Two phase heuristic algorithm for the multiple-travelling salesman problem

Abstract

The multiple-travelling salesman problem (MTSP) is a computationally complex combinatorial optimisation problem, with several theoretical and real-world applications. However, many state-of-the-art heuristic approaches intended to specifically solve MTSP, do not obtain satisfactory solutions when considering an optimised workload balance. In this article, we propose a method specifically addressing workload balance, whilst minimising the overall travelling salesman's distance. More specifically, we introduce the two phase heuristic algorithm (TPHA) for MTSP, which includes an improved version of the K -means algorithm by grouping the visited cities based on their locations based on specific capacity constraints. Secondly, a route planning algorithm is designed to assess the ideal route for each above sets. This is achieved via the genetic algorithm (GA), combined with the roulette wheel method with the elitist strategy in the design of the selection process. As part of the validation process, a mobile guide system for tourists based on the Baidu electronic map is discussed. In particular, the evaluation results demonstrate that TPHA achieves a better workload balance whilst minimising of the overall travelling distance, as well as a better performance in solving MTSP compared to the route planning algorithm solely based on GA.

Ant Colony Optimization With an Improved Pheromone Model for Solving MTSP With Capacity and Time Window Constraint

“…As Table 3 shown, new ACO can get better results than normal ACO. Next, we compare our method with other algrithems such as improved genetic algorithms (IGA) [39], invasive weed optimization algorithm (IWO) [40], improved partheno genetic algorithms (IPGA) [40] and the instance in [29] and [41]. The results of this comparison are shown in the Table 4.…”

Region Division in Logistics Distribution With a Two-Stage Optimization Algorithm

“…Subramaniam and Gounaris extended the definition of the TSP with time windows to allow a waiting time at each customer location and to incorporate maximum route duration limits [15]. Then, the constraints on a minimal or maximum number of nodes that a traveler must visit are also common [16]- [18]. In addition, some road network-related constraints such as multi depot [19], asymmetric network [20] and so on are also included.…”

“…Majd solved MTSP by K-means and crossover based modified ACO algorithms [38]. Xu et al introduced the two phase heuristic algorithm, which included the K-means algorithm by grouping the visited cities based on their locations, and the genetic algorithm to assess the idea route for each above set achieved [18]. Above all, the algorithms could handle the special constraints which we encountered in industrial projects.…”

Modified Ant Colony Optimization Algorithm for Multiple-vehicle Traveling Salesman Problems

“…Several researchers have discussed the MTSP. For example, Xu et al [6] described a Two Phase Heuristic Algorithm (TPHA) for MTSP. They achieved a balanced workload and minimized the total distance, that a salesman takes, by using a K-means algorithm in the first phase to group all cities into several subsets depending on their locations and by using a genetic algorithm (GA) in the second phase to assess the route for each subset.…”