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author | RemyaDebasis | 2018-07-23 20:01:22 +0530 |
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committer | RemyaDebasis | 2018-07-23 20:01:22 +0530 |
commit | 69460c03b8b53068d60fd08d3180efc91e627603 (patch) | |
tree | 1689256f9ca4b9ce8076d3da8d5dac1b76963859 /code/fmincon/spring.sci | |
parent | f2539f26af7794da4ea4ccd8ae5ec2c753e94212 (diff) | |
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-rw-r--r-- | code/fmincon/spring.sci | 120 |
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diff --git a/code/fmincon/spring.sci b/code/fmincon/spring.sci new file mode 100644 index 0000000..0409dce --- /dev/null +++ b/code/fmincon/spring.sci @@ -0,0 +1,120 @@ +//The problem consists of minimizing the weight of a tension/compression spring subject to constraints on +//minimum deflection, shear stress, surge frequency, limits on outside diameter and on design variables. The design +//variables are the mean coil diameter D, the wire diameter d and the number of active coils N. The problem can be +//expressed as follows: +//Min f(x) = ( N + 2)*D*d^2 +//ST +//g1(x) = 1-D^3*N/(71785*d^4) <= 0; +//g2(x) = 1-140.45*d/(D^2*N) <= 0; +//g3(x) = (4*D^2-d*D)/(12566*(d^3*D-d^4)) + 1/(5108*d^2)-1 <= 0; +//g4(x) = (D+d)/1.5 - 1 <=0; +//The following ranges for the variables were used +//0.05 <= d <= 2.0, 0.25<= D <=1.3, 2.0<=N<=15.0 +// +//Ref:Arora, J. S.. Introduction IO optimum design New York McGraw-Hill, 1989 +//====================================================================== +// Copyright (C) 2018 - IIT Bombay - FOSSEE +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt +// Author:Debasis Maharana +// Organization: FOSSEE, IIT Bombay +// Email: toolbox@scilab.in +//====================================================================== +clc; + +function y = spring(x) + y = (x(3)+2)*x(1)^2*x(2); +endfunction + +function [C,Ceq] = Nonlinconstraint(x) + C(1) = 1-x(2)^3*x(3)/(71785*x(1)^4); + C(2) = 1-140.45*x(1)/(x(2)^2*x(3)); + C(3) = (4*x(2)^2-x(1)*x(2))/(12566*(x(1)^3*x(2)-x(1)^4)) + 1/(5108*x(1)^2)-1; + Ceq = [];C = C'; +endfunction + +function f = fGrad(x) + f = [2*x(1)*x(2)*(x(3)+2) x(1)^2*(x(3)+2) x(1)^2*x(2)]; +endfunction + +mprintf('minimizing the weight of a tension/compression spring '); +mprintf('\n\n Design variables include mean coil diameter:D, the wire diameter:d and the number of active coils:N '); +disp('The objective is :( N + 2)*D*d^2'); +mprintf('\nNon-linear constraints are on minimum deflection, shear stress, surge frequency,'); +mprintf('\nlinear constraint is on outside diameter'); + + +A = [1 1 0]; +b = 1.5; +mprintf('Bounds on the variable are as follows'); + +lb = [0.05 0.25 2]; +ub = [2 1.3 15]; +table = [['bounds', 'lb','ub'];[['d';'D';'N'],string(lb'),string(ub')]]; +disp(table); +x0 = lb + rand(1)*(ub-lb); +disp(x0,'Initial Guess is :'); + +input('press enter to continue'); + +mprintf('Scilab is solving your problem'); +options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", fGrad); + +[xopt,fval,exitflag,output] =fmincon(spring, x0,A,b,[],[],lb,ub,Nonlinconstraint,options); + +clc +select exitflag +case 0 + mprintf('Optimal Solution Found'); + mprintf('\n\nThe optimal design parameters are d = %f ,D = %f and N = %f m',xopt(1),xopt(2),xopt(3)); + mprintf('\n\nThe optimal objective is %f ',fval); + mprintf('\n\nIterations completed %d',output.Iterations); + mprintf('\nTotal CPU time %f',output.Cpu_Time); + mprintf('\nTotal Functional Evaluations %d',output.Objective_Evaluation); +case 1 + mprintf('Maximum Number of Iterations Exceeded. Output may not be optimal'); + input('press enter to view results'); + mprintf('\nThe optimal design parameters are d = %f ,D = %f and N = %f m',xopt(1),xopt(2),xopt(3)); + mprintf('\nThe optimal objective is %f ',fval); + mprintf('\nIterations completed %d',output.Iterations); + mprintf('\nTotal CPU time %f',output.Cpu_Time); + mprintf('\nTotal Functional Evaluations %d',output.Objective_Evaluation); +case 2 + mprintf('Maximum amount of CPU Time exceeded. Output may not be optimal.'); + input('press enter to view results'); + mprintf('\nThe optimal design parameters are d = %f ,D = %f and N = %f m',xopt(1),xopt(2),xopt(3)); + mprintf('\nThe optimal objective is %f ',fval); + mprintf('\nIterations completed %d',output.Iterations); + mprintf('\nTotal CPU time %f',output.Cpu_Time); + mprintf('\nTotal Functional Evaluations %d',output.Objective_Evaluation); +case 3 + mprintf('Stop at Tiny Step'); + input('press enter to view results'); + mprintf('\nThe optimal design parameters are d = %f ,D = %f and N = %f m',xopt(1),xopt(2),xopt(3)); + mprintf('\nThe optimal objective is %f ',fval); + mprintf('\nIterations completed %d',output.Iterations); + mprintf('\nTotal CPU time %f',output.Cpu_Time); + mprintf('\nTotal Functional Evaluations %d',output.Objective_Evaluation); +case 4 + mprintf('Solved To Acceptable Level'); + input('press enter to view results'); + mprintf('\nThe optimal design parameters are d = %f ,D = %f and N = %f m',xopt(1),xopt(2),xopt(3)); + mprintf('\nThe optimal objective is %f ',fval); + mprintf('\nIterations completed %d',output.Iterations); + mprintf('\nTotal CPU time %f',output.Cpu_Time); + mprintf('\nTotal Functional Evaluations %d',output.Objective_Evaluation); +case 5 + mprintf('Converged to a point of local infeasibility.'); + input('press enter to view results'); + mprintf('\nThe optimal design parameters are d = %f ,D = %f and N = %f m',xopt(1),xopt(2),xopt(3)); + mprintf('\nThe optimal objective is %f ',fval); + mprintf('\nIterations completed %d',output.Iterations); + mprintf('\nTotal CPU time %f',output.Cpu_Time); + mprintf('\nTotal Functional Evaluations %d',output.Objective_Evaluation); +end + + + |