Discrete Marine Predators Algorithm for Symmetric Travelling Salesman Problem

This paper addresses the well-known NP-hard problem, the Symmetric Travelling Salesman Problem (STSP), which has numerous applications in logistics and graph theory. To solve this complex problem, a discrete version of the Marine Predators Algorithm (D-MPA) is introduced. Although MPA has been extensively studied for various optimization problems and real-world applications, its use in routing problems, particularly TSP, remains relatively unexplored. To adapt MPA for STSP, the positions of individuals are initially updated using the classical MPA algorithm. The continuous values generated by the classical MPA are then converted to discrete values, followed by the application of a permutation operator to maintain diversity in the population. In addition, a local search algorithm, 2-opt, is applied to further improve the results for STSP instances. The effectiveness of the proposed algorithm is demonstrated on STSP benchmark instances of sizes ranging from 14 to 439. The performance of D-MPA is compared against several existing algorithms, including the Genetic Algorithm (GA), Bat Algorithm (BA), Discrete Firefly Algorithm (DFA), Evolutionary Simulated Annealing (ESA), Island-Based Distributed Genetic Algorithm (IDGA), Discrete Imperialist Competitive Algorithm (DICA), and Discrete Grey Wolf Optimization (DGWO). To ensure an unbiased and rigorous comparison, descriptive statistics such as mean and standard deviation are used, and a Wilcoxon Signed-Rank test is conducted for statistical validation. The results demonstrate that D-MPA not only competes, but also consistently outperforms these algorithms, making it a valuable resource for the research community.