An Enhanced Dynamic Slope Scaling Procedure with Tabu Scheme for Fixed Charge Network Flow Problems

Abstract

A heuristic algorithm for solving large scale fixed charge network flow problems (FCNFP) based on the dynamic slope scaling procedure (DSSP) and tabu search strategies is presented. The proposed heuristic integrates the DSSP with short-term memory intensification and long-term memory diversification mechanisms in the tabu scheme to improve the performance of the pure DSSP. With the feature of dynamically evolving memory, the enhanced DSSP evaluates the solutions in the search history and iteratively adjusts the linear factors in the linear approximation of the FCNFP to produce promising search neighborhoods for good quality solutions. The comprehensive numerical experiments on various test problems ranging from sparse to dense network structures are reported. The overall comparison of the pure DSSP, the enhanced DSSP, and branch and bound (B&B by cutting-edge MIP optimizer in CPLEX) is shown in terms of solution quality and CPU time. The results show that the enhanced DSSP approach has a higher solution quality than the pure DSSP for larger scale problems.