Collaborative Research: Adaptive Search for Global Optimization

复杂系统的数学模型，特别是那些在工程应用中出现的，提供了一个机会，以优化其设计和操作。 这可以通过选择在数学上优化系统性能的目标函数和决策变量来实现。 存在许多局部搜索算法，可以找到这样的模型的局部最优值，但有效的全局搜索算法，承诺找到一个全局最优值才刚刚开始变得可用。 然而，这些全局优化算法由于无法扩展到解决实际的大规模优化问题而受到损害。 因此，特别重要的是，新的算法开发具有严格的理论基础，使其性能作为一个功能的大小或规模的问题要解决的可靠的预测。 本研究的总体目标是通过建立一类随机搜索方法的理论基础来提高全局优化方法的有效性。 提出的概念框架是，解决全局优化问题的随机仿真分布集中在全球最优。 快速采样算法的发展，从而导致有效的全局优化算法。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换。该方法有望导致一个有效的算法，将呈现像我们的三个应用领域的问题。

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. The overall objective of this proposed research is to improve the effectiveness of global optimization methods by establishing a theoretical foundation for a class of stochastic search methods. The conceptualframework proposed 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 toefficient 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 our three application areas.