An RLT approach for solving the binary-constrained mixed linear complementarity problem

•We give a new way to solve binary-constrained mixed linear complementarity problems.•These arise in energy, transportation, facility location, and land-use planning.•The algorithm does not relax the binary nor the complementarity constraints.•The algorithm is validated on some 1400 instances includ...

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Vydané v:Computers & operations research Ročník 110; s. 48 - 59
Hlavní autori: Djeumou Fomeni, Franklin, Gabriel, Steven A., Anjos, Miguel F.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Elsevier Ltd 01.10.2019
Pergamon Press Inc
Predmet:
Constraints
Electricity market
Integer programming
Linear equations
Linear programming
Mixed integer
Mixed integer linear programming
Mixed linear complementarity problems
Operations research
Optimization
Reformulation linearization technique
Linear programming
Mixed integer linear programming
Reformulation linearization technique
Mixed linear complementarity problems
Electricity market
ISSN:0305-0548, 1873-765X, 0305-0548
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Shrnutí:•We give a new way to solve binary-constrained mixed linear complementarity problems.•These arise in energy, transportation, facility location, and land-use planning.•The algorithm does not relax the binary nor the complementarity constraints.•The algorithm is validated on some 1400 instances including engineering test cases. It is well known that the mixed linear complementarity problem can be used to model equilibria in energy markets as well as a host of other engineering and economic problems. The binary-constrained, mixed linear complementarity problem is a formulation of the mixed linear complementarity problem in which some variables are restricted to be binary. This paper presents a novel approach for solving the binary-constrained mixed linear complementarity problem. First we solve a series of linear optimization problems that enables us to replace some of the complementarity constraints with linear equations. Then we solve an equivalent mixed integer linear programming formulation of the original binary-constrained mixed, linear complementarity problem (with a smaller number of complementarity constraints) to guarantee a solution to the problem. Our computational results on a wide range of test problems, including some engineering examples, demonstrate the usefulness and the effectiveness of this novel approach.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2019.05.008