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.

中文翻译：

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基于代理的协同优化框架，用于解决计算量大的黑盒问题

大多数基于代理的并行优化算法都只关注在每个循环中生成多个更新点的机制，而通过几种算法的协作来生成更新点的关注则较少。为此，在此提出了一种基于代理的协同优化框架。首先，基于将填充采样准则视为双目标优化问题的思想，开发了一类基于代理的并行优化算法。此类的每个算法称为顺序多点填充采样算法（SMISA），是选择替代模型，开发措施，探索措施和多目标优化方法求解的结果。SMISA是建立协作机制的基本算法。可以定义许多SMISA，并且重点放在解决双目标问题的标量方法上，例如\（\ varepsilon \）约束方法，使用响应曲面（CORS-RBF）方法和高效全局约束的并行约束优化方法。使用伪预期改进（EGO-PEI）算法作为SMISA的实例进行优化。此外，基于低置信区间的并行版本（LCB）算法作为SMISA类中的成员给出。其次，我们提出了SMISA之间的合作优化框架。SMISA之间的合作以两种方式发生：（1）它们共享解决方案和目标函数值以更新其代理模型；（2）他们使用从不同SMISA获得的采样点来指导自己的搜索过程。在弱条件下给出了该合作框架的一些收敛结果。EGO-PEI，并行CORS-RBF以及使用两者的协作方法CPEI的数值比较表明，CPEI提高了基线算法的性能。数值结果来自17个分析测试，结果表明，随着处理器数量的增加，挂钟时间的减少。