Research Initiation: Global Optimization Algorithms for Engineering Design

工程界需要高效的算法来解决设计中的全局优化问题。全局优化问题需要最小化一个具有多个局部极小值的函数。给出了飞机结构用复合材料层合加筋板的优化设计实例。本研究有三个目的。第一种是开发一种既包括整数变量又包括连续变量的随机搜索算法。由于模拟退火法在整数域和连续域上都已显示出一定的有效性，因此将开发一种求解整数/连续全局优化问题的模拟退火法。第二种是在优化算法中利用对Lipschitz常数的估计。第三个是降低算法陷入非全局最小值的概率。这些目标将共同改进算法，使制定和解决全局优化问题变得更加实用，工程师也更容易理解。其结果将适用于所有工程学科的设计方面。

The engineering community needs efficient algorithms for solving global optimization problems in design. Global optimization problems require minimizing a function possessing multiple local minima. A practical example is finding the optimal design of a composite laminated stiffened panel used in aircraft structures. This research has three objectives. The first is to develop a random search algorithm that includes both integer and continuous variables. A simulated annealing algorithm for mixed integer/continuous global optimization will be developed, because simulated annealing has already demonstrated some effectiveness in both the integer domain and the continuous domain. The second is to take advantage of estimates of a Lipschitz constant in the optimization algorithm. The third is to decrease an algorithm's probability of getting trapped in a local minimum that is not the global minimum. Together these objectives will improve algorithms in a manner that will make formulating and solving global optimization problems more practical and accessible to engineers. The results will be applicable to aspects of design in all engineering disciplines.