A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012 . doi: 10.1007/s10898-012-9874-7 ), this manuscript documents a computational framework for deterministica...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 161; H. 3; S. 905 - 932
Hauptverfasser: Misener, Ruth, Floudas, Christodoulos A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.06.2014
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computation
Engineering
Flattening
Integer programming
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization algorithms
Signal transduction
Software
Solvers
State of the art
Strategy
Studies
Theory of Computation
Trees
Variables
Numerical optimization software
Global optimization
Mixed-integer signomial optimization
ISSN:0022-3239, 1573-2878
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Zusammenfassung:Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012 . doi: 10.1007/s10898-012-9874-7 ), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε -global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0396-3