MATLAB Surrogate Model Toolbox.zip

MATSuMoTo Code Documentation

Juliane M¨uller

Cornell University

School of Civil and Environmental Engineering

Ithaca, NY, USA

email: juliane.mueller2901@gmail.com

March 28, 2014

1 Introduction

This documentation accompanies MATSuMoTo, the MATLAB Surrogate Model Toolbox for

running a computer simulation and hence the analytical description of the objective function is not

available (black box). Furthermore, these objective functions are generally multimodal, i.e. there are

several local minima and the goal is to find the global minimum.

MATSuMoTo contains ideas from the following published papers that should be cited when the

toolbox is used:

1. J. M¨uller and R. Pich´e, 2011. ”Mixture Surrogate Models Based on Dempster-Shafer Theory

2. J. M¨uller, C.A. Shoemaker, and R. Pich´e, 2013. ”SO-MI: A Surrogate Model Algorithm for

For better comprehension of the algorithmic concepts in MATSuMoTo, we recommend reading

these papers. However, it is also possible to learn how to use MATSuMoTo ”just as a tool” by

going through the examples provided in this document and formulating own optimization problems

by using these examples as templates. The code is thoroughly commented and we encourage the

interested user to look also at the code for implementation details.

This document is structured as follows. In Section 2, we summarize the steps of a general surrogate

model algorithm to give the user a broad idea of how MATSuMoTo works. The installation and

software requirements are briefly described in Section 3. Section 4 describes how to use the test

driver to check if the installation was successful. Section 5 describes the options for the user’s

2 Surrogate Model Algorithms

Computer simulations are used to approximate complex physical behavior. These simulations are

often computationally expensive, and thus during an optimization the goal is to find optimal solutions

by using only very few of these expensive function evaluations. Surrogate models (also known as

response surfaces or metamodels) are used to approximate the expensive simulation model [1]. During

the optimization phase information from the surrogate model is used to guide the search for improved

solutions. The predictions of the surrogate model at unsampled points are used to carefully select

new points where the computationally expensive objective function will be evaluated. This approach

reduces the computation time of the optimization considerably because fewer expensive function

evaluations are required for finding the optimum. Most surrogate model algorithms consist of the

5. Do the expensive function evaluation(s) at the point(s) selected in Step 4.

6. Check if the stopping criterion has been reached. If not, got to Step 3. If the stopping criterion

Surrogate model algorithms in the literature differ mainly with respect to

Typically used stopping criteria are a maximum number of allowed function evaluations (used in

MATSuMoTo), a maximal allowed CPU time, or a maximum number of failed iterative improvement

3 Installation

MATSuMoTo requires MATLAB version 2010b or newer and the MATLAB Statistics Toolbox. To use

MATSuMoTo, download the file MATSuMoTo.zip and unzip it in a location known to the MATLAB

search path. Alternatively, you can add a new folder to the MATLAB search path by clicking in the

MATLAB window on

and browse to the location of the unzipped folder MATSuMoTo. Click on the folder, and click on

Depending on the options selected, MATSuMoTo requires also the following MATLAB toolboxes:

option of selecting the minimum point of the surrogate model as new sample point will be disabled

(for options of selecting sample points, see Section 5.3).

4 Test Driver

You can try if your installation was successful by using the test driver included in the toolbox. Type

>> TestDriver

into the MATLAB command prompt. If you get an error similar to

??? Undefined function or method ’TestDriver’ for input arguments of type ’char’

then MATLAB does not know the folder in which to look for the files, indicating that something went

wrong when adding the folder to MATLAB’s search path. Should you get an error similar to

Error using feval

then not all subfolders were added to the MATLAB search path. Go back to Section 3, and select

If no error messages appear, the test driver will run the optimization of a continuous problem, a pure

Figure 2: Progress plot for the continuous test problem.

Figure 3: Progress plot for the integer test problem.

Figure 4: Progress plot for the mixed-integer test problem.

5 User Specified Input

The main file from which to start MATSuMoTo is MATSuMoTo.m. The user can define sev-

eral input arguments (see the details later in this section). The algorithm starts by checking

the user’s input (function InputCheck.m) and assigns default values to options that have not

been set by the user as input arguments. Then, depending on whether the optimization prob-

lem is continuous, integer, or mixed-integer, the corresponding optimization function is called

(Optimization continuous,Optimization integer, or Optimization mixedinteger). After the optimization

initial experimental design technique, the number of points in the initial experimental design, specific

starting points, or the number of points to be selected in every iteration of the algorithm are optional.

The general function call is as follows:

>> [xbest, fbest] = MATSuMoTo(data_file,maxeval,surogate_model,sampling_technique,...

initial_design,number_startpoints,starting_point,NumberNewSamples);