A trajectory-based method for mixed integer nonlinear programming problems

A local trajectory-based method for solving mixed integer nonlinear programming problems is proposed. The method is based on the trajectory-based method for continuous optimization problems. The method has three phases, each of which performs continuous minimizations via the solution of systems of d...

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Veröffentlicht in:Journal of global optimization Jg. 70; H. 3; S. 601 - 623
Hauptverfasser: Oliphant, Terry-Leigh, Ali, M. Montaz
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.03.2018
Springer
Springer Nature B.V
Schlagworte:
Computer Science
Differential equations
Mathematics
Mathematics and Statistics
Methods
Mixed integer
Nonlinear programming
Numerical integration
Operations Research/Decision Theory
Optimization
Real Functions
Trajectories
Local minimizer
Pattern search
Trajectory-based method
System of ordinary differential equations
Subproblem
Mixed integer nonlinear programming
Neighborhood
ISSN:0925-5001, 1573-2916
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Zusammenfassung:A local trajectory-based method for solving mixed integer nonlinear programming problems is proposed. The method is based on the trajectory-based method for continuous optimization problems. The method has three phases, each of which performs continuous minimizations via the solution of systems of differential equations. A number of novel contributions, such as an adaptive step size strategy for numerical integration and a strategy for updating the penalty parameter, are introduced. We have shown that the optimal value obtained by the proposed method is at least as good as the minimizer predicted by a recent definition of a mixed integer local minimizer. Computational results are presented, showing the effectiveness of the method.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-017-0570-5