To Repair or Not to Repair? Investigating the Importance of AB-Cycles for the State-of-the-Art TSP Heuristic EAX

TL;DR

This paper investigates the first stage of the EAX heuristic for TSP, introducing a method to verify and repair AB-cycles, leading to improved efficiency and solution quality on challenging instances.

Contribution

It presents a novel approach to verify and repair AB-cycles in EAX's first stage, enhancing its performance and robustness.

Findings

Improved EAX variants outperform the original on difficult TSP instances.

The verification and repair method increases computational efficiency.

Enhanced solutions demonstrate better quality on benchmark instances.

Abstract

The Edge Assembly Crossover (EAX) algorithm is the state-of-the-art heuristic for solving the Traveling Salesperson Problem (TSP). It regularly outperforms other methods, such as the Lin-Kernighan-Helsgaun heuristic (LKH), across diverse sets of TSP instances. Essentially, EAX employs a two-stage mechanism that focuses on improving the current solutions, first, at the local and, subsequently, at the global level. Although the second phase of the algorithm has been thoroughly studied, configured, and refined in the past, in particular, its first stage has hardly been examined. In this paper, we thus focus on the first stage of EAX and introduce a novel method that quickly verifies whether the AB-cycles, generated during its internal optimization procedure, yield valid tours -- or whether they need to be repaired. Knowledge of the latter is also particularly relevant before applying other powerful crossover operators such as the Generalized Partition Crossover (GPX). Based on our insights, we propose and evaluate several improved versions of EAX. According to our benchmark study across 10 000 different TSP instances, the most promising of our proposed EAX variants demonstrates improved computational efficiency and solution quality on previously rather difficult instances compared to the current state-of-the-art EAX algorithm.