DJAYA: A discrete Jaya algorithm for solving traveling salesman problem

Abstract

Jaya algorithm is a newly proposed stochastic population-based metaheuristic optimization algorithm to solve constrained and unconstrained continuous optimization problems. The main difference of this algorithm from the similar approaches, it uses best and worst solution in the population in order improve the intensification and diversification of the population, and this provides discovering potential solutions on the search space of the optimization problem. In this study, we propose discrete versions of the Jaya by using two major modifications in the algorithm. First is to generate initial solutions by using random permutations and nearest neighborhood approach to create population. Second is the update rule of the basic Jaya algorithm rearranged to solve discrete optimization problems. Due to characteristics of the discrete optimization problem, eight transformation operators are used for the discrete variants of the proposed algorithm. Based on these modifications, the discrete Jaya algorithm, called DJAYA, has been applied to solve fourteen different symmetric traveling salesman problem, which is one of the famous discrete problems in the discrete optimization. In order to improve the obtained best solution from DJAYA, 2-opt heuristic is also applied to the best solution of DJAYA. Once population size, search tendency and the other parameters of the proposed algorithm have been analyzed, it has been compared with the state-of-art algorithms and their variants, such as Simulated Annealing (SA), Tree-Seed Algorithm (TSA), State Transition Algorithm (STA) Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), Genetic Algorithm (GA) and Black Hole (BH). The experimental results and comparisons show that the proposed DJAYA is highly competitive and robust optimizer for the problem dealt with the study.