Algorithms, Vol. 16, Pages 92: A Hybrid Direct Search and Model-Based Derivative-Free Optimization Method with Dynamic Decision Processing and Application in Solid-Tank Design

Algorithms, Vol. 16, Pages 92: A Hybrid Direct Search and Model-Based Derivative-Free Optimization Method with Dynamic Decision Processing and Application in Solid-Tank Design

Algorithms doi: 10.3390/a16020092

Authors: Zhongda Huang Andy Ogilvy Steve Collins Warren Hare Michelle Hilts Andrew Jirasek

A derivative-free optimization (DFO) method is an optimization method that does not make use of derivative information in order to find the optimal solution. It is advantageous for solving real-world problems in which the only information available about the objective function is the output for a specific input. In this paper, we develop the framework for a DFO method called the DQLmethod. It is designed to be a versatile hybrid method capable of performing direct search, quadratic-model search, and line search all in the same method. We develop and test a series of different strategies within this framework. The benchmark results indicate that each of these strategies has distinct advantages and that there is no clear winner in the overall performance among efficiency and robustness. We develop the Smart DQLmethod by allowing the method to determine the optimal search strategies in various circumstances. The Smart DQLmethod is applied to a problem of solid-tank design for 3D radiation dosimetry provided by the UBCO (University of British Columbia—Okanagan) 3D Radiation Dosimetry Research Group. Given the limited evaluation budget, the Smart DQLmethod produces high-quality solutions.