Article ID Journal Published Year Pages File Type
476763 European Journal of Operational Research 2013 14 Pages PDF
Abstract

This paper addresses the elementary shortest path problem with forbidden paths. The main aim is to find the shortest paths from a single origin node to every other node of a directed graph, such that the solution does not contain any path belonging to a given set (i.e., the forbidden set). It is imposed that no cycle can be included in the solution. The problem at hand is formulated as a particular instance of the shortest path problem with resource constraints and two different solution approaches are defined and implemented. One is a Branch & Bound based algorithm, the other is a dynamic programming approach. Different versions of the proposed solution strategies are developed and tested on a large set of test problems.

► The elementary shortest path problem with forbidden paths is addressed. ► A mathematical formulation of the problem is developed. ► A B&B based algorithm and dynamic programming approaches are proposed. ► The B&B approach outperforms the dynamic programming methods on small-size problems. ► The dynamic programming methods behave the best on large-size test problems.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science (General)
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