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Reformulations in mathematical programming: Automatic symmetry detection and exploitation
 Mathematical Programming
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Symmetry in mathematical programming
 MIXED INTEGER NONLINEAR PROGRAMMING. VOLUME IMA
"... Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms. The most widespread approach rests on: (a) finding symmetries in the problem instance; (b) reformulating the problem so that it does not allow some of the symmetric optima; ( ..."
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Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms. The most widespread approach rests on: (a) finding symmetries in the problem instance; (b) reformulating the problem so that it does not allow some of the symmetric optima; (c) solving the modified problem. Sometimes (b) and (c) are performed concurrently: the solution algorithm generates a sequence of subproblems, some of which are recognized to be symmetrically equivalent and either discarded or treated differently. We review symmetrybased analyses and methods for Linear Programming, Integer Linear Programming, MixedInteger Linear Programming and Semidefinite Programming. We then discuss a method (introduced in [35]) for automatically detecting symmetries of general (nonconvex) Nonlinear and MixedInteger Nonlinear Programming problems and a reformulation based on adjoining symmetry breaking constraints to the original formulation. We finally present a new theoretical and computational study of the formulation symmetries of the Kissing Number Problem.
Reformulations in mathematical programming: Symmetry
 Mathematical Programming
, 2009
"... If a mathematical program (be it linear or nonlinear) has many symmetric optima, solving it via BranchandBound techniques often yields search trees of disproportionate sizes; thus, finding and exploiting symmetries is an important task. We propose a method for: (a) automatically finding the formul ..."
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If a mathematical program (be it linear or nonlinear) has many symmetric optima, solving it via BranchandBound techniques often yields search trees of disproportionate sizes; thus, finding and exploiting symmetries is an important task. We propose a method for: (a) automatically finding the formulation group of any given MixedInteger Nonlinear Program, and (b) reformulating the problem so that some symmetric solutions become infeasible. The reformulated problem can then be solved via standard BranchandBound codes such as CPLEX (for linear programs) and Couenne (for nonlinear programs). Our computational results include formulation group tables for the MIPLib3, MIPLib2003, GlobalLib and MINLPLib instance libraries, solution tables for some instances in the aforementioned libraries, and a theoretical and computational study of the symmetries of the Kissing Number Problem. 1
Automatic generation of symmetrybreaking constraints
"... Solution symmetries in integer linear programs often yield long BranchandBound based solution processes. We propose a method for finding elements of the permutation group of solution symmetries, and two different types of symmetrybreaking constraints to eliminate these symmetries at the modellin ..."
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Cited by 5 (2 self)
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Solution symmetries in integer linear programs often yield long BranchandBound based solution processes. We propose a method for finding elements of the permutation group of solution symmetries, and two different types of symmetrybreaking constraints to eliminate these symmetries at the modelling level. We discuss some preliminary computational results.
Optimization problems arising in software architecture
, 2006
"... Software architecture is the process of planning and designing a largescale software, and a fundamental industrial discipline within the field of software engineering. The current body of knowledge in software architecture is a mixture of personal experience and precise methods. In this paper we m ..."
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Software architecture is the process of planning and designing a largescale software, and a fundamental industrial discipline within the field of software engineering. The current body of knowledge in software architecture is a mixture of personal experience and precise methods. In this paper we move a step towards the formalization of this discipline by describing some optimization problems that arise in the field. 1
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"... 4OR manuscript No. (will be inserted by the editor) Compact linearization for binary quadratic problems ..."
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4OR manuscript No. (will be inserted by the editor) Compact linearization for binary quadratic problems
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"... 4OR manuscript No. (will be inserted by the editor) Compact linearization for binary quadratic problems ..."
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4OR manuscript No. (will be inserted by the editor) Compact linearization for binary quadratic problems