Niching-based Evolutionary Diversity Optimization for the Traveling Salesperson Problem

TL;DR

This paper introduces a niching-based evolutionary approach for the TSP that enhances diversity by exploring distant solution basins, outperforming baseline methods in quality and efficiency.

Contribution

The study presents a novel 2-stage niching memetic algorithm with randomized local search, improving diversity and solution quality in TSP optimization.

Findings

The proposed NMA finds more distant and higher quality solutions.

It outperforms baseline algorithms in diversity and runtime.

Solutions tend to cluster at tight quality constraints but occupy distant basins.

Abstract

In this work, we consider the problem of finding a set of tours to a traveling salesperson problem (TSP) instance maximizing diversity, while satisfying a given cost constraint. This study aims to investigate the effectiveness of applying niching to maximize diversity rather than simply maintaining it. To this end, we introduce a 2-stage approach where a simple niching memetic algorithm (NMA), derived from a state-of-the-art for multi-solution TSP, is combined with a baseline diversifying algorithm. The most notable feature of the proposed NMA is the use of randomized improvement-first local search instead of 2-opt. Our experiment on TSPLIB instances shows that while the populations evolved by our NMA tend to contain clusters at tight quality constraints, they frequently occupy distant basins of attraction rather than close-by regions, improving on the baseline diversification in terms of sum-sum diversity. Compared to the original NMA, ours, despite its simplicity, finds more distant solutions of higher quality within less running time, by a large margin.