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Adaptive Random Search for Continuous Simulation Optimization

机译：自适应随机搜索，用于连续仿真优化

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摘要

We present, analyze, and compare three random search methods for solving stochastic optimization problems with uncountable feasible regions. Our adaptive search with resampling (ASR) approach is a framework for designing provably convergent algorithms that are adaptive and may consequently involve local search. The deterministic and stochastic shrinking ball (DSB and SSB) approaches are also convergent, but they are based on pure random search with the only difference being the estimator of the optimal solution [the DSB method was originally proposed and analyzed by Baumert and Smith]. The three methods use different techniques to reduce the effects of noise in the estimated objective function values. Our ASR method achieves this goal through resampling of already sampled points, whereas the DSB and SSB approaches address it by averaging observations in balls that shrink with time. We present conditions under which the three methods are convergent, both in probability and almost surely, and provide a limited computational study aimed at comparing the methods. Although further investigation is needed, our numerical results suggest that the ASR approach is promising, especially for difficult problems where the probability of identifying good solutions using pure random search is small.
机译：我们介绍，分析和比较三种随机搜索方法来解决具有不可数的可行区域的随机优化问题。我们的带有重采样的自适应搜索（ASR）方法是一个框架，用于设计可证明的收敛算法，这些算法是自适应的，因此可能涉及局部搜索。确定性和随机收缩球（DSB和SSB）方法也可以收敛，但是它们基于纯随机搜索，唯一的不同是最优解的估计[DSB方法最初是由Baumert和Smith提出并分析的。三种方法使用不同的技术来减少估计的目标函数值中的噪声影响。我们的ASR方法通过对已经采样的点进行重新采样来实现此目标，而DSB和SSB方法通过对随时间缩小的球中的观测值求平均来解决该问题。我们提出了三种方法在概率和几乎确定性上都收敛的条件，并提供了旨在比较这些方法的有限的计算研究。尽管需要进一步研究，但我们的数值结果表明，ASR方法是有前途的，特别是对于那些使用纯随机搜索来识别良好解决方案的可能性很小的难题。

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