Dynamic slope scaling and trust interval techniques for solving concave piecewise linear network flow problems

Abstract

In this paper, we propose an efficient heuristic approach for solving concave Piecewise Linear Network Flow Problems (PLNFP) in which the cost is separable and each arc cost is concave piecewise linear function of the total flow along the arcs. The problem is well known to be WNP-hard and exact global optimization algorithms are of limited use. In this paper, PLNFP is transformed into an equivalent Fixed-Charge Network Flow Problem (FCNFP) using an arc separation procedure, and we develop an algorithm combining the Dynamic Slope Scaling Procedure (DSSP) and Trust Interval techniques. Due to the fast growing size of the transformed FCNFP, exact branch-and-bound methods are not able to handle the problems of practical size. Based on the dynamic slope scaling algorithm developed for solving FCNFP in previous work, we add a trust interval technique based on solution tendencies to speed up the algorithm. The numerical experiments show that the proposed algorithm is quite efficient and its performance is very stable. © 2000 John Wiley & Sons, Inc.