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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Published in:Optimization and engineering Vol. 21; no. 3; pp. 1053 - 1093
Main Authors: García-García, José Carlos, García-Ródenas, Ricardo, Codina, Esteve
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2020
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09526-7