A Reach and Bound algorithm for acyclic dynamic-programming networks

✍ Scribed by Matthew D. Bailey; Robert L. Smith; Jeffrey M. Alden

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 111 KB
• Volume: 52
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/net.20219

✦ Synopsis

Abstract

Node pruning is a commonly used technique for solution acceleration in a dynamic‐programming network. In pruning, nodes are adaptively removed from the dynamic programming network when they are determined not to lie on an optimal path. We introduce an ε‐pruning condition that extends pruning to include a possible error in the pruning step. This results in a greater reduction of the computation time; however, as a result of the inclusion of this error, the solution can be suboptimal or possibly infeasible. This condition requires the ability to compare the costs of an optimal path from a node to a terminal node. Therefore, we focus on the class of acyclic dynamic programming networks with monotonically decreasing optimal costs‐to‐go. We provide an easily implementable algorithm, Reach and Bound, which maintains feasibility and bounds the solution's error. We conclude by illustrating the applicability of Reach and Bound on a problem of single location capacity expansion. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008