PROPT Genetic 1
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This page is part of the PROPT Manual. See PROPT Manual. |
PROCEEDINGS OF WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY VOLUME 21 JANUARY 2007 ISSN 1307-6884
Optimal Control Problem, Quasi-Assignment Problem and Genetic Algorithm Omid S. Fard and Akbar H. Borzabadi
See paper for failure of GA toolbox algorithm.
Example 1
Problem Formulation
Find u over t in [0; 1 ] to minimize
subject to:
The initial condition are:
% Copyright (c) 2007-2008 by Tomlab Optimization Inc.
Problem setup
toms t
p = tomPhase('p', t, 0, 1, 50);
setPhase(p);
tomStates x
tomControls u
% Initial guess
x0 = {icollocate(x == 0.5*t); collocate(u == 0)};
% Boundary constraints
cbnd = {initial({x == 0}); final({x == 0.5})};
% ODEs and path constraints
ceq = collocate({dot(x) == x.^2+u});
% Objective
objective = integrate(u.^2);
Solve the problem
options = struct;
options.name = 'Genetic 1';
solution = ezsolve(objective, {cbnd, ceq}, x0, options);
t = subs(collocate(t),solution);
x = subs(collocate(x),solution);
u = subs(collocate(u),solution);
Problem type appears to be: qpcon Time for symbolic processing: 0.072891 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Genetic 1 f_k 0.178900993395126690 sum(|constr|) 0.000000000698073988 f(x_k) + sum(|constr|) 0.178900994093200680 f(x_0) 0.000000000000000000 Solver: snopt. EXIT=0. INFORM=1. SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 ConstrEv 23 ConJacEv 23 Iter 22 MinorIter 71 CPU time: 0.031200 sec. Elapsed time: 0.033000 sec.
Plot result
subplot(2,1,1)
plot(t,x,'*-');
legend('x');
title('Genetic 1 state variables');
subplot(2,1,2)
plot(t,u,'+-');
legend('u');
title('Genetic 1 control');