Graph transformations for the vehicle routing and job shop scheduling problems

Beck, J.C., Prosser, P. and Selensky, E. (2002) Graph transformations for the vehicle routing and job shop scheduling problems. Lecture Notes in Computer Science, 2502, pp. 60-74.

Abstract

The vehicle routing problem (VRP) and job shop scheduling problem (JSP) are two common combinatorial problems that can be naturally represented as graphs. A core component of solving each problem can be modeled as finding a minimum cost Hamiltonian path in a complete weighted graph. The graphs extracted from VRPs and JSPs have different characteristics however, notably in the ratio of edge weight to node weight. Our long term research question is to determine the extent to which such graph characteristics impact the performance of algorithms commonly applied to VRPs and JSPs. As a preliminary step, in this paper we investigate five transformations for complete weighted graphs that preserve the cost of Hamiltonian paths. These transformations are based on increasing node weights while reducing edge weights or the inverse. We demonstrate how the transformations affect the ratio of edge to node weight and how they change the relative weights of edges at a node. Finally, we conjecture how the different transformations will impact the performance of existing VRP and JSP solving techniques.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Prosser, Dr Patrick
• Authors: Beck, J.C., Prosser, P., and Selensky, E.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Lecture Notes in Computer Science
• Publisher: Springer
• ISSN: 0302-9743
• Copyright Holders: Copyright © 2002 Springer
• First Published: First published in Lecture Notes in Computer Science 2502:60-74
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher