Branch-and-bound algorithms for the partial inverse mixed integer linear programming problem

This paper presents branch-and-bound algorithms for the partial inverse mixed integer linear programming (PInvMILP) problem, which is to find a minimal perturbation to the objective function of a mixed integer linear program (MILP), measured by some norm, such that there exists an optimal solution t...

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Vydané v:Journal of global optimization Ročník 55; číslo 3; s. 491 - 506
Hlavný autor: Wang, Lizhi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.03.2013
Springer
Springer Nature B.V
Predmet:
Algorithms
Alternative energy
Branch & bound algorithms
Computation
Computer Science
Decision making
Inverse
Inverse problems
Linear programming
Mathematical models
Mathematics
Mathematics and Statistics
Mixed integer
Norms
Operations Research/Decision Theory
Optimization
Real Functions
Renewable resources
Studies
Variables
Branch-and-bound
Inverse optimization
Linear program with complementarity constraints
Partial inverse mixed integer linear programming
ISSN:0925-5001, 1573-2916, 1573-2916
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Shrnutí:This paper presents branch-and-bound algorithms for the partial inverse mixed integer linear programming (PInvMILP) problem, which is to find a minimal perturbation to the objective function of a mixed integer linear program (MILP), measured by some norm, such that there exists an optimal solution to the perturbed MILP that also satisfies an additional set of linear constraints. This is a new extension to the existing inverse optimization models. Under the weighted and norms, the presented algorithms are proved to finitely converge to global optimality. In the presented algorithms, linear programs with complementarity constraints (LPCCs) need to be solved repeatedly as a subroutine, which is analogous to repeatedly solving linear programs for MILPs. Therefore, the computational complexity of the PInvMILP algorithms can be expected to be much worse than that of MILP or LPCC. Computational experiments show that small-sized test instances can be solved within a reasonable time period.
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ISSN:0925-5001
1573-2916
1573-2916
DOI:10.1007/s10898-013-0036-3