Models Constrained Goal Attainment Problems: goals prob and mco prob
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The TOMLAB bundle testprob provides two sets of problems for constrained goal attainment problems: goals_prob and mco_prob.
An example of a constrained goal attainment problems
The basic structure of a constrained goal attainment problems is the following:
Failed to parse (unknown function "\multicolumn"): {\displaystyle \begin{array}{cccccc} \min\limits_x & \multicolumn{5}{l}{\max \ \ lam: r(x) - w * lam \leq g} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array} }
where , , , , , , and .
An example of a problem of this class, (that is also found in the TOMLAB quickguide) is goalsQG:
File: tomlab/quickguide/goalsQG_r.m, goalsQG_J.m, goalsQG_c, goalsQG_dc
r: Residual vector J: Jacobian matrix c: Nonlinear constraint vector dc: Nonlinear constraint gradient matrix
The following file illustrates how to define and solve a problem of this category in TOMLAB.
File: tomlab/quickguide/goalsQG.m
% goalsQG is a small example problem for defining and solving
% multi criteria optimization problems using the TOMLAB format.
Name='EASY-TP355';
% Constrained least squares problem, four quadratic terms and local solutions
% Hock W., Schittkowski K. (1981):
x_0 = zeros(4,1); % Lower bounds for x.
x_L = zeros(4,1); % Upper bounds for x.
x_U = 1e5*ones(4,1); % Starting point.
x_min = []; % For plotting.
x_max = []; % For plotting.
A = [1 0 0 0;0 1 0 0]; % Linear constraints.
b_L = [0.1;0.1]; % Lower bounds.
b_U = [0.1;0.1]; % Upper bounds.
c_L = 0; % Lower bounds.
c_U = 0; % Upper bounds.
y = zeros(2,1); % Residuals
Prob = clsAssign('goalsQG_r', 'goalsQG_J', [], x_L, x_U, Name, x_0,...
y, [], [], [], [], [],...
A, b_L, b_U, 'goalsQG_c', 'goalsQG_dc', [], c_L, c_U,...
x_min, x_max);
PriLev = 2;
Result = tomRun('goalSolve', Prob, PriLev);
mco_prob
In glb_prob there are 9 Multi-Criterium unconstrained and constrained nonlinear test problems with up to 10 variables and few constrains. In order to define the problem n and solve it execute the following in Matlab:
Prob = probInit('mco_prob',n); Result = tomRun('',Prob);
goals_prob
In goals_prob there are 9 constrained goal attainment test problems with sizes to 9 variables and about 10 constrains. In order to define the problem n and solve it execute the following in Matlab:
Prob = probInit('goals_prob',n); Result = goalSolve(Prob,1);