diff options
Diffstat (limited to 'code/fminbnd')
| -rw-r--r-- | code/fminbnd/Chichinadze.sce | 64 | ||||
| -rw-r--r-- | code/fminbnd/Cola.sce | 89 |
2 files changed, 153 insertions, 0 deletions
diff --git a/code/fminbnd/Chichinadze.sce b/code/fminbnd/Chichinadze.sce new file mode 100644 index 0000000..efd79f2 --- /dev/null +++ b/code/fminbnd/Chichinadze.sce @@ -0,0 +1,64 @@ +//Reference: Ernesto P. Adorio and U.P. Diliman,"MVF - Multivariate Test Functions +//Library in C for Unconstrained Global Optimization",2005, +//http://www.geocities.ws/eadorio/mvf.pdf, Last accessed, 11th June 2018 +//Example: The 2-dimensional function mvfChichinadze computes +//f = x1^2 - 12*x1 + 11 + 10*cos(%pi/2*x1)) + 8*sin(5*%pi*x1)) - 1/sqrt(5)*exp(-(x2)-0.5)^2/2) +//with domain −30 ≤ x0 ≤ 30, −10 ≤ x1 ≤ 10. The global minimum is 43.3159 at (5.90133, 0.5). +// + +clc; +//Objective Function +function f = Chichinadze(x) + f = x(1)^2 - 12*x(1) + 11 + 10*cos(%pi/2*x(1)) + 8*sin(5*%pi*x(1)) - 1/sqrt(5)*exp(-(x(2)-0.5)^2/2) +endfunction + +//Lower bound on the variables +x1 = [-30 -10]; +//Upper bound on the variables +x2 = [30 10]; + +Maxit = 1500; +CPU = 100; +Tolx = 1e-6; + +mprintf('The termination criteria is as follows: Maximum Iterations = %d, Maximum CPU time = %d, Tolerance on solution = %f',Maxit,CPU,Tolx); + +//Options structure +options=list("MaxIter",Maxit,"CpuTime", CPU,"TolX",Tolx) + +[xopt,fopt,exitflag,output,lambda]=fminbnd(Chichinadze,x1,x2,options) + +// Result representation +clc; +select exitflag +case 0 + disp("Optimal Solution Found") + disp(xopt',"The optimum solution obtained is") + disp(fopt,"The objective function value is") +case 1 + disp("Maximum Number of Iterations Exceeded. Output may not be optimal") + disp(xopt,"The solution obtained") + f = Chichinadze(xopt) + disp(f,"The objective function value is") +case 2 + disp("Maximum CPU Time exceeded. Output may not be optimal") + disp(xopt,"The solution obtained") + f = Chichinadze(xopt) + disp(f,"The objective function value is") +case 3 + disp("Stop at Tiny Step") + disp(xopt,"The solution obtained") + f = Chichinadze(xopt) + disp(f,"The objective function value is") +case 4 + disp("Solved To Acceptable Level") + disp(xopt,"The solution obtained") + f = Chichinadze(xopt) + disp(f,"The objective function value is") +case 5 + disp("Converged to a point of local infeasibility") + disp(xopt,"The solution obtained") + f = Chichinadze(xopt) + disp(f,"The objective function value is") +end +disp(output) diff --git a/code/fminbnd/Cola.sce b/code/fminbnd/Cola.sce new file mode 100644 index 0000000..203a3c4 --- /dev/null +++ b/code/fminbnd/Cola.sce @@ -0,0 +1,89 @@ +//Reference: Ernesto P. Adorio and U.P. Diliman,"MVF - Multivariate Test Functions +//Library in C for Unconstrained Global Optimization",2005, +//http://www.geocities.ws/eadorio/mvf.pdf, Last accessed, 11th June 2018 +//Example: The 17-dimensional function mvfCola computes indirectly the formula f(n,u) +//by setting x0 = y0, x1 = u0, x(i) = u(2(i−2)), y(i) = u(2(i−2)+1) +//f(n,u) = h(x,y) =sum((r(i,j) − d(i,j))^2) for all j<i +//r(i,j) = [(x(i) − x(j) )^2 + (y(i) − y(j))^2]^1/2 +//This function has bounds 0 ≤ x0 ≤ 4 and −4 ≤ xi ≤ 4 for i = 1 . . . n − 1. It +//has a global minimum of 11.7464. +//u = [0.651906,1.30194,0.099242,-0.883791,-0.8796,0.204651,-3.28414,0.851188,-3.46245,2.53245,-0.895246,1.40992,-3.07367,1.96257,-2.97872,-0.807849,-1.68978]; +// + +clc; +//Objective Function +function summation = Cola(u) + + d = [ 0 0 0 0 0 0 0 0 0 0 + 1.27 0 0 0 0 0 0 0 0. 0 + 1.69 1.43 0 0 0 0 0 0 0 0 + 2.04 2.35 2.43 0 0 0 0 0 0 0 + 3.09 3.18 3.26 2.85 0 0 0 0 0 0 + 3.20 3.22 3.27 2.88 1.55 0 0 0 0 0 + 2.86 2.56 2.58 2.59 3.12 3.06 0 0 0 0 + 3.17 3.18 3.18 3.12 1.31 1.64 3.00 0 0 0 + 3.21 3.18 3.18 3.17 1.70 1.36 2.95 1.32 0 0 + 2.38 2.31 2.42 1.94 2.85 2.81 2.56 2.91 2.97 0]; + summation = 0; + + for i = 1:10 + for j = 1:9 + if j<i + x(1) = 0; y(1) = 0;y(2) = 0; x(2)= u(1); + if i>2 + x(i) = u(2*(i-2));y(i) = u(2*(i-2)+1); + end + r(i,j) = ((x(i) - x(j))^2 + (y(i)-y(j))^2)^0.5; + summation = summation + (( r(i,j) - d(i,j) )^2) + end + end + end + +endfunction + + +//Lower bound +x1 = [0 -4*ones(1,16)]; +//Upper bound +x2 = 4*ones(1,17); + +//Options structure +options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6]) + +[xopt,fopt,exitflag,output,lambda]=fminbnd(Cola,x1,x2,options) + +// Result representation +clc; +select exitflag +case 0 + disp("Optimal Solution Found") + disp(xopt',"The optimum solution obtained is") + disp(fopt,"The objective function value is") +case 1 + disp("Maximum Number of Iterations Exceeded. Output may not be optimal") + disp(xopt,"The solution obtained") + f = Cola(xopt) + disp(f,"The objective function value is") +case 2 + disp("Maximum CPU Time exceeded. Output may not be optimal") + disp(xopt',"The solution obtained") + f = Cola(xopt) + disp(f,"The objective function value is") +case 3 + disp("Stop at Tiny Step") + disp(xopt',"The solution obtained") + f = Cola(xopt) + disp(f,"The objective function value is") +case 4 + disp("Solved To Acceptable Level") + disp(xopt',"The solution obtained") + f = Cola(xopt) + disp(f,"The objective function value is") +case 5 + disp("Converged to a point of local infeasibility") + disp(xopt',"The solution obtained") + f = Cola(xopt) + disp(f,"The objective function value is") +end +disp(output) + |