A New Memetic Algorithm to Solve the Stochastic TSP

Abstract

We consider in this work the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> -city Traveling Salesman Problem (TSP), where the travel times between the cities are non-deterministic. Our purpose is to compute the shortest but also most reliable TSP tours. We formulate the problem as a bi-objective optimization problem in which the travel time and its variation are considered under minimization. To efficiently solve the problem, we introduce a new memetic algorithm based on a combination of two meta-heuristics: the population-based Genetic Algorithm (GA) and the single solution-based Variable Neighborhood Search (VNS). We compare our approach with an exact method based on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\epsilon$</tex> -constraint. We also compare our results with the well-known Non-Dominated Sorting Genetic Algorithm (NSGA2). Solving real-world instances ranging from 29 to 101 cities has shown that our algorithm provides higher quality solutions compared to NSGA2 both in terms of convergence toward the optimal Pareto front and the diversity of the obtained solutions. Moreover, our algorithm provided more optimal non-dominated solutions than the exact approach in a shorter amount of computational time.