Insights from Multi-tasking the EAX Algorithm for the Travelling Salesperson Problem

2026-08-12

AI Summary

This work addresses the challenge of efficiently solving multiple related traveling salesman problem (TSP) instances under limited computational resources by proposing a multi-task evolutionary algorithm based on edge assembly crossover (MT-EAX). The approach incorporates a generational scaling strategy that leverages geometric differences among TSP instances to substantially enhance early-stage search efficiency without increasing overall computational cost. Additionally, a decoupled configuration mechanism is employed to preserve population diversity, thereby improving final solution quality. Experimental results demonstrate that the proposed method reduces computational expenditure by 60%–90% in the early search phase while achieving solution quality comparable to or better than that of the standard EAX, with particularly strong performance on clustered or normally distributed TSP instances.

Abstract

Evolutionary multitasking allows several related problems to be solved in a single run of an algorithm. In this paper, we investigate integrating evolutionary multitasking with Edge Assembly Crossover (MT-EAX) to solve the classical Travelling Salesperson Problem (TSP). To fairly compare MT-EAX against standard EAX under strict compute budgets, we evaluate three scaling methods: generation scaling, population scaling, and balanced scaling. Our results show that generationally scaled MT-EAX is highly effective compute-wise in the early stages of the search, saving $60\%$ to $90\%$ of compute for equal or better solution quality. We observe that instance geometry has a significant impact, with clustered, normally distributed instances securing larger improvements than uniformly distributed ones. However, when scaling by population or utilising explicit solution transfer, the results are negative due to population starvation and incompatible cross-instance parent selection. We demonstrate that the advantage of MT-EAX derives from increased diversity through parallel search in early generations, which can be successfully preserved using a decoupled configuration to often strictly outperform or match standard EAX performance at final convergence.

Problem

• evolutionary multitasking
• Travelling Salesperson Problem
• Edge Assembly Crossover
• compute efficiency
• instance geometry

Innovation

• evolutionary multitasking
• Edge Assembly Crossover
• Travelling Salesperson Problem
• compute efficiency
• population diversity