Memetic algorithm based on sequential variable neighborhood descent for the minmax multiple traveling salesman problem

Abstract

In this paper, we consider the multiple traveling salesman problem (MTSP) with the minmax objective, which includes more than one salesman to serve a set of cities while minimizing the maximum distance traveled by any salesman. For this problem, we have proposed a novel memetic algorithm, which integrates with a sequential variable neighborhood descent that is a powerful local search procedure to exhaustively search the areas near the high-quality solutions. However, there are some inefficient neighborhoods in the existing sequential variable neighborhood descent for the minmax MTSP, which could restrict the search performance. Therefore, we have redefined a new neighborhood sequence where only the neighborhoods that move cities from one tour to another unidirectionally are considered. Computational experiments on a wide range of benchmark problems within an acceptable time limit show that compared with six existing algorithms, the proposed algorithm is better than the other algorithms in terms of three aspects, including the precision, the robustness and the convergence speed. Meanwhile, we have also investigated the total distance traveled by all the salesmen when optimizing the minmax objective, and the results show that in comparison with the six existing algorithms, the proposed algorithm has a better or at least competitive capacity to maintain the total distance as short as possible. Furthermore, two kinds of statistical tests are utilized to examine the significance of the presented results, indicating the superiority of the proposed algorithm over the other algorithms on the minmax objective.

Turn-minimizing multirobot coverage

“…Solving the TSP on the complete weighted graph consisting of all rank endpoints and midpoints and the travel times between them gives a time-minimizing path on the graph (Figure 12 left). For multirobot coverage, we can find paths for each robot by solving the minmax m-TSP [30], [31], [32] on the same graph to minimize the time taken by the slowest robot (Figure 12 right). There exist variants of both the TSP and m-TSP which either specify or do not specify the robots' start and end locations.…”

Towards a Distributed Solution to the Multi-Robot Task Allocation Problem with Energetic and Spatiotemporal Constraints

“…The MRTA problem considered in this paper deals with energetic constraints. In the literature, there are several approaches that solve the TSP and its variants [22,34,51,52].…”

Optimize Grouping and Path of Pylon Inspection in Power System

“…For example, with the help of k-means clustering, the path planning is carried out for each cluster [46]- [48]. Nevertheless, due to the imbalance workload, recently, the problem associated with balancing the workload for MTSP has attracted increasing attention, such as minimizing the maximum journey or balancing the number of destinations of travel agents [49]- [51]. Comparing with balancing the journey or the number of travel destinations, it is fairer to balance the work time.…”