ORIGINAL RESEARCH Genetic algorithms for the travelling salesman problem: a crossover comparison Tariq Alzyadat 1 • Mohammad Yamin 2 • Girija Chetty 1 Received: 20 July 2019 / Accepted: 23 October 2019 Ó Bharati Vidyapeeth’s Institute of Computer Applications and Management 2019 Abstract This paper addresses an application of genetic algorithms (GA) for solving the travelling salesman prob- lem (TSP), it compares the results of implementing two different types of two-point (1 order) genes crossover, the static and the dynamic approaches, which are used to produce new offspring. By changing three factors; the number of cities, the number of generations and the pop- ulation size, the goal is to show which approach is better in terms of finding the optimal solution (the shortest path) in as short time as possible as a result of these changes. Besides, it will explore the effect of changing the above factors on finding the optimal solution. Keywords Dynamic crossover  Genetic algorithms  Permutation  Static crossover  Travelling salesman problem Abbreviations ANOVA Analysis of variance CX The cycle crossover ERX Edge recombination crossover GA Genetic algorithms GNX Generalized N-point crossover NP-problem Nondeterministic polynomial time problem SCX Sequential constructive crossover TSP Travelling salesman problem 1 Introduction The travelling salesman problem is considered a chal- lenging problem in the area of operational research, moreover it is a famous example of the most widely studied optimization problems [1]. The assumptions in this prob- lem; there are a finite number of cities, each city is visited only once, assuming that the distance or the cost to travel between each city is known and the main goal is to find an ordered set of all visited cities, such that the cost of trav- elling is minimized. The fundamental concepts of GAs were first introduced by Holland, derived from Darwinian evolution, Mendelian genetics and Weizmann species selection theory [2]. Since that time, through analytical and empirical studies GA has proven its robustness in solving optimization problems, in a way better than normal optimization and conventional search methods [3]. 2 Background The TSP is an old problem, which has been introduced mathematically by Sir William Rowan Hamilton and by Thomas Penyngton Kirkman in the nineteenth century [4]. In combinatorial optimization the TSP is a well-known computational problem, which is known to be NP-hard [5]. Many algorithms used GA in solving TSP, because GA has proven its efficiency in solving optimisation problems [3]. The technique of GA uses crossover and mutation opera- tors, as well as the survival of the fittest to solve opti- mization problems [5]. The crossover operator is very important in GA, because it is used to exchange informa- tion during the search for solution [6]. & Mohammad Yamin myamin@kau.edu.sa Tariq Alzyadat tariq.alzyadat@canberra.edu.au 1 University of Canberra, Canberra, Australia 2 Faculty of Economics and Administration, King Abdulaziz University, Jeddah, Saudi Arabia 123 Int. j. inf. tecnol. https://doi.org/10.1007/s41870-019-00377-9