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 varepsilon -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.
Highlights
In many engineering applications, such as thermodynamic analysis, engine design, structural analysis or reservoir simulation, computer simulations are used as models of real systems
The cooperation mechanisms are established in two ways: the first is to share the points generated in the updating of the surrogate models, and the second is that each Sequential Multi-point Infill Sampling Algorithm (SMISA) takes into account, in the sampling process, the regions that are being explored by the rest of the SMISAs to avoid over-emphasis on these regions
If we consider all values of q and count which configurations achieve the best results, we find that CPEI is the best option for 9 problems, CORS-radial basis functions (RBFs) for 7 problems and the Efficient Global Optimization with Pseudo Expected Improvement (EGO-Pseudo Expected Improvement (PEI)) for 6 problems
Summary
In many engineering applications, such as thermodynamic analysis, engine design, structural analysis or reservoir simulation, computer simulations are used as models of real systems. This study proposes a complementary approach based on the cooperation of parallel surrogate-based optimization methods To achieve this goal, first, we introduce a formal definition of the class of algorithms that can cooperate with each other. The key point is that the exploration measures are independent of the surrogate model and this means that: (1) the SMISAs may generate sequentially q points per cycle by updating the exploration measure and (2) there is coordination between these SMISAs through exploration measures This framework allows existing parallel infill criteria to be described but is a way to generate new methods. This framework has been applied to derive a parallel version of the Lower Confidence Bound-based algorithm given in Dennis and Torczon (1997).
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