson problem (TSP). Often, it is desirable to compute not just a single solution for a given problem, but a diverse set of high quality solutions from which a decision maker can choose one for implementation. Currently, there are only a few approaches for computing a diverse solution set for the TSP. Furthermore, almost all of them assume that the optimal solution is known. In this paper, we introduce evolutionary diversity optimisation (EDO) approaches for the TSP that find a diverse set of tours when the optimal tour is known or unknown. We show how to adopt EAX to not only find a high-quality solution but also to maximise the diversity of the population. The resulting EAX-based EDO approach, termed EAX-EDO is capable of obtaining diverse high-quality tours when the optimal solution for the TSP is known or unknown. A comparison to existing approaches shows that they are clearly outperformed by EAX-EDO.