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authorRemyaDebasis2018-07-23 20:08:46 +0530
committerRemyaDebasis2018-07-23 20:08:46 +0530
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+// Reference: E. Sandgren,Nonlinear Integer and Discrete Programming in Mechanical I Design Optimization,Journal of Mechanical Design,JUNE 1990, Vol. 112/223
+
+//A cylindrical pressure vessel is capped at both ends by hemispherical heads.The total cost,
+//including the cost of material, cost of forming and welding,is to be minimized. The design variables are Ts and Th are the thicknesses of the shell and head, and R and L, the inner radius and length of the cylindrical section.These variables are denoted by X1 x2 , x3, and x4, respectively, and units for each are inches. The variables are such that R and L are continuous while Ts and Th are integer multiples of 0.0625 inch, the available thicknesses of rolled steel plates.
+// Min f = 0.6224*X(1)*X(3)*X(4) + 1.7781*X(2)*X(3)^2 + 3.1661*X(1)^2*X(4) + 19.84*X(1)^2*X(3)
+// subject to
+// g1(X) - X1 + 0.0193 X3 < = 0
+// g2(X) - x2 + 0.00954X3 <= 0
+// g3(X) -%pi*X3^2*X4 - (4/3)*%pi*X3^3 + 1296000 <= 0
+// g4(X) X4 - 240 <= 0
+
+//======================================================================
+// 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: Remya Kommadath
+// Organization: FOSSEE, IIT Bombay
+// Email: toolbox@scilab.in
+//======================================================================
+clc;
+
+// Onjective fucntion
+function f = ObjectiveFunction (X)
+ X(1:2) = X(1:2)*0.0625;
+ f = 0.6224*X(1)*X(3)*X(4) + 1.7781*X(2)*X(3)^2 + 3.1661*X(1)^2*X(4) + 19.84*X(1)^2*X(3);
+endfunction
+// Non linear equality and inequality constraints
+function [C,Ceq] = NLconstraints(X)
+ X(1:2) = (X(1:2))*0.0625;
+ C = -%pi*X(3)^2*X(4) - (4/3)*%pi*X(3)^3 + 1296000;
+ Ceq = [];
+endfunction
+// Linear inequality constraints
+A = [-0.0625 0 0.0193 0;0 -0.0625 0.00954 0;0 0 0 1];
+b = [0 0 240]';
+// Bounds of the variables
+lb = [1 1 10 10];
+ub = [99 99 200 200];
+nVar = length(lb);
+// Initial guess given to the solver
+x0 = [20 10 58.291 43.69];
+// indices of the integer decision variables
+int = [1 2];
+// Calling the solver
+[xopt,fopt,exitflag,output,lambda] = intfmincon(ObjectiveFunction,x0,int,A,b,[],[],lb,ub,NLconstraints)
+
+// Result representation
+// Converting the integer variables to the discrete variable
+x0(1:2) = x0(1:2)*0.0625;
+clc;
+disp(x0,"Initial guess given to the solver")
+select exitflag
+case 0
+ disp("Optimal Solution Found")
+ disp(xopt',"The optimum solution obtained")
+ disp(fopt,"The optimum value of the objective function")
+case 1
+ disp("Converged to a point of local infeasibility")
+case 2
+ disp("Objective Function is Continuous Unbounded")
+case 3
+ disp("Limit Exceeded")
+case 4
+ disp("User Interupt")
+case 5
+ disp("MINLP Errors")
+end