A multiobjective non-dominated sorting genetic algorithm (NSGA-II) for the Multiple Traveling Salesman Problem

Abstract

This paper considers a multi-objective version of the Multiple Traveling Salesman Problem (MOmTSP). In particular, two objectives are considered: the minimization of the total traveled distance and the balance of the working times of the traveling salesmen. The problem is formulated as an integer multi-objective optimization model. A non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the MOmTSP. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. Tests on real world instances and instances adapted from the literature show the effectiveness of the proposed algorithm.

Tackling the Bi-criteria Facet of Multiple Traveling Salesman Problem with Ant Colony Systems

“…For each instance, the depot city is considered to be the first city from the list of cities. The description of these SD-MTSP instances 4 along with the obtained results for the MinMax formulation are publicly available as MTSPLIB 5 . It should be noted that not all problem instances were solved to optimality because of imposed time limits (for difficult problem instances set to 8 days); in such cases, in addition to the best found solution, a bound on the optimal value is given which is a worst-case estimate of how far the solution reported is from the optimal solution.…”

“…A multi-objective evolutionary algorithm enhanced with a post-optimization phase that follows a path-relinking scheme is proposed for solving the problem. In [5] a different bi-objective version of the SD-MTSP is considered. The first objective is to minimize the distance traveled by all salesmen while the second one is to balance the working times of the salesmen.…”

Supply chain optimization with variable demand by considering financial criteria and scenarios

“…Furthermore, other methodologies to solve lineal stochastic programing problems might be considered. Finally, decisions on transportation mode, type of vehicles and routes to be performed together, might be included in the mathematical model such as considered in [30][31][32][33].…”

A multi-objective Pareto ant colony algorithm for the Multi-Depot Vehicle Routing problem with Backhauls

“…Finally, an evolutionary approach and a fuzzy programming for the multi-objective vehicle routing problems with backhauls were presented by García-Nájera et al (2015) and Yalcın and Erginel (2015), respectively. Other multiobjective algorithms proposed for solving related logistic combinatorial problems could be consulted in Nezhad et al (2013), Mortezaei and JabalAmeli (2011), Mohammadi et al (2011), Rao and Patel (2014, Yazdian andShahanaghi (2011), Escobar et al (2013), Escobar et al (2014b), Escobar et al (2015) and Bolaños et al (2015).…”