The decomposition-based outer approximation algorithm for convex mixed-integer nonlinear programming

This paper presents a new two-phase method for solving convex mixed-integer nonlinear programming (MINLP) problems, called Decomposition-based Outer Approximation Algorithm (DECOA). In the first phase, a sequence of linear integer relaxed sub-problems (LP phase) is solved in order to rapidly generat...

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Veröffentlicht in:Journal of global optimization Jg. 77; H. 1; S. 75 - 96
Hauptverfasser: Muts, Pavlo, Nowak, Ivo, Hendrix, Eligius M. T
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Springer US 01.05.2020
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Computer Science
Convex MINLP
DECOA
Decomposition
Decomposition method
Global optimization
Hyperplanes
Integer programming
Linear programming
Mathematics
Mathematics and Statistics
Mixed integer
Nonlinear programming
Operations Research/Decision Theory
Optimization
Outer approximation
Real Functions
Global optimization
DECOA
Convex MINLP
Outer approximation
Decomposition method
ISSN:1573-2916, 0925-5001, 1573-2916
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Zusammenfassung:This paper presents a new two-phase method for solving convex mixed-integer nonlinear programming (MINLP) problems, called Decomposition-based Outer Approximation Algorithm (DECOA). In the first phase, a sequence of linear integer relaxed sub-problems (LP phase) is solved in order to rapidly generate a good linear relaxation of the original MINLP problem. In the second phase, the algorithm solves a sequence of mixed integer linear programming sub-problems (MIP phase). In both phases the outer approximation is improved iteratively by adding new supporting hyperplanes by solving many easier sub-problems in parallel. DECOA is implemented as a part of Decogo (Decomposition-based Global Optimizer), a parallel decomposition-based MINLP solver implemented in Python and Pyomo. Preliminary numerical results based on 70 convex MINLP instances up to 2700 variables show that due to the generated cuts in the LP phase, on average only 2–3 MIP problems have to be solved in the MIP phase.
Bibliographie:ObjectType-Article-1
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ISSN:1573-2916
0925-5001
1573-2916
DOI:10.1007/s10898-020-00888-x