A label correcting approach for solving bicriterion shortest-path problems

Abstract

This article contributes with a very fast algorithm for solving the bicriterion shortest-path problem. By imposing some simple domination conditions, we reduce the number of iterations needed to find all the efficient (Pareto optimal) paths in the network. We have implemented the algorithm and tested it with the Label Correcting algorithm. We have also made a theoretical argument of the performance of all the existing algorithms, in order to rank them by performance. Included is a discussion on the structure of random generated networks, generated with two different methods, and of the characteristics of these networks. Scope and purpose: Consider a network through which you have to send some commodities from a source node s to a terminal node t in the cheapest way. If you have only a single attribute on each link, the problem is easily solved with e.g. Dijkstra's shortest-path algorithm. If each link is assigned two attributes, e.g. cost and travel time, the problem of finding all efficient s - t paths is much harder. The problem often occurs as a subproblem in transportation models and combinatorial optimization. We have examined the existing algorithms for the bicriterion shortest-path (BSP) problem, and made a ranking based on their computational complexity. By imposing preprocessing conditions on the fastest algorithm, we have been able to reduce cpu-times considerably. The structure of random networks turned out to be important for the computational results, and has therefore been investigated. A new program for generating random networks is presented. (C) 2000 Elsevier Science Ltd. All rights reserved.