Enhanced surrogate assisted framework for constrained global optimization of expensive black-box functions

Abstract An enhanced surrogate assisted framework, based on Probability of Improvement (PI) method, is proposed in this paper. We made some modifications to the original PI approach to enhance the performance of the modeling and optimization framework, leading to fewer rigorous simulations to find the optimal solution without loss of accuracy. We also extended the algorithm for handling general constraints using a fully probabilistic approach. The behavior of the proposed framework was investigated through a set of 9 Unconstrained Test Functions (UTF), 7 Constrained Optimization Problems (COP) and 3 Chemical Engineering Problems (CEP). The numerical results indicate that a lower number of rigorous model simulations were needed for optimizing UTF compared to the classic PI method and that the proposed framework was capable of achieving sustained near optimal solutions for COP and CEP. These results indicate that the proposed framework is suitable for solving computationally expensive constrained black-box optimization problems.

[1]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[2]  Fan Ye,et al.  Two-level Multi-surrogate Assisted Optimization method for high dimensional nonlinear problems , 2016, Appl. Soft Comput..

[3]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox, Version 2.0 , 2002 .

[4]  Mohammad Reza Hadjmohammadi,et al.  Response surface methodology and support vector machine for the optimization of separation in linear gradient elution. , 2008, Journal of separation science.

[5]  Christine A. Shoemaker,et al.  SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems , 2013, Comput. Oper. Res..

[6]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[7]  Min Xie,et al.  A systematic comparison of metamodeling techniques for simulation optimization in Decision Support Systems , 2010, Appl. Soft Comput..

[8]  Rommel G. Regis,et al.  Multi-objective constrained black-box optimization using radial basis function surrogates , 2016, J. Comput. Sci..

[9]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[10]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[11]  Malte Prieß,et al.  Marine ecosystem model calibration with real data using enhanced surrogate-based optimization , 2013, J. Comput. Sci..

[12]  Bjarne Grimstad,et al.  Global optimization of multiphase flow networks using spline surrogate models , 2016, Comput. Chem. Eng..

[13]  Ignacio E. Grossmann,et al.  Disjunctive Programming Techniques for the Optimization of Process Systems with Discontinuous Investment Costs−Multiple Size Regions , 1996 .

[14]  Argimiro Resende Secchi,et al.  EMSO: A new environment for modelling, simulation and optimisation , 2003 .

[15]  Andy J. Keane,et al.  On the Design of Optimization Strategies Based on Global Response Surface Approximation Models , 2005, J. Glob. Optim..

[16]  Zilong Wang,et al.  Surrogate-based Optimization for Pharmaceutical Manufacturing Processes , 2017 .

[17]  José Antonio Caballero,et al.  Large scale optimization of a sour water stripping plant using surrogate models , 2016, Comput. Chem. Eng..

[18]  Matthew J. Realff,et al.  Metamodeling Approach to Optimization of Steady-State Flowsheet Simulations: Model Generation , 2002 .

[19]  Andrea Cipollina,et al.  A neural network-based optimizing control system for a seawater-desalination solar-powered membrane distillation unit , 2013, Comput. Chem. Eng..

[20]  David C. Miller,et al.  Learning surrogate models for simulation‐based optimization , 2014 .

[21]  Christodoulos A. Floudas,et al.  Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO , 2016, Eur. J. Oper. Res..

[22]  Christodoulos A. Floudas,et al.  Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption , 2017, J. Glob. Optim..

[23]  Sujin Bureerat,et al.  Optimum plate-fin heat sinks by using a multi-objective evolutionary algorithm , 2010 .

[24]  Jerome Sacks,et al.  Choosing the Sample Size of a Computer Experiment: A Practical Guide , 2009, Technometrics.

[25]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[26]  Atharv Bhosekar,et al.  Advances in surrogate based modeling, feasibility analysis, and optimization: A review , 2018, Comput. Chem. Eng..

[27]  Jack P. C. Kleijnen,et al.  Regression and Kriging metamodels with their experimental designs in simulation: A review , 2017, Eur. J. Oper. Res..

[28]  Tao Chen,et al.  Meta-modelling in chemical process system engineering , 2017 .

[29]  Christine A. Shoemaker,et al.  A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions , 2007, INFORMS J. Comput..

[30]  Tao Chen,et al.  Response surface methodology with prediction uncertainty: A multi-objective optimisation approach , 2012 .

[31]  Wei-Ling Liu,et al.  Expected improvement in efficient experimental design supported by a global optimizer , 2014 .

[32]  David Herrero Pérez,et al.  Kriging-based infill sampling criterion for constraint handling in multi-objective optimization , 2016, J. Glob. Optim..

[33]  Christodoulos A. Floudas,et al.  Global optimization of grey-box computational systems using surrogate functions and application to highly constrained oil-field operations , 2018, Comput. Chem. Eng..

[34]  Morad Behandish,et al.  Concurrent Pump Scheduling and Storage Level Optimization Using Meta-Models and Evolutionary Algorithms , 2017, ArXiv.

[35]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[36]  Wolfgang Marquardt,et al.  The validity domain of hybrid models and its application in process optimization , 2007 .

[37]  Ke Li,et al.  Energy and cost optimization of shell and tube heat exchanger with helical baffles using Kriging metamodel based on MOGA , 2016 .

[38]  Argimiro Resende Secchi,et al.  Enhanced Surrogate Assisted Global Optimization Algorithm Based on Maximizing Probability of Improvement , 2017 .

[39]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[40]  Efstratios N. Pistikopoulos,et al.  Optimal design of energy systems using constrained grey-box multi-objective optimization , 2018, Comput. Chem. Eng..

[41]  Argimiro R. Secchi,et al.  Optimization of chemical engineering problems with EMSO software , 2018, Comput. Appl. Eng. Educ..