Heterogeneous Min-Max Multi-Vehicle Multi-Depot Traveling Salesman Problem: Heuristics and Computational Results

TL;DR

This paper introduces a heuristic for a complex multi-vehicle routing problem involving heterogeneous vehicles and multiple depots, with extensive computational testing on varied instances to improve solution quality and efficiency.

Contribution

A novel three-stage heuristic for the heterogeneous min-max multi-vehicle multi-depot TSP, including multiple neighborhood searches and initial solution methods, benchmarked against existing heuristics.

Findings

Two heuristics outperform previous methods in solution quality.

The proposed methods are effective across diverse instance types.

Computational results demonstrate improved efficiency and solution quality.

Abstract

In this paper, a heuristic for a heterogeneous min-max multi-vehicle multi-depot traveling salesman problem is proposed, wherein heterogeneous vehicles start from given depot locations and need to cover a given set of targets. In the considered problem, vehicles can be structurally heterogeneous due to different vehicle speeds and/or functionally heterogeneous due to different vehicle-target assignments originating from different sensing capabilities of vehicles. The proposed heuristic for the considered problem has three stages: an initialization stage to generate an initial feasible solution, a local search stage to improve the incumbent solution by searching through different neighborhoods, and a perturbation/shaking stage, wherein the incumbent solution is perturbed to break from a local minimum. In this study, three types of neighborhood searches are employed. Furthermore, two different methods for constructing the initial feasible solution are considered, and multiple variations in the neighborhoods considered are explored in this study. The considered variations and construction methods are evaluated on a total of 128 instances generated with varying vehicle-to-target ratios, distribution for generating the targets, and vehicle-target assignment and are benchmarked against the best-known heuristic for this problem. Two heuristics were finally proposed based on the importance provided to objective value or computation time through extensive computational studies.