Bell-Curved Based Optimization for Mixed Continuous and Discrete Structural Optimization Problems

Abstract

The BCB heuristic procedure, first presented in Sobieszczanski-Sobieski, Laba, and Kincaid [13] is similar in spirit to Evolutionary Search strategies (ESs) and Evolutionary Programming methods (EPs) but has fewer parameters to adjust. In Sobieszczanski-Sobieski et al. [13] BCB was tested on a structural design optimization problem. The quality of the solutions generated were verified by comparing BCB solutions to ones generated by a standard nonlinear programming technique. Kincaid, Weber, and Sobieszczanski-Sobieski [7] provide a preliminary investigation into BCB parameter selection as well as document improvements in the performance of BCB. Computational results for continuous problems with constraints is reported. Further experiments with BCB for purely discrete optimization problems is provided in Kincaid, Weber, and Sobieszczanski-Sobieski [6]. Plassman and SobieszczanskiSobieski [11] implement and test a parallel version of BCB for continuous optimization problems. Lastly Kincaid, Griffith, Sykes and Sobieszczanski-Sobieski [8] provide experimental results for BCB applied to mixed continuous and discrete optimization problems. This paper continues computational experiments in this direction. The goal is to see if the performance of BCB for mixed continuous and discrete optimization problems is improved if BCB is linked with pattern search. Pattern search is a derivative free local search procedure that has been shown to perform well on a variety of nonlinear optimization problems (see Lewis et al. [10] for details). The idea exploited is that BCB does a good job of identifying valleys (peaks) of interest but takes too long getting to the bottom (top). Such a linking of BCB with local search procedures has been shown (Kincaid et al. [6]) to work well for the continuous version of BCB.