Abstract
Amid the most widely studied NP-hard combinatorial optimization problems, the Probabilistic Traveling Salesman Problem (PTSP), which is an extension of the well-known Traveling Salesman Problem, offers a fundamental basis for analyzing the stochastic impacts in routing problems. In this paper, a new meta-heuristic approach, Genetic Minimum Matrix Search (GMMS), is introduced for the solution of the Probabilistic Traveling Salesman Problem. This evolutionary algorithm is founded upon the Minimum Matrix Search construction algorithm that uses dimension reduction in the matrix edge set to obtain a reduce matrix network within which lies the optimal solution in whole or clusters. GMMS uses family competitive metamorphosis and short-term memory selection to maintain the diversity of the population in each generation which is useful in avoiding local optimum. The proposed evolutionary algorithm showed very satisfactory results in testing on well-known benchmark problems from TSPLIB. Comparisons is performed with the results of numerous implementations of well-known meta-heuristic approaches from the literature, such as; Honey Bee Mating Optimization, Particle Swarm Optimization, Tabu Search, Greedy Randomized Adaptive Search Procedure, Genetic Algorithm, Ant Colony Optimization, etc. Having found 9 new best solution out of 20 cases, the computational study shows that the GMMS algorithm is a competitive tool for solving the PTSP.