A branch-and-cut technique to solve multiobjective integer quadratic programming problems

This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted by MOIQP). The proposed algorithm is a branch and bound based technique suitable for MOIQP problems to generate the set of all efficient sol...

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Published in:Annals of operations research Vol. 267; no. 1-2; pp. 431 - 446
Main Authors: Ouaïl, Fatma Zohra, Chergui, Mohamed El-Amine
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2018
Springer Nature B.V
Subjects:
Algorithms
Branch & bound algorithms
Business and Management
Combinatorics
Integer programming
Linear functions
Multiple objective analysis
Multiple Objective Optimization
Operations research
Operations Research/Decision Theory
Problem solving
Quadratic equations
Quadratic programming
Studies
Theory of Computation
90C20
Efficient cuts
90C10
Branch and bound
90C57
Multiobjective optimization
90C29
Quadratic programming
Multiobjective quadratic integer programming
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Abstract This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted by MOIQP). The proposed algorithm is a branch and bound based technique suitable for MOIQP problems to generate the set of all efficient solutions. The features of the method are as follows. First, the branch and bound technique allows solving the relaxed problem according to any linear function and progressively generates integer solutions. Then, the efficient cut proposed reduces the search area by truncating domains containing non efficient solutions without having to enumerate them. Finally, at each node of the tree search, three fathoming rules are used to enhance the speed of the procedure. Computational experiments are presented in order to analyze the performance of the algorithm.
AbstractList This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted by MOIQP). The proposed algorithm is a branch and bound based technique suitable for MOIQP problems to generate the set of all efficient solutions. The features of the method are as follows. First, the branch and bound technique allows solving the relaxed problem according to any linear function and progressively generates integer solutions. Then, the efficient cut proposed reduces the search area by truncating domains containing non efficient solutions without having to enumerate them. Finally, at each node of the tree search, three fathoming rules are used to enhance the speed of the procedure. Computational experiments are presented in order to analyze the performance of the algorithm.
Author Ouaïl, Fatma Zohra
Chergui, Mohamed El-Amine
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  givenname: Fatma Zohra
  surname: Ouaïl
  fullname: Ouaïl, Fatma Zohra
  email: ouail.fatmazohra@yahoo.fr
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  givenname: Mohamed El-Amine
  surname: Chergui
  fullname: Chergui, Mohamed El-Amine
  organization: RECITS Laboratory, Faculty of Mathematics, USTHB
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CitedBy_id crossref_primary_10_1080_01605682_2024_2416510
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Cites_doi 10.1016/j.ejor.2015.04.035
10.1007/978-3-540-87477-5_8
10.1016/j.dam.2006.08.007
10.1016/j.ejor.2013.07.024
10.1080/00207548708919840
10.1002/nav.3800060109
10.1007/s10479-012-1079-4
10.1007/s11573-012-0642-4
10.1007/s10479-006-0137-1
10.1109/CEC.2003.1299372
10.1007/s10479-017-2484-5
ContentType Journal Article
Copyright Springer Science+Business Media, LLC 2017
Annals of Operations Research is a copyright of Springer, (2017). All Rights Reserved.
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Issue 1-2
Keywords 90C20
Efficient cuts
90C10
Branch and bound
90C57
Multiobjective optimization
90C29
Quadratic programming
Multiobjective quadratic integer programming
Language English
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Snippet This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted...
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SubjectTerms Algorithms
Branch & bound algorithms
Business and Management
Combinatorics
Integer programming
Linear functions
Multiple objective analysis
Multiple Objective Optimization
Operations research
Operations Research/Decision Theory
Problem solving
Quadratic equations
Quadratic programming
Studies
Theory of Computation
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Title A branch-and-cut technique to solve multiobjective integer quadratic programming problems
URI https://link.springer.com/article/10.1007/s10479-017-2698-6
https://www.proquest.com/docview/2064636646
Volume 267
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