A discrete tree-seed algorithm for solving symmetric traveling salesman problem

Abstract

Tree-Seed algorithm (TSA) is a recently developed nature inspired population-based iterative search algorithm. TSA is proposed for solving continuous optimization problems by inspiring the relations between trees and their seeds. The constrained and binary versions of TSA are present in the literature but there is no discrete version of TSA which decision variables represented as integer values. In the present work, the basic TSA is redesigned by integrating the swap, shift, and symmetry transformation operators in order to solve the permutation-coded optimization problems and it is called as DTSA. In the basic TSA, the solution update rules can be used for the decision variables whose are defined in continuous solution space, this rules are replaced with the transformation operators in the proposed DTSA. In order to investigate the performance of DTSA, well-known symmetric traveling salesman problems are considered in the experiments. The obtained results are compared with well-known metaheuristic algorithms and their variants, such as Ant Colony Optimization (ACO), Genetic Algorithm (GA), Simulated Annealing (SA), State Transition Algorithm (STA), Artificial Bee Colony (ABC), Black Hole (BH), and Particle Swarm Optimization (PSO). Experimental results show that DTSA is another qualified and competitive solver on discrete optimization.