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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Vydáno v:	Journal of global optimization Ročník 59; číslo 4; s. 865 - 889
Hlavní autoři:	Müller, Juliane, Shoemaker, Christine A., Piché, Robert
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Boston Springer US 01.08.2014 Springer Springer Nature B.V
Témata:	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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Abstract	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.
AbstractList	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 (See CR48)), 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. 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. 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 (Mueller 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. 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.
Audience	Academic
Author	Piché, Robert Müller, Juliane Shoemaker, Christine A.
Author_xml	– sequence: 1 givenname: Juliane surname: Müller fullname: Müller, Juliane email: juliane.mueller2901@gmail.com organization: School of Civil and Environmental Engineering, Cornell University – sequence: 2 givenname: Christine A. surname: Shoemaker fullname: Shoemaker, Christine A. organization: School of Civil and Environmental Engineering, Center of Applied Mathematics, Cornell University, School of Operations Research and Information Engineering, Center of Applied Mathematics, Cornell University – sequence: 3 givenname: Robert surname: Piché fullname: Piché, Robert organization: Department of Mathematics, Tampere University of Technology
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Snippet	This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box...
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SubjectTerms	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
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Title	SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications
URI	https://link.springer.com/article/10.1007/s10898-013-0101-y https://www.proquest.com/docview/1541727169 https://www.proquest.com/docview/1567070130
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