(482c) Argonaut: Algorithms for Global Optimization of Constrained Grey-Box Computational Problems

Constrained grey-box optimization methods do not employ derivative information of the objective function and/or constraints of the original model for obtaining the global optimum. In typical applications of the above methods, derivative information may be available but deceptive or prohibitively expensive, or even completely unavailable [1, 2]. Development of efficient constrained grey-box methods is of high interest since it enables the optimization of costly simulation models developed to represent industrial processes with a high level of detail, coupling multiple physical, chemical, and mechanical phenomena. In addition, the independency of grey-box methods from derivatives allows the optimization of problems with embedded numerical noise, discontinuities and multiple local optima, which are all reasons for failure of finite-differencing techniques and consequently derivative-based methods [1].

Constrained grey-box methods have a vast pool of application areas ranging from expensive finite-element or partial-differential equation systems and flowsheet optimization to mechanical engineering design, molecular design, material screening, supply chain optimization and pharmaceutical product development, to name a few. In previous work, we have developed a constrained grey-box optimization method to optimize a Pressure Swing Adsorption (PSA) process for CO₂ capture [3, 4] and natural gas purification [5], while current and future applications of interest are Simulated Moving Bed (SMB) processes for separation of p-xylene, o-xylene and m-xylene, H₂ separation and air enrichment using zeolites and  natural gas liquefaction using multi-stream heat exchangers.

During the past decades there have been significant developments in the area of derivative-free methods, however, the vast majority of methods have been developed for box-constrained problems, or problems with known linear constraints [1, 6]. Moreover, dimensionality of the original problem and the number of constraints are two major limitations of the performance of existing methods, which are typically tested on a small set of problems with low dimensionality and small number of constraints.

In this work, we present a novel AlgoRithm for Global Optimization of coNstrAined grey-box compUTational problems (ARGONAUT), which is developed to solve constrained grey-box problems with a large number of input variables and constraints. The novel components of the algorithm involve variable selection, model identification for the objective and each of the grey-box constraints using a large pool of possible basis functions, surrogate model fitting and global optimization of the model parameters, global optimization of the grey-box formulation using a global optimization solver [7], clustering of the obtained local and global solutions, and iterative bound refinement until convergence. The capacity of ARGONAUT is shown through a large set of problems from known standard libraries for constrained optimization, a selected set of in-house applications, such as SMB process and protein structure prediction, and several applications from the open literature. In fact, this work aims to formalize a comprehensive test suite for constrained derivative-free algorithms. Finally, ARGONAUT is compared with commercially available constrained derivative-free software.

References:

1.         Conn AR, Scheinberg K, and Vicente LN, Introduction to derivative-free optimization. MPS-SIAM Series on Optimization. 2009, Philadelphia: SIAM.

2.         Forrester AIJ, Sóbester A, and Keane AJ, Engineering Design via Surrogate Modelling - A Practical Guide. 2008: John Wiley & Sons.

3.         Hasan MMF, et al., Nationwide, Regional, and Statewide CO2 Capture, Utilization, and Sequestration Supply Chain Network Optimization. Industrial & Engineering Chemistry Research, 2014; 53(18): p. 7489-7506

4.         Hasan MMF, First EL, and Floudas CA, Cost-effective CO2 capture based on in silico screening of zeolites and process optimization. Physical Chemistry Chemical Physics, 2013; 15(40): p. 17601-17618

5.         First EL, Hasan MMF, and Floudas CA, Discovery of novel zeolites for natural gas purification through combined material screening and process optimization. AIChE Journal, 2014; 60(5): p. 1767-1785

6.         Rios LM and Sahinidis NV, Derivative-free optimization: a review of algorithms and comparison of software implementations. Journal of Global Optimization, 2013; 56(3): p. 1247-1293.10.1007/s10898-012-9951-y

7.         Misener R and Floudas C, ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations. Journal of Global Optimization, In Press, DOI: 10.1007/s10898-014-0166-2, 2014