Average Complexity of Global Optimization

9500173卡尔文这项研究的目标之一是使用平均性能标准比较全局优化问题的不同算法。我们考虑了几类函数，包括光滑函数和不可微连续函数。该函数集被赋予概率度量，并且比较了不同算法相对于给定概率分布的期望性能。这种平均性能可以与算法的计算要求进行权衡。考虑了一系列算法，从选择固定点网格上的观测值的简单算法到选择每个站点以最大化所有先前观测的某些功能性的复杂方法。研究的第二个目标是开发用于全局优化的高效算法，其中效率是根据平均性能来衡量的。这项研究的结果将服务于几个目的。首先，它将填补全球优化研究的空白。空白是算法的激增，没有系统的方法来评估它们的性能质量。这项研究将提供全局优化算法的特征。其次，从算法性能质量结果中获得的知识将有助于确定需要额外工作的领域。第三，通过对算法进行基准测试，可以表征当前全局优化的研究进展状况。这一特征对于预测该领域未来的研究方向是必要的。第四，这项研究还将有助于验证和推翻在开发全局优化算法时所做的一些假设。最后，研究结果将为选择解决具有一定结构和特征的问题的技术和算法提供一些启示。所获得的洞察力可以转化为研究人员通过更好地理解问题来节省时间和资源，以及由于错误应用算法而节省时间和成本。。

9500173 Calvin One of the objectives of this research is to compare different algorithms for global optimization problems using an average performance criteria. Several classes of functions are considered, including smooth functions and non-differentiable continuous functions. The set of functions is endowed with a probability measure and the expected performance with respect to the given probability distribution of different algorithms are compared. This average performance can be traded off with the computational requirements of the algorithms. A range of algorithms is considered, from simple ones that choose the observations on a fixed grid of points to complex methods that choose each site to maximize some functional of all previous observations. A second objective of the research is to develop efficient algorithms for global optimization, where efficiency is measured in terms of average performance. The outcome of this research will serve several purposes. First, it will fill a void in global optimization studies. The void is the proliferation of algorithms with no systematic methods of assessing their performance quality. This research will provide a characterization of global optimization algorithms. Second, the knowledge gained from the results of the algorithmic performance quality will help identify areas where additional work is needed. Third, by benchmarking the algorithms, the current state of research advancement in global optimization can be characterized. This characterization is necessary in projecting future research directions in the area. Fourth, the research will also help to validate and invalidate some of the assumptions made in developing global optimization algorithms. Finally, the outcome of the research will provide some insights in choosing the techniques and algorithms to solve problems with certain structures and characteristics. The insights gained can translate into savings in time and resources by researchers from better problem understanding and savings in time and cost due to misapplications of algorithms. .