A Self-Organizing Extreme-Point Tabu-Search Algorithm for Fixed Charge Network Problems with Extensions

TL;DR

This paper introduces a novel self-organizing ghost image algorithm for fixed-charge network flow problems, significantly improving solution speed while maintaining solution quality across large benchmark instances.

Contribution

The paper presents a new self-organizing ghost image algorithm that efficiently solves fixed-charge network flow problems, outperforming existing methods in speed and scalability.

Findings

Achieves solutions at least 700 times faster than Cplex 12.8 on large instances.

Performs comparably to the best existing methods on benchmark problems.

Effectively solves large fixed-charge network problems across various applications.

Abstract

We propose a new self-organizing algorithm for fixed-charge network flow problems based on ghost image (GI) processes as proposed in Glover (1994) and adapted to fixed-charge transportation problems in Glover, Amini and Kochenberger (2005). Our self-organizing GI algorithm iteratively modifies an idealized representation of the problem embodied in a parametric ghost image, enabling all steps to be performed with a primal network flow algorithm operating on the parametric GI. Computational tests are carried out on an extensive set of benchmark problems which includes the previous largest set in the literature, comparing our algorithm to the best methods previously proposed for fixed-charge transportation problems, though our algorithm is not specialized to this class. We also provide comparisons for additional more general fixed-charge network flow problems against Cplex 12.8 to demonstrate that the new self-organizing GI algorithm is effective on large problem instances, finding solutions with statistically equivalent objective values at least 700 times faster. The attractive outcomes produced by the current GI/TS implementation provide a significant advance in our ability to solve fixed-cost network problems efficiently and invites its use for larger instances from a variety of application domains.