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.
This work was supported by EPSRC research grant GR/M90641 and ILOG SA.
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Beck, J.C., Prosser, P., Selensky, E. (2002). Graph Transformations for the Vehicle Routing and Job Shop Scheduling Problems. In: Corradini, A., Ehrig, H., Kreowski, H.J., Rozenberg, G. (eds) Graph Transformation. ICGT 2002. Lecture Notes in Computer Science, vol 2505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45832-8_7
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DOI: https://doi.org/10.1007/3-540-45832-8_7
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