Improved integral simplex using decomposition for the set partitioning problem

Abdelouahab Zaghrouti (), Issmail El Hallaoui () and François Soumis ()
Additional contact information
Abdelouahab Zaghrouti: Polytechnique Montreal and GERAD
Issmail El Hallaoui: Polytechnique Montreal and GERAD
François Soumis: Polytechnique Montreal and GERAD

EURO Journal on Computational Optimization, 2018, vol. 6, issue 2, No 3, 185-206

Abstract: Abstract 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.

Keywords: Primal algorithms; Set partitioning problem; Integral simplex; 90C99; 90C27; 90C10 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s13675-018-0098-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurjco:v:6:y:2018:i:2:d:10.1007_s13675-018-0098-6

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/13675

DOI: 10.1007/s13675-018-0098-6

Access Statistics for this article

EURO Journal on Computational Optimization is currently edited by Martine C. Labbé

More articles in EURO Journal on Computational Optimization from Springer, EURO - The Association of European Operational Research Societies
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().