The dual-path fixing strategy and its application to the set-covering problem

TL;DR

This paper presents a dual-path fixing strategy that leverages dual algorithms to improve the efficiency and effectiveness of solving set-covering problems via branch-and-bound, outperforming traditional fixing methods.

Contribution

The paper introduces a novel dual-path fixing strategy that enhances variable fixing in branch-and-bound, combining power and speed by exploiting dual algorithms for relaxations.

Findings

Successfully tested on set-covering instances from literature

Outperforms standard fixing strategies in efficiency

Enhances branch-and-bound success rate

Abstract

We introduce the dual-path fixing strategy to exploit dual algorithms for solving relaxations of mixed-integer nonlinear-optimization problems. Such dual algorithms are naturally applied in the context of branch-and-bound, and eventual impact on the success of branch-and-bound is our strong motivation. Our fixing strategy aims to be more powerful than the common strategy of fixing variables based on a single dual-feasible solution (e.g., standard reduced-cost fixing for mixed-integer linear optimization), but to be much faster than ``strong fixing'', essentially requiring no more time than that of the dual algorithm that we exploit. We have successfully tested our ideas on mixed-integer linear-optimization set-covering instances from the literature, in the context of the dual-simplex method applied to the continuous relaxations.