Chu–Beasley Genetic Algorithm and Google’s OR-Tools for the Bi-Objective Multiple Traveling Salesman Problem with Weighted Arcs
摘要
The Multiple Traveling Salesman Problem (MTSP) can be applied to logistics industry problems that do not involve freight transportation, such as home service delivery associated with utility operations. This article presents a methodology to address the bi-Objective Multiple Traveling Salesman Problem (BMTSP), accounting for pollutant emissions and minimizing cost/time using weighted arcs. The bi-objective approach combines the objectives in a weighted matrix using a scalarization method to obtain local Pareto-optimal fronts. The effects of pollution are quantified by the difference in altitude between customers, with steeper arcs generating higher emissions. The study compares two distance matrices: one calculated using the Haversine formula for spherical distances, and another using Google Maps services to account for traffic and travel time. The results obtained using a weighted matrix are compared with simulated results of common inefficient logistics scenarios. A Chu-Beasley genetic algorithm with the Or-Opt operator and Google’s OR-Tools is implemented to solve the bi-objective Multiple TSP as a reference and state-of-the-art methodology. The algorithms were compared in terms of solution quality, time efficiency, and projected area of the Pareto frontier, also known as hypervolume. Several test instances of customers were used to simulate the operations of a power distribution company in real-world logistics scenarios, including fault response and maintenance services for power grids.