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+//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
+
+
+