SMBO_TeachingTool

SMBO_TeachingTool: A modular code for teaching Surrogate Modeling-Based Optimization.

This code is designed for students to understand basic concept of Surrogate Modeling-Based Optimization.

Author

Yong Hoon Lee
Engineering System Design Laboratory (PI: Professor James T. Allison),
University of Illinois at Urbana-Champaign

Prerequisites

• MATLAB with Optimization and Global Optimization Toolboxes
• (optional for plot export) Ghostscript

How to execute

• Run "main_SMBO.m" Script

• Specify the problem name (= problem folder name) in the "prob" variable before run the script to solve a different problem.

  • Example (in "main_SMBO.m" file):

    prob = 'AckleyFn';

How to create a customized problem

• Create a folder with problem name (e.g., "MatyasFn").

• Create a MATLAB function file: "obj.m" in the created problem folder.

  • Example:

    function f = obj(x)
        f = 0.26*(x(1)^2 + x(2)^2) - 0.48*x(1)*x(2);
    end

• Create a MATLAB function file: "conf.m" in the created problem folder.

  • Example:

    function pc = conf()
        pc.nvar = 2;                % Number of variables
        pc.lb = [-10,-10];          % Lower bounds
        pc.ub = [5,5];              % Upper bounds
        pc.fs_g = 0.75;             % Shrink factor for global sample range
        pc.xtrue = [0,0];           % True soltuion in x (for comparison)
        pc.ftrue = 0;               % True solution in f (for comparison)
    end

Course Material: Practical implementation of Surrogate modeling-based optimization

Yong Hoon Lee

References

• Wang, G. G. and Shan, S. (2006) Review of Metamodeling Techniques in Support of Engineering Design Optimization. J. Mech. Design 129:4, pp. 370-380. doi: 10.1115/1.2429697
• Koziel, S. and Leifsson, L. (2016) Introduction to Surrogate Modeling and Surrogate-Based Optimization. In: Simulation-Driven Design by Knowledge-Based Response Correction Techniques. Springer, Cham. pp. 31-61. doi: 10.1007/978-3-319-30115-0_4
• Forrester, A., Sobester, A., Keane, A. (2008) Engineering Design via Surrogate Modelling: A Practical Guide. Wiley.
• Lee, Y. H. (2017) SMBO_TeachingTool: A modular code for teaching Surrogate Modeling-Based Optimization v1.5 (April 17, 2017). https://github.com/yonghoonlee/SMBO_TeachingTool/releases

Concept and flow of the SMBO tool

• Conventional Optimization

  

  

  Koziel, S. and Leifsson, L. (2016)

• Surrogate-Based Optimization

  

  

  Koziel, S. and Leifsson, L. (2016)

: utility function, which is a scalar value

: objective function, values could be a scalar or vector

In this code, we are only looking at a single-objective optimization problem. If the problem has multiple objective functions, the utility function can be formulated for the SMBO tool, which is developed for single-objective problem.

Surrogate model construction flow

Pseudo-code explaination with line numbers

While-loop: Adaptive surrogate modeling refinement (Line 94-177)
    Design Space Sampling (Line 97-124)
    High Fidelity Model Evaluation (Line 126-132)
    Surrogate Modeling-Based Optimization (Line 134-176)
        Compile results of (1) Current and (2) Previous iterations (Line 135-144)
        Surrogate-model construction / Surrogate-based optimization (Line 146-158)
    Error evaluation using high fidelity model (Line 160-172)
        Run high fidelity model evaluation for predicted optimum (Line 161-162)
        Save high fidelity function result at the predicted optimum (Line 164-166)
    Adjust sampling range for the next iteration (Line 174-176)
End while

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Sampling: Space-filling DoE (Line 97-124)

High fidelity response of training points (Line 126-132)

Compile results of current and previous iterations to construct surrogate model (Line 135-144)

Surrogate-model construction / Surrogate-based optimization (Line 146-158)

Radial Basis Function

Error evaluation using high fidelity model (Line 160-172)

Adjust sampling range for the next iteration (Line 174-176)