SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications

This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box objective functions and that may have computationally expensive constraints. The algorithm was developed for solving global optimization problem...

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Veröffentlicht in:Journal of global optimization Jg. 59; H. 4; S. 865 - 889
Hauptverfasser: Müller, Juliane, Shoemaker, Christine A., Piché, Robert
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.08.2014
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Applied mathematics
Computation
Computer Science
Engineering
Environmental engineering
Genetic algorithms
Hydroelectric power
Integer programming
Inventory control
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Maximization
Mutation
Nonlinear programming
Operations Research/Decision Theory
Optimization
Production planning
Real Functions
Searching
Studies
Radial basis functions
Global optimization
Surrogate model
Multimodal
Integer optimization
Response surface
Computationally expensive
Nonconvex
Derivative-free
Linear and nonlinear
ISSN:0925-5001, 1573-2916
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Zusammenfassung:This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box objective functions and that may have computationally expensive constraints. The algorithm was developed for solving global optimization problems, meaning that the relaxed optimization problems have many local optima. However, the method is also shown to perform well on many local optimization problems, and problems with linear objective functions. The performance of SO-I, a genetic algorithm, Nonsmooth Optimization by Mesh Adaptive Direct Search (NOMAD), SO-MI (Müller et al. in Comput Oper Res 40(5):1383–1400, 2013 ), variable neighborhood search, and a version of SO-I that only uses a local search has been compared on 17 test problems from the literature, and on eight realizations of two application problems. One application problem relates to hydropower generation, and the other one to throughput maximization. The numerical results show that SO-I finds good solutions most efficiently. Moreover, as opposed to SO-MI, SO-I is able to find feasible points by employing a first optimization phase that aims at minimizing a constraint violation function. A feasible user-supplied point is not necessary.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-013-0101-y