Models Constrained Global Optimization Problems: glc prob

This page is part of TOMLAB Models. See TOMLAB Models.

In glc_prob there are 30 global mixed-integer nonlinear programming test problems with sizes to 20 variables and 5 constrains. In order to define the problem n and solve it execute the following in Matlab:

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

The basic structure of a constrained global optimization problems is the following

${\begin{array}{ll}\min \limits _{x}&f(x)\\&\\s/t&{\begin{array}{llcccll}-\infty <&x_{L}&\leq &x&\leq &x_{U}&<\infty \\&b_{L}&\leq &Ax&\leq &b_{U}&\\&c_{L}&\leq &c(x)&\leq &c_{U},&~x_{j}\in \mathbb {N} \ ~~\forall j\in I,\\\end{array}}\end{array}}$

where $x,x_{L},x_{U}\in \mathbb {R} ^{n}$, $f(x)\in \mathbb {R}$, $A\in \mathbb {R} ^{m_{1}\times n}$, $b_{L},b_{U}\in \mathbb {R} ^{m_{1}}$ and $c_{L},c(x),c_{U}\in \mathbb {R} ^{m_{2}}$. The variables $x\in I$, the index subset of $1,...,n$, are restricted to be integers.

The following files are required to define a problem of this category in TOMLAB.

File: tomlab/quickguide/glcQG f.m, glcQG c.m

f:	Function
c: 	Constraints

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

File: tomlab/quickguide/glcQG.m

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

Name = 'Hock-Schittkowski 59';
u = [75.196    3.8112    0.0020567  1.0345E-5  6.8306    0.030234   1.28134E-3 ...
     2.266E-7  0.25645   0.0034604  1.3514E-5  28.106    5.2375E-6  6.3E-8     ...
     7E-10     3.405E-4  1.6638E-6  2.8673     3.5256E-5];

x_L = [0 0]';     % Lower bounds for x.
x_U = [75 65]';   % Upper bounds for x.
b_L = []; b_U = []; A = []; % Linear constraints
c_L = [0 0 0];    % Lower bounds for nonlinear constraints.
c_U = [];         % Upper bounds for nonlinear constraints.
x_opt = [13.55010424 51.66018129]; % Optimum vector
f_opt = -7.804226324;              % Optimum
x_min = x_L;      % For plotting
x_max = x_U;      % For plotting
x_0 = [90 10]';   % If running local solver

Prob = glcAssign('glcQG_f', x_L, x_U, Name, A, b_L, b_U, ...
                  'glcQG_c', c_L, c_U, x_0, ...
                  [], [], [], [], ...
                  [], x_min, x_max, f_opt, x_opt);

Prob.user.u = u;
Prob.optParam.MaxFunc = 1500;

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