A surrogate-based cooperative optimization framework for computationally expensive black-box problems

Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimizat...

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Veröffentlicht in:	Optimization and engineering Jg. 21; H. 3; S. 1053 - 1093
Hauptverfasser:	García-García, José Carlos, García-Ródenas, Ricardo, Codina, Esteve
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.09.2020 Springer Nature B.V
Schlagworte:	Algorithms Control Cooperation Engineering Environmental Management Financial Engineering Global optimization Mathematical models Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimization Optimization algorithms Performance enhancement Redevelopment Research Article Response surface methodology Sampling Search process Systems Theory Cooperative optimization Expected improvement Radial basis functions Parallel surrogate-based optimization Black-box function
ISSN:	1389-4420, 1573-2924
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Abstract	Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimization framework is here proposed. Firstly, a class of parallel surrogate-based optimization algorithms is developed, based on the idea of viewing the infill sampling criterion as a bi-objective optimization problem. Each algorithm of this class is called a Sequential Multipoint Infill Sampling Algorithm (SMISA) and is the combination resulting from choosing a surrogate model, an exploitation measure, an exploration measure and a multi-objective optimization approach to its solution. SMISAs are the basic algorithms on which collaboration mechanisms are established. Many SMISAs can be defined, and the focus has been on scalar approaches for bi-objective problems such as the ε -constrained method, revisiting the Parallel Constrained Optimization using Response Surfaces (CORS-RBF) method and the Efficient Global Optimization with Pseudo Expected Improvement (EGO-PEI) algorithm as instances of SMISAs. In addition, a parallel version of the Lower Confidence Bound-based (LCB) algorithm is given as a member within the SMISA class. Secondly, we propose a cooperative optimization framework between the SMISAs. The cooperation between SMISAs occurs in two ways: (1) they share solutions and their objective function values to update their surrogate models and (2) they use the sampled points obtained from different SMISAs to guide their own search process. Some convergence results for this cooperative framework are given under weak conditions. A numerical comparison between EGO-PEI, Parallel CORS-RBF and a cooperative method using both, named CPEI, shows that CPEI improves the performance of the baseline algorithms. The numerical results were derived from 17 analytic tests and they show the reduction of wall-clock time with respect to the increase in the number of processors.
AbstractList	Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimization framework is here proposed. Firstly, a class of parallel surrogate-based optimization algorithms is developed, based on the idea of viewing the infill sampling criterion as a bi-objective optimization problem. Each algorithm of this class is called a Sequential Multipoint Infill Sampling Algorithm (SMISA) and is the combination resulting from choosing a surrogate model, an exploitation measure, an exploration measure and a multi-objective optimization approach to its solution. SMISAs are the basic algorithms on which collaboration mechanisms are established. Many SMISAs can be defined, and the focus has been on scalar approaches for bi-objective problems such as the ε-constrained method, revisiting the Parallel Constrained Optimization using Response Surfaces (CORS-RBF) method and the Efficient Global Optimization with Pseudo Expected Improvement (EGO-PEI) algorithm as instances of SMISAs. In addition, a parallel version of the Lower Confidence Bound-based (LCB) algorithm is given as a member within the SMISA class. Secondly, we propose a cooperative optimization framework between the SMISAs. The cooperation between SMISAs occurs in two ways: (1) they share solutions and their objective function values to update their surrogate models and (2) they use the sampled points obtained from different SMISAs to guide their own search process. Some convergence results for this cooperative framework are given under weak conditions. A numerical comparison between EGO-PEI, Parallel CORS-RBF and a cooperative method using both, named CPEI, shows that CPEI improves the performance of the baseline algorithms. The numerical results were derived from 17 analytic tests and they show the reduction of wall-clock time with respect to the increase in the number of processors. Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimization framework is here proposed. Firstly, a class of parallel surrogate-based optimization algorithms is developed, based on the idea of viewing the infill sampling criterion as a bi-objective optimization problem. Each algorithm of this class is called a Sequential Multipoint Infill Sampling Algorithm (SMISA) and is the combination resulting from choosing a surrogate model, an exploitation measure, an exploration measure and a multi-objective optimization approach to its solution. SMISAs are the basic algorithms on which collaboration mechanisms are established. Many SMISAs can be defined, and the focus has been on scalar approaches for bi-objective problems such as the $$\varepsilon $$ ε -constrained method, revisiting the Parallel Constrained Optimization using Response Surfaces (CORS-RBF) method and the Efficient Global Optimization with Pseudo Expected Improvement (EGO-PEI) algorithm as instances of SMISAs. In addition, a parallel version of the Lower Confidence Bound-based (LCB) algorithm is given as a member within the SMISA class. Secondly, we propose a cooperative optimization framework between the SMISAs. The cooperation between SMISAs occurs in two ways: (1) they share solutions and their objective function values to update their surrogate models and (2) they use the sampled points obtained from different SMISAs to guide their own search process. Some convergence results for this cooperative framework are given under weak conditions. A numerical comparison between EGO-PEI, Parallel CORS-RBF and a cooperative method using both, named CPEI, shows that CPEI improves the performance of the baseline algorithms. The numerical results were derived from 17 analytic tests and they show the reduction of wall-clock time with respect to the increase in the number of processors. Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimization framework is here proposed. Firstly, a class of parallel surrogate-based optimization algorithms is developed, based on the idea of viewing the infill sampling criterion as a bi-objective optimization problem. Each algorithm of this class is called a Sequential Multipoint Infill Sampling Algorithm (SMISA) and is the combination resulting from choosing a surrogate model, an exploitation measure, an exploration measure and a multi-objective optimization approach to its solution. SMISAs are the basic algorithms on which collaboration mechanisms are established. Many SMISAs can be defined, and the focus has been on scalar approaches for bi-objective problems such as the ε -constrained method, revisiting the Parallel Constrained Optimization using Response Surfaces (CORS-RBF) method and the Efficient Global Optimization with Pseudo Expected Improvement (EGO-PEI) algorithm as instances of SMISAs. In addition, a parallel version of the Lower Confidence Bound-based (LCB) algorithm is given as a member within the SMISA class. Secondly, we propose a cooperative optimization framework between the SMISAs. The cooperation between SMISAs occurs in two ways: (1) they share solutions and their objective function values to update their surrogate models and (2) they use the sampled points obtained from different SMISAs to guide their own search process. Some convergence results for this cooperative framework are given under weak conditions. A numerical comparison between EGO-PEI, Parallel CORS-RBF and a cooperative method using both, named CPEI, shows that CPEI improves the performance of the baseline algorithms. The numerical results were derived from 17 analytic tests and they show the reduction of wall-clock time with respect to the increase in the number of processors.
Author	Codina, Esteve García-Ródenas, Ricardo García-García, José Carlos
Author_xml	– sequence: 1 givenname: José Carlos surname: García-García fullname: García-García, José Carlos email: josecarlos.garcia@uclm.es organization: Departamento de Matemáticas, Escuela Superior de Informática, Universidad de Castilla-La Mancha, Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha – sequence: 2 givenname: Ricardo surname: García-Ródenas fullname: García-Ródenas, Ricardo organization: Departamento de Matemáticas, Escuela Superior de Informática, Universidad de Castilla-La Mancha, Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha – sequence: 3 givenname: Esteve surname: Codina fullname: Codina, Esteve organization: Estadística i Investigació Operativa, Universitat Politécnica de Catalunya
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SubjectTerms	Algorithms Control Cooperation Engineering Environmental Management Financial Engineering Global optimization Mathematical models Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimization Optimization algorithms Performance enhancement Redevelopment Research Article Response surface methodology Sampling Search process Systems Theory
Title	A surrogate-based cooperative optimization framework for computationally expensive black-box problems
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