Derivative-Free Pattern Search Methods for Multidisciplinary Design Problems
نویسندگان
چکیده
There have been interesting recent developments in methods for solving optimization problems without making use of derivative (sensitivity) information. While calculus based methods that employ derivative information can be extremely eecient and very eeec-tive, they are not applicable to all MDO problems, for instance, when the function to be optimized is nondiierentiable, when sensitivity information is not available or is not reliable, or when the function values are inaccurate. In these settings, we have found that the multidirectional search method, a derivate-free method we have developed for solving nonlinear optimization problems, can be used eeectively. Our analysis of the multidirectional search algorithm has led us to discover that its algebraic structure and resulting convergence theory can be related to an entire class of derivative-free methods, which we now call pattern search methods, that have been in use for decades. The goal of this paper is to give an introduction to pattern search methods, to describe the features they share by using coordinate search, one of the earliest and best-known (if not as eeective) pattern search methods, as an example, and to review some recent developments that suggest that these methods can be extended to handle problems with a mix of continuous and discrete variables|another situation that can arise in MDO problems. Finally, we will discuss when these methods are an appropriate choice for solving MDO problems.
منابع مشابه
Derivative - Free Pattern Search Methods forMultidisciplinary Design
There have been interesting recent developments in methods for solving optimization problems without making use of derivative (sensitivity) information. While calculus based methods that employ derivative information can be extremely eecient and very eeec-tive, they are not applicable to all MDO problems, for instance, when the function to be optimized is nondiierentiable, when sensitivity info...
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