Discrete Starfish Optimization Algorithm for Symmetric Travelling Salesman Problem

This paper introduces a new discrete StarFish Optimization Algorithm (D-SFOA) to solve a complex discrete Symmetric Travelling Salesman Problem (STSP). The discrete SFOA algorithm is initialized with the initial population of classical SFOA, and the continuous values of the individuals in the population are converted to the discrete version using the random key method. Ten neighbourhood methods used in this study provide diversity to the starfish population, and the 2-opt local search algorithm allows the study to find shorter tours. The performance of D-SFOA is tested on STSP samples ranging in size from 30 to 1084 from TSPLIB. Discrete versions of the Grey Wolf Optimizer (D-GWO) and Harris Hawk Optimization (D-HHO) algorithms are applied with the same parameters to compare the performance of the proposed algorithm. The algorithm uses descriptive statistics such as average tour, best tour, percentage of deviation of the mean tour, percentage of deviation of the best tour, and execution time to ensure a fair comparison. The Wilcoxon signed-rank test and Ablation test are applied to measure the significant difference in the values of the algorithms and to observe the performance effect of the main components used in the proposed algorithm on tour length and execution time, respectively. This study’s numerical and statistical results show that D-SFOA has significantly outperformed other alternative algorithms and provided better solutions than the best-known solution.