Improved integral simplex using decomposition for the set partitioning problem

Integral simplex using decomposition (ISUD) is a method that efficiently solves set partitioning problems. It is an iterative method that starts from a known integer solution and moves through a sequence of integer solutions, decreasing the cost at each iteration. At each iteration, the method decom...

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Autores principales:	Abdelouahab Zaghrouti, Issmail El Hallaoui, François Soumis
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2018
Materias:	90C99 90C27 90C10 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/70369344f7704cafbe00834a504a623c
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spelling	oai:doaj.org-article:70369344f7704cafbe00834a504a623c2021-12-02T05:01:07ZImproved integral simplex using decomposition for the set partitioning problem2192-440610.1007/s13675-018-0098-6https://doaj.org/article/70369344f7704cafbe00834a504a623c2018-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S219244062100099Xhttps://doaj.org/toc/2192-4406Integral simplex using decomposition (ISUD) is a method that efficiently solves set partitioning problems. It is an iterative method that starts from a known integer solution and moves through a sequence of integer solutions, decreasing the cost at each iteration. At each iteration, the method decomposes the original problem into a reduced problem (RP) and a complementary problem (CP). Given an integer solution to RP (that is also solution to the original problem), CP finds a descent direction having the minimum ratio between its cost and the number of its positive variables. We loop on until an optimal or near-optimal solution to the original problem is reached. In this paper, we introduce a modified model for CP. The new model finds a descent direction that minimizes the ratio between the cost of the direction and an overestimation of the number of variables taking one in the next solution. The new CP presents higher chances of finding improved integer solutions without branching. We present results for the same large instances (with up to 570,000 columns) as the ones previously used to test ISUD. For all the instances, optimality is always reached with a speedup factor of at least five.Abdelouahab ZaghroutiIssmail El HallaouiFrançois SoumisElsevierarticle90C9990C2790C10Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 6, Iss 2, Pp 185-206 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C99 90C27 90C10 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C99 90C27 90C10 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Abdelouahab Zaghrouti Issmail El Hallaoui François Soumis Improved integral simplex using decomposition for the set partitioning problem
description	Integral simplex using decomposition (ISUD) is a method that efficiently solves set partitioning problems. It is an iterative method that starts from a known integer solution and moves through a sequence of integer solutions, decreasing the cost at each iteration. At each iteration, the method decomposes the original problem into a reduced problem (RP) and a complementary problem (CP). Given an integer solution to RP (that is also solution to the original problem), CP finds a descent direction having the minimum ratio between its cost and the number of its positive variables. We loop on until an optimal or near-optimal solution to the original problem is reached. In this paper, we introduce a modified model for CP. The new model finds a descent direction that minimizes the ratio between the cost of the direction and an overestimation of the number of variables taking one in the next solution. The new CP presents higher chances of finding improved integer solutions without branching. We present results for the same large instances (with up to 570,000 columns) as the ones previously used to test ISUD. For all the instances, optimality is always reached with a speedup factor of at least five.
format	article
author	Abdelouahab Zaghrouti Issmail El Hallaoui François Soumis
author_facet	Abdelouahab Zaghrouti Issmail El Hallaoui François Soumis
author_sort	Abdelouahab Zaghrouti
title	Improved integral simplex using decomposition for the set partitioning problem
title_short	Improved integral simplex using decomposition for the set partitioning problem
title_full	Improved integral simplex using decomposition for the set partitioning problem
title_fullStr	Improved integral simplex using decomposition for the set partitioning problem
title_full_unstemmed	Improved integral simplex using decomposition for the set partitioning problem
title_sort	improved integral simplex using decomposition for the set partitioning problem
publisher	Elsevier
publishDate	2018
url	https://doaj.org/article/70369344f7704cafbe00834a504a623c
work_keys_str_mv	AT abdelouahabzaghrouti improvedintegralsimplexusingdecompositionforthesetpartitioningproblem AT issmailelhallaoui improvedintegralsimplexusingdecompositionforthesetpartitioningproblem AT francoissoumis improvedintegralsimplexusingdecompositionforthesetpartitioningproblem
_version_	1718400835712450560

Improved integral simplex using decomposition for the set partitioning problem

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