Weighted iterated local branching for mathematical programming problems with binary variables

Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of bi...

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Vydáno v:	Journal of heuristics Ročník 28; číslo 3; s. 329 - 350
Hlavní autoři:	Rodrigues, Filipe, Agra, Agostinho, Hvattum, Lars Magnus, Requejo, Cristina
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.06.2022 Springer Nature B.V
Témata:	Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Heuristic Integer programming Iterative methods Management Science Mathematical programming Mathematics Mathematics and Statistics Mixed integer Operations Research Operations Research/Decision Theory Optimization Search algorithms Solvers Matheuristic Neighborhood search Mixed-integer programming Boolean optimization
ISSN:	1381-1231, 1572-9397
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Abstract	Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of binary variables whose values are allowed to change in a given iteration. Recognizing that not all variables are equally promising to change when searching for better neighboring solutions, we propose a weighted iterated local branching heuristic. This new procedure differs from similar existing methods since it considers groups of binary variables and associates with each group a limit on the number of variables that can change. The groups of variables are defined using weights that indicate the expected contribution of flipping the variables when trying to identify improving solutions in the current neighborhood. When the mixed-integer programming solver fails to identify an improving solution in a given iteration, the proposed heuristic may force the search into new regions of the search space by utilizing the group of variables that are least promising to flip. The weighted iterated local branching heuristic is tested on benchmark instances of the optimum satisfiability problem, and computational results show that the weighted method is superior to an alternative method without weights.
AbstractList	Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of binary variables whose values are allowed to change in a given iteration. Recognizing that not all variables are equally promising to change when searching for better neighboring solutions, we propose a weighted iterated local branching heuristic. This new procedure differs from similar existing methods since it considers groups of binary variables and associates with each group a limit on the number of variables that can change. The groups of variables are defined using weights that indicate the expected contribution of flipping the variables when trying to identify improving solutions in the current neighborhood. When the mixed-integer programming solver fails to identify an improving solution in a given iteration, the proposed heuristic may force the search into new regions of the search space by utilizing the group of variables that are least promising to flip. The weighted iterated local branching heuristic is tested on benchmark instances of the optimum satisfiability problem, and computational results show that the weighted method is superior to an alternative method without weights.
Author	Agra, Agostinho Requejo, Cristina Rodrigues, Filipe Hvattum, Lars Magnus
Author_xml	– sequence: 1 givenname: Filipe orcidid: 0000-0002-3770-5456 surname: Rodrigues fullname: Rodrigues, Filipe organization: ISEG-School of Economics and Management, University of Lisbon – sequence: 2 givenname: Agostinho orcidid: 0000-0002-4672-6099 surname: Agra fullname: Agra, Agostinho organization: Department of Mathematics, University of Aveiro – sequence: 3 givenname: Lars Magnus orcidid: 0000-0003-0490-9978 surname: Hvattum fullname: Hvattum, Lars Magnus email: hvattum@himolde.no organization: Faculty of Logistics, Molde University College – sequence: 4 givenname: Cristina orcidid: 0000-0003-0529-5090 surname: Requejo fullname: Requejo, Cristina organization: Department of Mathematics, University of Aveiro
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Cites_doi	10.1016/j.entcs.2019.08.039 10.1007/s10107-004-0518-7 10.1007/s10107-003-0395-5 10.1016/j.dam.2017.09.010 10.1007/s10732-021-09466-0 10.1016/j.cor.2008.09.003 10.1007/s10732-020-09460-y 10.1287/trsc.1090.0295 10.1016/j.cor.2016.06.016 10.4249/scholarpedia.6532 10.1007/s10732-018-9392-y 10.1287/ijoc.1060.0189 10.1007/s10732-014-9266-x 10.1023/A:1023717307746 10.1145/937503.937505 10.1126/science.220.4598.671 10.1016/j.dam.2003.06.006 10.1007/s11590-020-01577-0 10.1287/ijoc.2018.0822 10.1016/j.ejor.2016.07.004 10.1007/978-1-4615-6089-0 10.1016/j.ins.2013.02.041 10.1007/978-3-540-78295-7_2 10.1007/978-3-642-20364-0_7
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Snippet	Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search...
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SubjectTerms	Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Heuristic Integer programming Iterative methods Management Science Mathematical programming Mathematics Mathematics and Statistics Mixed integer Operations Research Operations Research/Decision Theory Optimization Search algorithms Solvers
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Title	Weighted iterated local branching for mathematical programming problems with binary variables
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