Algorithms for Multiple Vehicle Routing Problems

Abstract

Surveillance and monitoring applications require a collection of heterogeneous vehicles to visit a set of targets. This dissertation considers three fundamental routing problems involving multiple vehicles that arise in these applications. The main objective of this dissertation is to develop novel approximation algorithms for these routing problems that find feasible solutions and also provide a bound on the quality of the solutions produced by the algorithms.

The first routing problem considered is a multiple depot, multiple terminal, Hamiltonian Path problem. Given multiple vehicles starting at distinct depots, a set of targets and terminal locations, the objective of this problem is to find a vertex-disjoint path for each vehicle such that each target is visited once by a vehicle, the paths end at the terminals and the sum of the distances travelled by the vehicles is a minimum. A 2-approximation algorithm is presented for this routing problem when the costs are symmetric and satisfy the triangle inequality. For the case where all the vehicles start from the same depot, a 5/3-approximation algorithm is developed.

The second routing problem addressed in this dissertation is a multiple depot, heterogeneous traveling salesman problem. The objective of this problem is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances travelled by the vehicles is minimized. A primal-dual algorithm with an approximation ratio of 2 is presented for this problem when the vehicles involved are ground vehicles that can move forwards and backwards with a constraint on their minimum turning radius.

Finally, this dissertation addresses a multiple depot heterogeneous traveling salesman problem when the travel costs are asymmetric and satisfy the triangle inequality. An approximation algorithm and a heuristic is developed for this problem with simulation results that corroborate the performance of the proposed algorithms. All the main algorithms presented in the dissertation advance the state of art in the area of approximation algorithms for multiple vehicle routing problems.

This dissertation has its value for providing approximation algorithms for the routing problems that involves multiple vehicles with additional constraints. Some algorithms have constant approximation factor, which is very useful in the application but difficult to find. In addition to the approximation algorithms, some heuristic algorithms were also proposed to improve solution qualities or computation time.