Dynamic Multi-Vehicle Routing with Multiple Classes of Demands

In this paper we study a dynamic vehicle routing problem in which there are multiple vehicles and multiple classes of demands. Demands of each class arrive in the environment randomly over time and require a random amount of on-site service that is characteristic of the class. To service a demand, one of the vehicles must travel to the demand location and remain there for the required on-site service time. The quality of service provided to each class is given by the expected delay between the arrival of a demand in the class, and that demand's service completion. The goal is to design a routing policy for the service vehicles which minimizes a convex combination of the delays for each class. First, we provide a lower bound on the achievable values of the convex combination of delays. Then, we propose a novel routing policy and analyze its performance under heavy load conditions (i.e., when the fraction of time the service vehicles spend performing on-site service approaches one). The policy performs within a constant factor of the lower bound (and thus the optimal), where the constant depends only on the number of classes, and is independent of the number of vehicles, the arrival rates of demands, the on-site service times, and the convex combination coefficients.Comment: Extended version of paper presented in American Control Conference 200

Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dimensionality problem by exploiting properties of an optimal solution. We also obtain a Linear Programming (LP) formulation allowing us to decompose it into two simpler problems yielding near-optimal solutions. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into "subflows". We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control and Automation, MED'1

An Artificial Life Approach to Multi-Vehicle Routing Problem

This paper proposes a new method for multi-vehicle routing problems (MVRP). MVRP is to determine the optimal routes for all vehicles through the minimal total tour length subject to vehicle capacity constraints and other restrictions. All nodes have some packages to deliver to other nodes before vehicles start. Each time a vehicle arrives at a node, it drops off packages and picks up others. Vehicles go on moving until all packages in the area are completely delivered. The aim of this paper is to indicate that MVRP can be solved by artificial life, which is a methodology of the modern heuristics such as genetic algorithms, tabu search or simulated annealing. The proposed approach is basis on a point of view that a vehicle can be regarded as an artificial life. For instance, picking up goods is corresponded to the act of predatory, and dropping off ones to the act of excretory. The method makes use of three indicators to characterize the artificial life. First is a moving length, second is a loading tendency, and last is a standing by at the same node. Each indicator takes one integer value among zero to 99. If the value of moving length indicator is relatively small, then it means that the vehicle tends to prefer a short-distance movement to a long-distance. Other two indicators can be made similarly interpretation