The effectiveness of derivative-free hybrid methods for black-box optimisation. (5th April 2011)

• Record Type: Journal Article
• Authors: Gray, G.A.; Fowler, K.R.
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 2:Number 2(2011)
• Page Start: 112
• Page End: 133
• Publication Date: 2011-04-05
• Subjects: black-box function -- derivative-free optimisation -- hybrid optimisation -- mixed-variable optimisation -- nonlinear optimisation -- MINLP -- black-box optimisation -- derivatives -- asynchronous parallel pattern search -- APPS -- implicit filtering -- dividing rectangles -- genetic algorithms -- statistical emulation; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

Abstract

Black-box optimisation problems are common in many applications of science and engineering. However, they are complicated in the sense that derivatives are unavailable and approximate derivatives are often unreliable. Moreover, evaluation the objective function and/or the constraints typically requires the results of a computationally expensive simulation. Derivative-free methods have emerged as invaluable for finding solutions to these problems. A wide variety of methods have been developed and each has distinct advantages and disadvantages. Therefore, we consider a hybrid approach to optimisation which allows the combining of beneficial elements of multiple methods in order to more efficiently search the design space. In this paper, we will first describe four derivative-free optimisation approaches – asynchronous parallel pattern search (APPS), implicit filtering, dividing rectangles (DIRECT), and a genetic algorithm (GA). We will also describe how statistical emulation can be used as an alternative to traditional optimisation. We will give the advantages and disadvantages of each approach. Then, we will explain how these five approaches are used to form the hybrids APPS-TGP, DIRECT-IFFCO, DIRECT-TGP, and EAGLS which exploiting the advantages and overcoming the disadvantages of the underlying methods. We also include references to papers which illustrate practical examples of these methods.