A diving heuristic for mixed-integer problems with unbounded semi-continuous variables

Fuente: arXiv
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Autores principales: Halbig, Katrin, Hoen, Alexander, Gleixner, Ambros, Witzig, Jakob, Weninger, Dieter
Formato: Preprint
Publicado: 2024
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author Halbig, Katrin
Hoen, Alexander
Gleixner, Ambros
Witzig, Jakob
Weninger, Dieter
author_facet Halbig, Katrin
Hoen, Alexander
Gleixner, Ambros
Witzig, Jakob
Weninger, Dieter
contents Semi-continuous decision variables arise naturally in many real-world applications. They are defined to take either value zero or any value within a specified range, and occur mainly to prevent small nonzero values in the solution. One particular challenge that can come with semi-continuous variables in practical models is that their upper bound may be large or even infinite. In this article, we briefly discuss these challenges, and present a new diving heuristic tailored for mixed-integer optimization problems with general semi-continuous variables. The heuristic is designed to work independently of whether the semi-continuous variables are bounded from above, and thus circumvents the specific difficulties that come with unbounded semi-continuous variables. We conduct extensive computational experiments on three different test sets, integrating the heuristic in an open-source MIP solver. The results indicate that this heuristic is a successful tool for finding high-quality solutions in negligible time. At the root node the primal gap is reduced by an average of 5 % up to 21 %, and considering the overall performance improvement, the primal integral is reduced by 2 % to 17 % on average.
format Preprint
id arxiv_https___arxiv_org_abs_2403_19411
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A diving heuristic for mixed-integer problems with unbounded semi-continuous variables
Halbig, Katrin
Hoen, Alexander
Gleixner, Ambros
Witzig, Jakob
Weninger, Dieter
Optimization and Control
90C10, 90C59, 90C90
Semi-continuous decision variables arise naturally in many real-world applications. They are defined to take either value zero or any value within a specified range, and occur mainly to prevent small nonzero values in the solution. One particular challenge that can come with semi-continuous variables in practical models is that their upper bound may be large or even infinite. In this article, we briefly discuss these challenges, and present a new diving heuristic tailored for mixed-integer optimization problems with general semi-continuous variables. The heuristic is designed to work independently of whether the semi-continuous variables are bounded from above, and thus circumvents the specific difficulties that come with unbounded semi-continuous variables. We conduct extensive computational experiments on three different test sets, integrating the heuristic in an open-source MIP solver. The results indicate that this heuristic is a successful tool for finding high-quality solutions in negligible time. At the root node the primal gap is reduced by an average of 5 % up to 21 %, and considering the overall performance improvement, the primal integral is reduced by 2 % to 17 % on average.
title A diving heuristic for mixed-integer problems with unbounded semi-continuous variables
topic Optimization and Control
90C10, 90C59, 90C90
url https://arxiv.org/abs/2403.19411