A new genetic algorithm for the asymmetric traveling salesman problem

The asymmetric traveling salesman problem (ATSP) is one of the most important combinatorial optimization problems. It allows us to solve, either directly or through a transformation, many real-world problems. We present in this paper a new competitive genetic algorithm to solve this problem. This algorithm has been checked on a set of 153 benchmark instances with known optimal solution and it outperforms the results obtained with previous ATSP heuristic methods. © 2012 Elsevier Ltd. All rights reserved.This work has been partially supported by the Ministerio de Educacion y Ciencia of Spain (Project No. TIN2008-06441-C02-01).Yuichi Nagata; Soler Fernández, D. (2012). A new genetic algorithm for the asymmetric traveling salesman problem. Expert Systems with Applications. 39(10):8947-8953. https://doi.org/10.1016/j.eswa.2012.02.029S89478953391

Genetic algorithms for the traveling salesman problem using edge assembly crossovers

The central issue in creating new genetic algorithms is the algorithm\u27s crossover method. My focus is on a particular crossover known as the Edge Assembly Crossover, or EAX, by Nagata and Kobayashi. The basics of a what make up a genetic algorithm is reviewed. The traveling salesman problem is defined. The EAX as an algorithm within an algorithm is explained. The crossover\u27s implementation is original and is listed. The use of the graphic user interface, TSP View, used to run algorithms is explained as well as the extensions to the interface that were implemented for this study. The results of running a genetic algorithm using the EAX against traveling salesman problems, with a focus on ATT532, is discussed and compared to runs using other optimization algorithms. The question of why EAX works is addressed with conjectures for a possible future research path

Metaheuristics and combinatorial optimization problems

This thesis will use the traveling salesman problem (TSP) as a tool to help present and investigate several new techniques that improve the overall performance of genetic algorithms (GA). Improvements include a new parent selection algorithm, harem select, that outperforms all other parent selection algorithms tested, some by up to 600%. Other techniques investigated include population seeding, random restart, heuristic crossovers, and hybrid genetic algorithms, all of which posted improvements in the range of 1% up to 1100%. Also studied will be a new algorithm, GRASP, that is just starting to enjoy a lot of interest in the research community and will also been applied to the traveling salesman problem (TSP). Given very little time to run, relative to other popular metaheuristic algorithms, GRASP was able to come within 5% of optimal on several of the TSPLIB maps used for testing. Both the GA and the GRASP algorithms will be compared with commonly used metaheuristic algorithms such as simulated annealing (SA) and reactive tabu search (RTS) as well as a simple neighborhood search - greedy search

A Hybrid Genetic Algorithm for the min-max Multiple Traveling Salesman Problem

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual, and a dynamic programming algorithm is employed to evaluate the individual and find the optimal mTSP solution for the given sequence of cities. A novel crossover operator is designed to combine similar tours from two parents and offers great diversity for the population. For some of the generated offspring, we detect and remove intersections between tours to obtain a solution with no intersections. This is particularly useful for the min-max mTSP. The generated offspring are also improved by a self-adaptive random local search and a thorough neighborhood search. Our algorithm outperforms all existing algorithms on average, with similar cutoff time thresholds, when tested against multiple benchmark sets found in the literature. Additionally, we improve the best-known solutions for 21 out of 89 instances on four benchmark sets