Global optimization with the direct algorithm
Global optimization with the direct algorithm
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发表时间：
2005
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通讯作者：
D. Finkel;C. Kelley
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作者：
D. Finkel;C. Kelley
本文描述了DIRECT算法的理论结果和实际改进，DIRECT算法是一种针对有界约束问题的直接搜索全局优化算法。我们严格地证明了该算法采样点的子序列满足光滑和非光滑问题的一阶必要条件。我们展示了线性问题的算法的线性收敛性，并演示了为什么我们的分析不能扩展到更一般的问题。我们分析了DIRECT的一个参数，表明它对算法的性能有负面影响。介绍了DIRECT的一个改进版本。通过算例验证了改进算法的有效性。我们将DIRECT应用于文献中的六个井场优化问题。我们使用DIRECT收集问题数据，并利用统计方法从数据中收集有关井场问题的信息。
This work describes theoretical results, and practical improvements to the DIRECT Algorithm, a direct search global optimization algorithm for bound-constrained problems. We rigorously show that a sub-sequence of the points sampled by the algorithm satisfy first order necessary conditions for both smooth and non-smooth problems. We show linear convergence of the algorithm for linear problems, and demonstrate why our analysis cannot be extended to more general problems. We analyze a parameter of DIRECT, and show that it negatively affects the performance of the algorithm. A modified version of the DIRECT is introduced. Test examples are used to demonstrate the effectiveness of the modified algorithm. We apply DIRECT to six well-field optimization problems from the literature. We collect data on the problems with DIRECT, and utilize statistical methods to glean information from the data about the well-field problems.