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Diffstat (limited to 'code/fmincon/Tankprob.sci')
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1 files changed, 95 insertions, 0 deletions
diff --git a/code/fmincon/Tankprob.sci b/code/fmincon/Tankprob.sci new file mode 100644 index 0000000..500090e --- /dev/null +++ b/code/fmincon/Tankprob.sci @@ -0,0 +1,95 @@ +//Design a circular tank, closed at both ends, with a volume of 200 m3.The cost is proportional to the surface area of material, which is priced +//at $400/m2. The tank is contained within a shed with a sloping roof,thus the height of the tank h is limited by h ≤ 12 − d/2, where d is +//the tank diameter. Formulate the minimum cost problem and solve the design problem. +//Ref:Diwekar, Urmila,Introduction to Applied Optimization, Introduction to Applied Optimization, Editor:Ding-Zhu Du, Springer Optimization and Its Applications Springer Optimization and Its Applications, VOL 22, Chapter 3 + +// 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 cost = Tankprob(x) + r = x(1);h = x(2); + cost = (2*%pi*r*h+2*%pi*r^2)*400; +endfunction + +function [ceq,c] = Nonlinearcon(x) + r = x(1);h = x(2); + c = []; + ceq = 200-%pi*r^2*h; +endfunction + +function y=Gradobj(x) + y= [800*%pi*x(2) + 1600*%pi*x(1),800*%pi*x(1)]; +endfunction + +mprintf('\nDesign a circular tank, closed at both ends, with a volume of 200 m3 with minimum cost.\n The tank is contained within a shed with a sloping roof,thus the height of the tank h is limited') +mprintf('\nCost of material is: %f',400); +mprintf('The design variables are radius and height of the tank') + +A = [1 1];b = 12; + +x0 = input('Enter initial guess as vector:'); +if (sum(x0<=0) | (length(x0)~=2)) + x0 = [1 2]; + mprintf('Incorrect initial guess...\n changing initial guess to r = %d and h = %d',x0(1),x0(2)); +end + + +lb = [0 0]; +input('press enter to continue') +options=list("MaxIter",1000,"GradObj", Gradobj); + +[xopt,fopt,exitflag,output1] = fmincon(Tankprob,x0,A,b,[],[],lb,[],Nonlinearcon,options); + +[xopt1,fopt1,exitflag1,output2] = fmincon(Tankprob,x0,A,b,[],[],lb,[],Nonlinearcon); + +clc +select exitflag +case 0 + mprintf('Optimal Solution Found'); + mprintf('\nThe optimal radius and height of the tank are %f m and %f m',xopt(1),xopt(2)); + mprintf('\nThe volume of the tank is %f m^3',%pi*xopt(1)^2*xopt(2)); + mprintf('\nThe total surface area and cost of the tank are %f m^2 and %f $',fopt/400,fopt) + mprintf('\nTime taken to solve the problem with gradient information is %f s and without gradient information is %f s',output1.Cpu_Time,output2.Cpu_Time); +case 1 + mprintf('Maximum Number of Iterations Exceeded. Output may not be optimal'); + input('press enter to view results'); + printf('\nThe optimal radius and height of the tank are %f m and %f m',xopt(1),xopt(2)); + mprintf('\nThe volume of the tank is %f m^3',%pi*xopt(1)^2*xopt(2)); + mprintf('\nThe total surface area and cost of the tank are %f m^2 and %f $',fopt/400,fopt) +case 2 + mprintf('Maximum amount of CPU Time exceeded. Output may not be optimal.'); + input('press enter to view results'); + printf('\nThe optimal radius and height of the tank are %f m and %f m',xopt(1),xopt(2)); + mprintf('\nThe volume of the tank is %f m^3',%pi*xopt(1)^2*xopt(2)); + mprintf('\nThe total surface area and cost of the tank are %f m^2 and %f $',fopt/400,fopt) +case 3 + mprintf('Stop at Tiny Step'); + input('press enter to view results'); + printf('\nThe optimal radius and height of the tank are %f m and %f m',xopt(1),xopt(2)); + mprintf('\nThe volume of the tank is %f m^3',%pi*xopt(1)^2*xopt(2)); + mprintf('\nThe total surface area and cost of the tank are %f m^2 and %f $',fopt/400,fopt) +case 4 + mprintf('Solved To Acceptable Level'); + input('press enter to view results'); + printf('\nThe optimal radius and height of the tank are %f m and %f m',xopt(1),xopt(2)); + mprintf('\nThe volume of the tank is %f m^3',%pi*xopt(1)^2*xopt(2)); + mprintf('\nThe total surface area and cost of the tank are %f m^2 and %f $',fopt/400,fopt) +case 5 + mprintf('Converged to a point of local infeasibility.'); + input('press enter to view results'); + printf('\nThe optimal radius and height of the tank are %f m and %f m',xopt(1),xopt(2)); + mprintf('\nThe volume of the tank is %f m^3',%pi*xopt(1)^2*xopt(2)); + mprintf('\nThe total surface area and cost of the tank are %f m^2 and %f $',fopt/400,fopt) +end + + |