A Powerful Genetic Algorithm Using Edge Assembly Crossover for the Traveling Salesman Problem

Abstract

This paper presents a genetic algorithm (GA) for solving the traveling salesman problem (TSP). To construct a powerful GA, we use edge assembly crossover (EAX) and make substantial enhancements to it: (i) localization of EAX together with its efficient implementation and (ii) the use of a local search procedure in EAX to determine good combinations of building blocks of parent solutions for generating even better offspring solutions from very high-quality parent solutions. In addition, we develop (iii) an innovative selection model for maintaining population diversity at a negligible computational cost. Experimental results on well-studied TSP benchmarks demonstrate that the proposed GA outperforms state-of-the-art heuristic algorithms in finding very high-quality solutions on instances with up to 200,000 cities. In contrast to the state-of-the-art TSP heuristics, which are all based on the Lin–Kernighan (LK) algorithm, our GA achieves top performance without using an LK-based algorithm.

On the Empirical Scaling Behaviour of State-of-the-art Local Search Algorithms for the Euclidean TSP

“…Computational results by Nagata & Kobayashi indicate that on many large Euclidean TSP instances, EAX performs better than LKH 2; specifically, they reported that on 50 out of 57 TSPLIB, VLSI and National instances of sizes between 4 461 and 60 000 cities, EAX produced statistically significantly better solutions than LKH in shorter computation times [13]. (Our experiments comparing EAX to LKH 2 shed further light on their relative performance.…”

“…The first such algorithm known to have reached the performance of LKH, and hence state-of-the-art performance, in finding very high quality solutions to a broad range of Euclidean TSP instances (as considered in our work) is EAX, the genetic algorithm by Nagata & Kobayashi [13]. In a nutshell, EAX exploits improved local and global variants of the edge assembly cross-over operator, specific diversity preservation techniques that uses edge entropy measures in the population replacement scheme, and initialization of the population by local optimization.…”

“…In a nutshell, EAX exploits improved local and global variants of the edge assembly cross-over operator, specific diversity preservation techniques that uses edge entropy measures in the population replacement scheme, and initialization of the population by local optimization. (For a detailed description of the algorithm and the operators, we refer the reader to the original publication by Nagata & Kobayashi [13]. )…”

“…Until recently, the state of the art in exact and inexact TSP solving has been defined by two long-standing incumbents: Concorde [2] and the Lin-Kernighan heuristic (LKH) [4,5]. In 2013, Nagata and Kobayashi introduced EAX [13] -a new evolutionary algorithm for the TSP that makes use of an improved version of the edge assembly crossover operator [12] to achieve an effective recombination of sub-tours. Their empirical results suggest that EAX tends to perform better than the latest version of LKH and hence represents an improvement in the state of the art in inexact TSP solving.…”

Machine scheduling with outsourcing

“…Population-heuristic solution procedures using different encoding schemes Besides the DP-based heuristic, population-based heuristic is another solution procedure often used to solve NP-hard problems (Li and Wang, 2007;Nagata and Kobayashi, 2013). In this paper, we focus on one special type of population-based heuristic: GA for multi-objective problems.…”