Deep Dual-Optimal Inequalities for Generalized Capacitated Fixed-Charge Network Design Problems

14 Pages Posted: 23 Nov 2020

See all articles by David Franz Koza

David Franz Koza

Vattenfall Vindkraft A/S

Erik Orm Hellsten

affiliation not provided to SSRN

David Pisinger

Technical University of Denmark - Management Engineering

Date Written: October 4, 2020

Abstract

Capacitated fixed-charge network design problems and generalizations, such as service network design problems, have a wide range of applications but are known to be very difficult to solve. Many exact and heuristic algorithms to solve these problems rely on column-and-row generation (CRG), which frequently suffer from primal degeneracy. We present a set of dual inequalities, equivalent to a simple primal relaxation, that speed up CRG algorithms for generalized capacitated fixed charge network design problems. We investigate the impact of the dual inequalities theoretically as well as experimentally. For practical applications, the presented technique is simple to implement, has no additional computational cost and can accelerate CRG by orders of magnitude, depending on the problem size and structure.

Keywords: Capacitated Fixed-Charge Network Design, Deep Dual Optimal Inequalities, Dual Stabilization, Column Generation, Branch-Price-and-Cut

Suggested Citation

Koza, David Franz and Hellsten, Erik Orm and Pisinger, David, Deep Dual-Optimal Inequalities for Generalized Capacitated Fixed-Charge Network Design Problems (October 4, 2020). Available at SSRN: https://ssrn.com/abstract=3704539 or http://dx.doi.org/10.2139/ssrn.3704539

David Franz Koza (Contact Author)

Vattenfall Vindkraft A/S ( email )

Jupitervej 6
Kolding, 6000
Denmark

Erik Orm Hellsten

affiliation not provided to SSRN

David Pisinger

Technical University of Denmark - Management Engineering ( email )

Produktionstorvet 424
room 043
Kgs. Lyngby, 2800
Denmark

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