Parallel and Serial Algorithms for Vehicle Routing Problems

The vehicle routing problem (VRP) is a widely studied combinatorial optimization problem that has many applications. Due to its intrinsic difficulty and the size of problems encountered in practice, most solution methods for the VRP are heuristic in nature and lead to high quality, yet probably not optimal solutions. When one considers the additional constraints that can be encountered in practice, the need for high quality heuristic methods is clear. We present two new variations of the VRP suggested to us by industry contacts, the Consistent VRP and the Balanced Billing Cycle VRP. We develop solution algorithms that incorporate heuristic methods as well as integer programming. Additionally, we develop a highly effective cooperative parallel algorithm for the classical VRP that generates new best solutions to a number of well-studied benchmark instances. We present extensive computational results and describe the C/C++ library that we developed to solve these vehicle routing problems. We describe the features and design philosophy behind this library and discuss how the framework can be used to implement additional heuristic algorithms and incorporate additional constraints

A Genetic Algorithm for UAV Routing Integrated with a Parallel Swarm Simulation

This research investigation addresses the problem of routing and simulating swarms of UAVs. Sorties are modeled as instantiations of the NP-Complete Vehicle Routing Problem, and this work uses genetic algorithms (GAs) to provide a fast and robust algorithm for a priori and dynamic routing applications. Swarms of UAVs are modeled based on extensions of Reynolds\u27 swarm research and are simulated on a Beowulf cluster as a parallel computing application using the Synchronous Environment for Emulation and Discrete Event Simulation (SPEEDES). In a test suite, standard measures such as benchmark problems, best published results, and parallel metrics are used as performance measures. The GA consistently provides efficient and effective results for a variety of VRP benchmarks. Analysis of the solution quality over time verifies that the GA exponentially improves solution quality and is robust to changing search landscapes - making it an ideal tool for employment in UAV routing applications. Parallel computing metrics calculated from the results of a PDES show that consistent speedup (almost linear in many cases) can be obtained using SPEEDES as the communication library for this UAV routing application. Results from the routing application and parallel simulation are synthesized to produce a more advanced model for routing UAVs

Parallel local search for the time-constrained traveling salesman problem

In the time-constrained TSP, each city has to be visited within a given time interval. Such `time windows' often occur in practice. When practical vehicle routing problems are solved in an interactive setting, one needs algorithms for the time-constrained TSP that combine a low running time with a high solution quality. Local search seems a natural approach. It is not obvious, however, how local search for the TSP has to be implemented so as to handle time windows efficiently. This is particularly true when parallel computer architectures are available. We consider these questions

A Computational Study of Genetic Crossover Operators for Multi-Objective Vehicle Routing Problem with Soft Time Windows

The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simple, but effective local search approach for multi-objective combinatorial optimization problems

Capacitated Vehicle Routing with Non-Uniform Speeds

The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having non-uniform speeds (that we call Heterogenous CVRP), and present a constant-factor approximation algorithm. The technical heart of our result lies in achieving a constant approximation to the following TSP variant (called Heterogenous TSP). Given a metric denoting distances between vertices, a depot r containing k vehicles with possibly different speeds, the goal is to find a tour for each vehicle (starting and ending at r), so that every vertex is covered in some tour and the maximum completion time is minimized. This problem is precisely Heterogenous CVRP when vehicles are uncapacitated. The presence of non-uniform speeds introduces difficulties for employing standard tour-splitting techniques. In order to get a better understanding of this technique in our context, we appeal to ideas from the 2-approximation for scheduling in parallel machine of Lenstra et al.. This motivates the introduction of a new approximate MST construction called Level-Prim, which is related to Light Approximate Shortest-path Trees. The last component of our algorithm involves partitioning the Level-Prim tree and matching the resulting parts to vehicles. This decomposition is more subtle than usual since now we need to enforce correlation between the size of the parts and their distances to the depot