Adaptive Search for Global Optimization

本研究项目的总体目标是通过为一类随机搜索方法建立理论基础来提高全局优化方法的有效性。概念框架是通过随机模拟集中在全局最优周围的分布来解决全局优化问题。快速采样算法的发展可以导致高效的全局优化算法。这些算法将在三个应用领域进行测试：(1)结构优化；(2)形状优化；(3)技术变革下的设备更新。该方法有望产生一种有效的算法，可以解决像这三个应用领域这样的可处理问题。复杂系统的数学模型，特别是在工程应用中出现的数学模型，为优化其设计和操作提供了机会。这可以通过选择目标函数和决策变量来实现，从而在数学上优化系统性能。已有许多局部搜索算法可以为这些模型找到局部最优解，但有效的全局搜索算法才刚刚开始出现。然而，这些全局优化算法由于无法按比例扩展以解决实际的大规模优化问题而受到损害。因此，开发具有严格理论基础的新算法尤其重要，该理论基础可以可靠地预测其性能作为待解决问题的大小或规模的函数。

The overall objective of this research project is to improve the effectiveness of global optimization methods by establishing a theoretical foundation for a class of stochastic search methods. The conceptual framework is that of solving global optimization problems by stochastic emulation of distributions that concentrate around the global optimum. Development of rapid sampling algorithms can thereby lead to efficient global optimization algorithms. These algorithms will be tested on three application areas: (1) structural optimization; (2) shape optimization; and (3) equipment replacement under technological change. The approach promises to lead to an efficient algorithm that will render tractable problems like the three application areas.Mathematical models of complex systems, in particular those arising in engineering applications, offer an opportunity to optimize their design and operation. This can be accomplished through the selection of an objective function and decision variables that mathematically optimize system performance. Many local search algorithms exist which can find a local optimum for such models, but effective global search algorithms that promise to find a global optimum are just beginning to become available. These global optimization algorithms are compromised however by an inability to be scaled up to solve practical large-scale optimization problems. It is particularly important therefore that new algorithms be developed with a rigorous theoretical foundation that makes reliable predictions about their performance as a function of the size or scale of the problems to be solved.