A Hybrid Direct Search and Model-Based Derivative-Free Optimization Method with Dynamic Decision Processing and Application in Solid-Tank Design

Abstract

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 DQL method. 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 DQL method by allowing the method to determine the optimal search strategies in various circumstances. The Smart DQL method 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 DQL method produces high-quality solutions.