A $\Delta$-evaluation function for column permutation problems

TL;DR

This paper introduces a new $$-evaluation method for column permutation problems on sparse binary matrices, enhancing local search algorithms' efficiency, especially for large, dense instances in graph theory and manufacturing.

Contribution

A novel $$-evaluation technique tailored for column permutation problems, improving computational efficiency in local search methods for complex NP-hard problems.

Findings

The $$-evaluation method is generally competitive with existing methods.

It is particularly effective for large and dense problem instances.

The method can be easily integrated into existing local search algorithms.

Abstract

In this study, a new $\Delta$-evaluation method is introduced for solving a column permutation problem defined on a sparse binary matrix with the consecutive ones property. This problem models various $\mathcal{NP}$-hard problems in graph theory and industrial manufacturing contexts. The computational experiments compare the processing time of the $\Delta$-evaluation method with two other methods used in well-known local search procedures. The study considers a comprehensive set of instances of well-known problems, such as Gate Matrix Layout and Minimization of Open Stacks. The proposed evaluation method is generally competitive and particularly useful for large and dense instances. It can be easily integrated into local search and metaheuristic algorithms to improve solutions without significantly increasing processing time.