Symmetry in Integer Linear Programming

Margot, François

doi:10.1007/978-3-540-68279-0_17

Cited by 183 publications

(163 citation statements)

References 103 publications

Supporting

Mentioning

161

Contrasting

Unclassified

Order By: Relevance

“…In this section, another approach is proposed in order to break the symmetries which can be detected in the SOS model. It is based on the concept of static symmetrybreaking constraints as presented by Margot 19 . Figure 5.…”

Section: Symmetry-breaking Constraintsmentioning

confidence: 99%

A Novel Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems

Mouret

Grossmann

Pestiaux

2009

Ind. Eng. Chem. Res.

107

170

View full text Add to dashboard Cite

The optimal scheduling of crude-oil operations in refineries has been studied by various groups during the past decade leading to different mixed integer linear programming (MILP) or mixed integer nonlinear programming (MINLP) formulations. This paper presents a new continuous-time formulation, called single-operation sequencing (SOS) model, which can be used to solve the crude-oil operations problem introduced by Lee et al. 1 . It is different from previous formulations as it requires to postulate the number of priority-slots in which operations take place instead of specifying the number of time intervals or event points to be used in the schedule. This MINLP model is also based on the representation of a crude-oil schedule by a single sequence of transfer operations. It allows breaking symmetries involved in the problem, thus tremendously reducing the computational expenses (all instances can be solved within 2 minutes). A simple two step MILP -NLP procedure has been used to solve the non-convex MINLP model leading to an optimality gap lower than 5% in all cases.

show abstract

Section: Symmetry-breaking Constraintsmentioning

confidence: 99%

A Novel Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems

Mouret

Grossmann

Pestiaux

2009

Ind. Eng. Chem. Res.

107

170

View full text Add to dashboard Cite

show abstract

“…There exists a vast literature on explicit symmetry breaking in constraint programming and integer programming, see Gent et al [2006] and Margot [2010] for recent surveys. In contrast, certain types of symmetry breaking are implicitly accounted for in semidefinite relaxations; see for example Anjos and Vannelli [2008].…”

Section: Discussionmentioning

confidence: 99%

Semidefinite Programming and Constraint Programming

Hoeve

2011

International Series in Operations Research &Amp; Management Science

View full text Add to dashboard Cite

“…However, these perturbations may have an adverse impact on the performance of the solution algorithms (Margot, 2010), whereby more elegant approaches may have a superior performance (Margot, 2010).…”

Section: Symmetry In Unit Commitment Problemsmentioning

confidence: 99%

Symmetry breaking in MILP formulations for Unit Commitment problems

Lima

Novais

2016

Computers & Chemical Engineering

View full text Add to dashboard Cite

Please cite this article as: Ricardo M. Lima, Augusto Q. Novais, Symmetry Breaking in MILP Formulations for Unit Commitment Problems, Computers and Chemical Engineering (2015), http://dx.doi.org/10. 1016/j.compchemeng.2015.11.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. • Symmetry issues are discussed in the context of UC formulations.• Three sets of SBC are proposed and analyzed.• Three well-known UC MILP models are used to implement the SBC.• The results presented are completely disruptive compared with the results presented in the literature.• The SBC derived have a clear advantage over general methods available in two MILP solvers. *HighlightsPage 2 of 43 show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed.The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers.

show abstract

Symmetry in Integer Linear Programming

Cited by 183 publications

References 103 publications

A Novel Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems

A Novel Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems

Semidefinite Programming and Constraint Programming

Symmetry breaking in MILP formulations for Unit Commitment problems

Contact Info

Product

Resources

About