Objective Function Effect Based Pattern Search—An Implementation for 3D Component Layout

Generalized pattern search (GPS) algorithms have been used successfully to solve three-dimensional (3D) component layout problems. These algorithms use a set of patterns and successively decreasing step sizes of these patterns to explore the search space before converging to good local minima. A shortcoming of conventional GPS algorithms is the lack of recognition of the fact that patterns affect the objective function by different amounts and hence it might be efficient to introduce them into the search in a certain order rather than introduce all of them at the beginning of the search. To address this shortcoming, it has been shown by the authors in previous work that it is more efficient to schedule patterns in decreasing order of their effect on the objective function. The effect of the patterns on the objective function was estimated by the a priori expectation of the objective function change due to the patterns. However, computing the a priori expectation is expensive, and to practically implement the scheduling of patterns, an inexpensive estimate of the effect on the objective function is necessary. This paper introduces a metric for geometric layout called the sensitivity metric that is computationally inexpensive, to estimate the effect of pattern moves on the objective function. A new pattern search algorithm that uses the sensitivity metric to schedule patterns is shown to perform as well as the pattern search algorithm that used the a priori expectation of the objective function change. Though the sensitivity metric applies to the class of geometric layout or placement problems, the foundation and approach is useful for developing metrics for other optimization problems.