A Hierarchical Market Solution to the Min-Max Multiple Depots Vehicle Routing Problem

The problem of assigning a group of Unmanned Aerial Vehicles (UAVs) to perform spatially distributed tasks often requires that the tasks will be performed as quickly as possible. This problem can be defined as the Min–Max Multiple Depots Vehicle Routing Problem (MMMDVRP), which is a benchmark combinatorial optimization problem. In this problem, UAVs are assigned to service tasks so that each task is serviced once and the goal is to minimize the longest tour performed by any UAV in its motion from its initial location (depot) to the tasks and back to the depot. This problem arises in many time-critical applications, e.g. mobile targets assigned to UAVs in a military context, wildfire fighting, and disaster relief efforts in civilian applications. In this work, we formulate the problem using Mixed Integer Linear Programming (MILP) and Binary Programming and show the scalability limitation of these formulations. To improve scalability, we propose a hierarchical market-based solution (MBS). Simulation results demonstrate the ability of the MBS to solve large scale problems and obtain better costs compared with other known heuristic solution.

[1]  Gilbert Laporte,et al.  An adaptive memory heuristic for a class of vehicle routing problems with minmax objective , 1997, Comput. Oper. Res..

[2]  Ann Melissa Campbell,et al.  Routing for Relief Efforts , 2008, Transp. Sci..

[3]  Manish Kumar,et al.  On the Scalability of the Market-Based Solution to the Multiple Traveling Salesmen Problem , 2012, Infotech@Aerospace.

[4]  Manish Kumar,et al.  A Binary Programming Solution to the Multiple-Depot, Multiple Traveling Salesman Problem with Constant Profits , 2012, Infotech@Aerospace.

[5]  Chunyu Ren Heuristic Algorithm for Min-max Vehicle Routing Problems , 2012, J. Comput..

[6]  Nicholas Ernest Fuzzy Logic Clustering of Multiple Traveling Salesman Problem for Self -Crossover Based Genetic Algorithm , 2012 .

[7]  Han-Lim Choi,et al.  Consensus-Based Decentralized Auctions for Robust Task Allocation , 2009, IEEE Transactions on Robotics.

[8]  Y. Shoham Introduction to Multi-Agent Systems , 2002 .

[9]  Timo Latvala,et al.  On Scaling Multi-Agent Task Reallocation Using Market-Based Approach , 2007, First International Conference on Self-Adaptive and Self-Organizing Systems (SASO 2007).

[10]  Gang Yu,et al.  A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows , 2002, Transp. Sci..

[11]  Nicos Christofides,et al.  The vehicle routing problem , 1976, Revue française d'automatique, informatique, recherche opérationnelle. Recherche opérationnelle.

[12]  Juliane Jung,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[13]  Hong Zhang,et al.  Cooperative Decision-Making in Decentralized Multiple-Robot Systems: The Best-of-N Problem , 2009, IEEE/ASME Transactions on Mechatronics.

[14]  Manish Kumar,et al.  An ant colony optimization technique for solving min-max Multi-Depot Vehicle Routing Problem , 2013, Swarm Evol. Comput..

[15]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[16]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics) , 2007 .

[17]  Chunyu Ren,et al.  Solving Min-Max Vehicle Routing Problem , 2011, J. Softw..

[18]  T. Bektaş The multiple traveling salesman problem: an overview of formulations and solution procedures , 2006 .

[19]  Kelly Cohen,et al.  Fuzzy Clustering Based Genetic Algorithm for the Multi-Depot Polygon Visiting Dubins Multiple Traveling Salesman Problem , 2012, Infotech@Aerospace.

[20]  John Gunnar Carlsson,et al.  Solving Min-Max Multi-Depot Vehicle Routing Problem ⁄ , 2007 .

[21]  Tal Shima,et al.  Multiple task assignments for cooperating uninhabited aerial vehicles using genetic algorithms , 2006, Comput. Oper. Res..

[22]  Manish Kumar,et al.  Ant colony optimization technique to solve the min-max Single Depot Vehicle Routing Problem , 2011, Proceedings of the 2011 American Control Conference.

[23]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[24]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[25]  Manish Kumar,et al.  Market-Based Solution to the Allocation of Tasks to Agents , 2011, Complex Adaptive Systems.

[26]  Michel Gendreau,et al.  Traveling Salesman Problems with Profits , 2005, Transp. Sci..

[27]  Manish Kumar,et al.  A Market-based Solution to the Multiple Traveling Salesmen Problem , 2013, J. Intell. Robotic Syst..