Models Global Optimization Problems: glb prob, lgo1 prob, lgo2 prob and gkls prob

Example of a global optimization problem

The basic structure of a global optimization problem with simple bounds is the following

${\begin{array}{ll}\min \limits _{x}&f(x)\\&\\s/t&{\begin{array}{llcccll}-\infty <&x_{L}&\leq &x&\leq &x_{U}&<\infty \\\end{array}}\end{array}}$

where $x,x_{L},x_{U}\in \mathbb {R} ^{n}$, $f(x)\in \mathbb {R}$. The variables $x\in I$, the index subset of $1,...,n$, are restricted to be integers.

The following file is required to define a problem of this category in TOMLAB.

File: tomlab/quickguide/glbQGf.m

f:	Function

An example of a problem of this class, (that is also found in the TOMLAB quickguide) is glbQG:

File: tomlab/quickguide/glbQG.m

% glbQG is a small example problem for defining and solving
% unconstrained global programming problems using the TOMLAB format.

Name = 'Shekel 5';
x_L = [ 0  0  0  0]';  % Lower bounds for x.
x_U = [10 10 10 10]';  % Upper bounds for x.
x_0 = [-3.0144 -2.4794 -3.1584 -3.1790]; % May not be used.
x_opt = [];
f_opt = -10.1531996790582;
f_Low=-20;             % Lower bound on function.
x_min = [ 0  0  0  0]; % For plotting
x_max = [10 10 10 10]; % For plotting

Prob = glcAssign('glbQG_f', x_L, x_U, Name, [], [], [], ...
                  [], [], [], x_0, ...
                  [], [], [], [], ...
                  f_Low, x_min, x_max, f_opt, x_opt);

Prob.optParam.MaxFunc = 1500;

Result1 = tomRun('glbFast', Prob, 1);  %Global solver
Result2 = tomRun('conSolve', Prob, 1); %Local solver

% Result = tomRun('glbSolve', Prob, 1);
% Result = tomRun('glcSolve', Prob, 1);
% Result = tomRun('glcFast', Prob, 1);
% Result = tomRun('lgo', Prob, 1);
% Result = tomRun('oqnlp', Prob, 1);

glb_prob

In glb_prob there are 51 unconstrained global optimization test problems with sizes to 100 variables. In order to define the problem n and solve it execute the following in Matlab:

Prob	= probInit('glb_prob',n); 
Result  = tomRun('',Prob);

lgo1_prob

In glo1_prob there are 30 global optimization test problems in one dimension. In order to define the problem n and solve it execute the following in Matlab:

Prob	= probInit('lgo1_prob',n); 
Result  = tomRun('',Prob);

lgo2_prob

In glo2_prob there are 30 global optimization test problems in two up to four dimensions. In order to define the problem n and solve it execute the following in Matlab:

Prob	= probInit('lgo2_prob',n); 
Result  = tomRun('',Prob);

gkls_prob

In gkls_prob there are 300 global optimization test problems in two dimensions. In order to define the problem n and solve it execute the following in Matlab:

Prob	= probInit('gkls_prob',n); 
Result  = tomRun('',Prob);