Constrained efficient global optimization with support vector machines
Constrained efficient global optimization with support vector machines
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DOI：
10.1007/s00158-011-0745-5
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发表时间：
2012-01
影响因子：
3.9
通讯作者：
Anirban Basudhar;C. Dribusch;Sylvain Lacaze;S. Missoum
中科院分区：
文献类型：
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作者：
Anirban Basudhar;C. Dribusch;Sylvain Lacaze;S. Missoum
提出了一种基于支持向量机的约束有效全局优化方法。虽然目标函数近似使用克里格，在原来的EGO制定，可行域的边界近似明确的设计变量的函数使用SVM。由于支持向量机是一种分类方法，并且不涉及响应近似，因此这种方法可以缓解由于不连续或二元响应而导致的问题。更重要的是，几个约束，甚至相关的，可以表示使用一个唯一的SVM，从而大大简化了约束问题。为了考虑约束条件，本文引入了一个基于SVM的“可行性概率”使用一个新的ProbabilitySVM模型。所提出的优化方案由两个层次组成。在第一阶段中，基于目标函数的“预期改进”和可行性概率来执行对最优解的全局搜索。在第二阶段，SVM边界局部细化使用自适应采样方案。一个无约束和约束的最优化问题的制定和比较。几个分析实施例用于测试配方。特别是，一个问题与99个约束和气动弹性问题与二进制输出。总体而言，结果表明，约束配方是更强大和有效的。
This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based “probability of feasibility” using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the “expected improvement” of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.