Collaborative Research: Adaptive Search for Global Optimization

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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.