Error using fmincon Too many input arguments

15 Dec 2021
2 Answers
Updated 16 Dec 2021
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Hello , I have an emargency problem as the due date of my project is close. while every things is correct I dont know why when I run my code, it gives me an error of too many input arguments.
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% Wheelchair
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function Wheelchair
% clc;
clear all; close all;
dp=design_parameters; % Generate structure variable containing all design parameters
f=@(x)objective_function(x,dp); % Objective function handle
nonlcon=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
x0=[25e-3;1.5e-3;20e-3;1e-3]; % Initial design point
A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
b=[-1,-1,1,-1,1,-1,1,-1,1];
% Minimization using fmincon and the specified options:
options=optimoptions('fmincon','Display','iter','OptimalityTolerance',1e-12,'ConstraintTolerance',1e-6,'StepTolerance',1e-12);
[x,fval]=fmincon(f,x0,A,b,[],[],lb,ub,nonlcon,options);
% Display of the optimal design results:
disp(['Optimal value of d1: ',num2str(x(1)),' mm']);
disp(['Optimal value of t1: ',num2str(x(2)),' mm']);
disp(['Optimal value of d2: ',num2str(x(3)),' mm']);
disp(['Optimal value of t2: ',num2str(x(4)),'mm']);
disp(['Optimal value of f: ',num2str(fval),' kg']);
end
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function dp=design_parameters
dp.L1=0.82; %(m)
dp.L2=0.691; %(m)
dp.L3=0.270; %(m)
dp.L4=0.04; %(m)
dp.L5=1.59; %(m)
dp.L6=0.627; %(m)
dp.L7=0.568;
dp.Lad=0.601;
dp.Lss=0.4;
dp.mb=150;
dp.Rho=2700;
dp.g=10;
dp.db=6e-3;
dp.sigmau=110e6;
dp.E=70e9;
dp.K=2.1;
dp.deltamax=1e-3;
dp.X1_min=20e-3; dp.X1_max=30e-3; %
dp.X2_min=1e-3; dp.X2_max=2e-3; %
dp.X3_min=1e-3; dp.X3_max=22e-3; %
dp.X4_min=0.8e-3; dp.X4_max=1.5e-3;
end
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function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;
f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); %
end
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function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;
c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
ceq=[]; % There are no nonlinear equality constraints
end
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Walter Roberson
Walter Roberson on 15 Dec 2021
Ran in:
Ran in:
Works for me ?
Wheelchair()
First-order Norm of Iter F-count f(x) Feasibility optimality step 0 5 1.849113e+00 0.000e+00 2.879e+02 1 16 1.682777e+00 0.000e+00 7.068e+01 1.137e-03 2 21 1.051250e+00 0.000e+00 4.107e+02 1.876e-02 3 26 9.346769e-01 0.000e+00 4.646e+01 1.911e-03 4 37 8.589080e-01 0.000e+00 1.529e+01 2.648e-04 5 68 8.589079e-01 0.000e+00 1.529e+01 2.200e-10 6 77 8.589079e-01 0.000e+00 1.529e+01 2.200e-10 7 87 8.589079e-01 0.000e+00 1.529e+01 2.200e-10 8 97 8.589079e-01 0.000e+00 1.529e+01 2.200e-10 9 107 8.589079e-01 0.000e+00 1.529e+01 2.200e-10 10 117 8.589078e-01 0.000e+00 1.529e+01 2.200e-10 11 127 8.589078e-01 0.000e+00 1.529e+01 2.200e-10 12 137 8.589078e-01 0.000e+00 1.529e+01 2.200e-10 13 147 8.589078e-01 0.000e+00 1.529e+01 2.200e-10 14 157 8.589077e-01 0.000e+00 1.529e+01 2.200e-10 15 167 8.589077e-01 0.000e+00 1.529e+01 2.200e-10 16 177 8.589077e-01 0.000e+00 1.529e+01 2.200e-10 17 187 8.589077e-01 0.000e+00 1.529e+01 2.200e-10 18 197 8.589077e-01 0.000e+00 1.529e+01 2.200e-10 19 207 8.589076e-01 0.000e+00 1.529e+01 2.200e-10 20 217 8.589076e-01 0.000e+00 1.529e+01 2.200e-10 21 227 8.589076e-01 0.000e+00 1.529e+01 2.200e-10 22 237 8.589076e-01 0.000e+00 1.529e+01 2.200e-10 23 247 8.589076e-01 0.000e+00 1.529e+01 2.200e-10 24 257 8.589075e-01 0.000e+00 1.529e+01 2.200e-10 25 267 8.589075e-01 0.000e+00 1.529e+01 2.200e-10 26 277 8.589075e-01 0.000e+00 1.529e+01 2.200e-10 27 287 8.589075e-01 0.000e+00 1.529e+01 2.200e-10 28 297 8.589074e-01 0.000e+00 1.529e+01 2.200e-10 29 307 8.589074e-01 0.000e+00 1.529e+01 2.200e-10 30 317 8.589074e-01 0.000e+00 1.529e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 31 327 8.589074e-01 0.000e+00 1.529e+01 2.200e-10 32 337 8.589074e-01 0.000e+00 1.529e+01 2.200e-10 33 347 8.589073e-01 0.000e+00 1.529e+01 2.200e-10 34 357 8.589073e-01 0.000e+00 1.529e+01 2.200e-10 35 367 8.589073e-01 0.000e+00 1.529e+01 2.200e-10 36 377 8.589073e-01 0.000e+00 1.529e+01 2.200e-10 37 387 8.589073e-01 0.000e+00 1.529e+01 2.200e-10 38 397 8.589072e-01 0.000e+00 1.529e+01 2.200e-10 39 407 8.589072e-01 0.000e+00 1.529e+01 2.200e-10 40 417 8.589072e-01 0.000e+00 1.529e+01 2.200e-10 41 427 8.589072e-01 0.000e+00 1.529e+01 2.200e-10 42 437 8.589071e-01 0.000e+00 1.529e+01 2.200e-10 43 447 8.589071e-01 0.000e+00 1.529e+01 2.200e-10 44 457 8.589071e-01 0.000e+00 1.529e+01 2.200e-10 45 467 8.589071e-01 0.000e+00 1.529e+01 2.200e-10 46 477 8.589071e-01 0.000e+00 1.529e+01 2.200e-10 47 487 8.589070e-01 0.000e+00 1.529e+01 2.200e-10 48 497 8.589070e-01 0.000e+00 1.529e+01 2.200e-10 49 507 8.589070e-01 0.000e+00 1.529e+01 2.200e-10 50 517 8.589070e-01 0.000e+00 1.529e+01 2.200e-10 51 527 8.589070e-01 0.000e+00 1.529e+01 2.200e-10 52 537 8.589069e-01 0.000e+00 1.529e+01 2.200e-10 53 547 8.589069e-01 0.000e+00 1.529e+01 2.200e-10 54 557 8.589069e-01 0.000e+00 1.529e+01 2.200e-10 55 567 8.589069e-01 0.000e+00 1.529e+01 2.200e-10 56 577 8.589068e-01 0.000e+00 1.529e+01 2.200e-10 57 587 8.589068e-01 0.000e+00 1.529e+01 2.200e-10 58 597 8.589068e-01 0.000e+00 1.529e+01 2.200e-10 59 607 8.589068e-01 0.000e+00 1.529e+01 2.200e-10 60 617 8.589068e-01 0.000e+00 1.529e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 61 627 8.589067e-01 0.000e+00 1.529e+01 2.200e-10 62 637 8.589067e-01 0.000e+00 1.529e+01 2.200e-10 63 647 8.589067e-01 0.000e+00 1.529e+01 2.200e-10 64 657 8.589067e-01 0.000e+00 1.529e+01 2.200e-10 65 667 8.589067e-01 0.000e+00 1.529e+01 2.200e-10 66 677 8.589066e-01 0.000e+00 1.529e+01 2.200e-10 67 687 8.589066e-01 0.000e+00 1.529e+01 2.200e-10 68 697 8.589066e-01 0.000e+00 1.529e+01 2.200e-10 69 707 8.589066e-01 0.000e+00 1.529e+01 2.200e-10 70 717 8.589065e-01 0.000e+00 1.529e+01 2.200e-10 71 727 8.589065e-01 0.000e+00 1.529e+01 2.200e-10 72 737 8.589065e-01 0.000e+00 1.529e+01 2.200e-10 73 747 8.589065e-01 0.000e+00 1.529e+01 2.200e-10 74 757 8.589065e-01 0.000e+00 1.529e+01 2.200e-10 75 767 8.589064e-01 0.000e+00 1.529e+01 2.200e-10 76 777 8.589064e-01 0.000e+00 1.529e+01 2.200e-10 77 787 8.589064e-01 0.000e+00 1.529e+01 2.200e-10 78 797 8.589064e-01 0.000e+00 1.529e+01 2.200e-10 79 807 8.589064e-01 0.000e+00 1.529e+01 2.200e-10 80 817 8.589063e-01 0.000e+00 1.529e+01 2.200e-10 81 827 8.589063e-01 0.000e+00 1.529e+01 2.200e-10 82 837 8.589063e-01 0.000e+00 1.529e+01 2.200e-10 83 847 8.589063e-01 0.000e+00 1.529e+01 2.200e-10 84 857 8.589063e-01 0.000e+00 1.529e+01 2.200e-10 85 867 8.589062e-01 0.000e+00 1.529e+01 2.200e-10 86 877 8.589062e-01 0.000e+00 1.529e+01 2.200e-10 87 887 8.589062e-01 0.000e+00 1.529e+01 2.200e-10 88 897 8.589062e-01 0.000e+00 1.529e+01 2.200e-10 89 907 8.589061e-01 0.000e+00 1.529e+01 2.200e-10 90 917 8.589061e-01 0.000e+00 1.529e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 91 927 8.589061e-01 0.000e+00 1.529e+01 2.200e-10 92 937 8.589061e-01 0.000e+00 1.529e+01 2.200e-10 93 947 8.589061e-01 0.000e+00 1.529e+01 2.200e-10 94 957 8.589060e-01 0.000e+00 1.529e+01 2.200e-10 95 967 8.589060e-01 0.000e+00 1.529e+01 2.200e-10 96 977 8.589060e-01 0.000e+00 1.529e+01 2.200e-10 97 987 8.589060e-01 0.000e+00 1.529e+01 2.200e-10 98 997 8.589060e-01 0.000e+00 1.529e+01 2.200e-10 99 1007 8.589059e-01 0.000e+00 1.529e+01 2.200e-10 100 1017 8.589059e-01 0.000e+00 1.529e+01 2.200e-10 101 1027 8.589059e-01 0.000e+00 1.529e+01 2.200e-10 102 1037 8.589059e-01 0.000e+00 1.529e+01 2.200e-10 103 1047 8.589058e-01 0.000e+00 1.529e+01 2.200e-10 104 1057 8.589058e-01 0.000e+00 1.529e+01 2.200e-10 105 1067 8.589058e-01 0.000e+00 1.529e+01 2.200e-10 106 1077 8.589058e-01 0.000e+00 1.529e+01 2.200e-10 107 1087 8.589058e-01 0.000e+00 1.529e+01 2.200e-10 108 1097 8.589057e-01 0.000e+00 1.529e+01 2.200e-10 109 1107 8.589057e-01 0.000e+00 1.529e+01 2.200e-10 110 1117 8.589057e-01 0.000e+00 1.529e+01 2.200e-10 111 1127 8.589057e-01 0.000e+00 1.529e+01 2.200e-10 112 1137 8.589057e-01 0.000e+00 1.529e+01 2.200e-10 113 1147 8.589056e-01 0.000e+00 1.529e+01 2.200e-10 114 1157 8.589056e-01 0.000e+00 1.529e+01 2.200e-10 115 1167 8.589056e-01 0.000e+00 1.529e+01 2.200e-10 116 1177 8.589056e-01 0.000e+00 1.529e+01 2.200e-10 117 1187 8.589055e-01 0.000e+00 1.529e+01 2.200e-10 118 1197 8.589055e-01 0.000e+00 1.529e+01 2.200e-10 119 1207 8.589055e-01 0.000e+00 1.529e+01 2.200e-10 120 1217 8.589055e-01 0.000e+00 1.529e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 121 1227 8.589055e-01 0.000e+00 1.529e+01 2.200e-10 122 1237 8.589054e-01 0.000e+00 1.529e+01 2.200e-10 123 1247 8.589054e-01 0.000e+00 1.529e+01 2.200e-10 124 1257 8.589054e-01 0.000e+00 1.529e+01 2.200e-10 125 1267 8.589054e-01 0.000e+00 1.529e+01 2.200e-10 126 1277 8.589054e-01 0.000e+00 1.529e+01 2.200e-10 127 1287 8.589053e-01 0.000e+00 1.529e+01 2.200e-10 128 1297 8.589053e-01 0.000e+00 1.529e+01 2.200e-10 129 1307 8.589053e-01 0.000e+00 1.529e+01 2.200e-10 130 1317 8.589053e-01 0.000e+00 1.529e+01 2.200e-10 131 1327 8.589052e-01 0.000e+00 1.529e+01 2.200e-10 132 1337 8.589052e-01 0.000e+00 1.529e+01 2.200e-10 133 1347 8.589052e-01 0.000e+00 1.529e+01 2.200e-10 134 1357 8.589052e-01 0.000e+00 1.529e+01 2.200e-10 135 1367 8.589052e-01 0.000e+00 1.529e+01 2.200e-10 136 1377 8.589051e-01 0.000e+00 1.529e+01 2.200e-10 137 1387 8.589051e-01 0.000e+00 1.529e+01 2.200e-10 138 1397 8.589051e-01 0.000e+00 1.529e+01 2.200e-10 139 1407 8.589051e-01 0.000e+00 1.529e+01 2.200e-10 140 1417 8.589051e-01 0.000e+00 1.529e+01 2.200e-10 141 1427 8.589050e-01 0.000e+00 1.529e+01 2.200e-10 142 1437 8.589050e-01 0.000e+00 1.529e+01 2.200e-10 143 1447 8.589050e-01 0.000e+00 1.529e+01 2.200e-10 144 1457 8.589050e-01 0.000e+00 1.529e+01 2.200e-10 145 1467 8.589049e-01 0.000e+00 1.529e+01 2.200e-10 146 1477 8.589049e-01 0.000e+00 1.529e+01 2.200e-10 147 1487 8.589049e-01 0.000e+00 1.529e+01 2.200e-10 148 1497 8.589049e-01 0.000e+00 1.529e+01 2.200e-10 149 1507 8.589049e-01 0.000e+00 1.529e+01 2.200e-10 150 1517 8.589048e-01 0.000e+00 1.529e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 151 1527 8.589048e-01 0.000e+00 1.529e+01 2.200e-10 152 1537 8.589048e-01 0.000e+00 1.529e+01 2.200e-10 153 1547 8.589048e-01 0.000e+00 1.529e+01 2.200e-10 154 1557 8.589048e-01 0.000e+00 1.529e+01 2.200e-10 155 1567 8.589047e-01 0.000e+00 1.529e+01 2.200e-10 156 1577 8.589047e-01 0.000e+00 1.529e+01 2.200e-10 157 1587 8.589047e-01 0.000e+00 1.529e+01 2.200e-10 158 1597 8.589047e-01 0.000e+00 1.529e+01 2.200e-10 159 1607 8.589046e-01 0.000e+00 1.528e+01 2.200e-10 160 1617 8.589046e-01 0.000e+00 1.528e+01 2.200e-10 161 1627 8.589046e-01 0.000e+00 1.528e+01 2.200e-10 162 1637 8.589046e-01 0.000e+00 1.528e+01 2.200e-10 163 1647 8.589046e-01 0.000e+00 1.528e+01 2.200e-10 164 1657 8.589045e-01 0.000e+00 1.528e+01 2.200e-10 165 1667 8.589045e-01 0.000e+00 1.528e+01 2.200e-10 166 1677 8.589045e-01 0.000e+00 1.528e+01 2.200e-10 167 1687 8.589045e-01 0.000e+00 1.528e+01 2.200e-10 168 1697 8.589045e-01 0.000e+00 1.528e+01 2.200e-10 169 1707 8.589044e-01 0.000e+00 1.528e+01 2.200e-10 170 1717 8.589044e-01 0.000e+00 1.528e+01 2.200e-10 171 1727 8.589044e-01 0.000e+00 1.528e+01 2.200e-10 172 1737 8.589044e-01 0.000e+00 1.528e+01 2.200e-10 173 1747 8.589043e-01 0.000e+00 1.528e+01 2.200e-10 174 1757 8.589043e-01 0.000e+00 1.528e+01 2.200e-10 175 1767 8.589043e-01 0.000e+00 1.528e+01 2.200e-10 176 1777 8.589043e-01 0.000e+00 1.528e+01 2.200e-10 177 1787 8.589043e-01 0.000e+00 1.528e+01 2.200e-10 178 1797 8.589042e-01 0.000e+00 1.528e+01 2.200e-10 179 1807 8.589042e-01 0.000e+00 1.528e+01 2.200e-10 180 1817 8.589042e-01 0.000e+00 1.528e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 181 1827 8.589042e-01 0.000e+00 1.528e+01 2.200e-10 182 1837 8.589042e-01 0.000e+00 1.528e+01 2.200e-10 183 1847 8.589041e-01 0.000e+00 1.528e+01 2.200e-10 184 1857 8.589041e-01 0.000e+00 1.528e+01 2.200e-10 185 1867 8.589041e-01 0.000e+00 1.528e+01 2.200e-10 186 1877 8.589041e-01 0.000e+00 1.528e+01 2.200e-10 187 1887 8.589040e-01 0.000e+00 1.528e+01 2.200e-10 188 1897 8.589040e-01 0.000e+00 1.528e+01 2.200e-10 189 1907 8.589040e-01 0.000e+00 1.528e+01 2.200e-10 190 1917 8.589040e-01 0.000e+00 1.528e+01 2.200e-10 191 1927 8.589040e-01 0.000e+00 1.528e+01 2.200e-10 192 1937 8.589039e-01 0.000e+00 1.528e+01 2.200e-10 193 1947 8.589039e-01 0.000e+00 1.528e+01 2.200e-10 194 1957 8.589039e-01 0.000e+00 1.528e+01 2.200e-10 195 1967 8.589039e-01 0.000e+00 1.528e+01 2.200e-10 196 1977 8.589039e-01 0.000e+00 1.528e+01 2.200e-10 197 1987 8.589038e-01 0.000e+00 1.528e+01 2.200e-10 198 1997 8.589038e-01 0.000e+00 1.528e+01 2.200e-10 199 2007 8.589038e-01 0.000e+00 1.528e+01 2.200e-10 200 2017 8.589038e-01 0.000e+00 1.528e+01 2.200e-10 201 2027 8.589038e-01 0.000e+00 1.528e+01 2.200e-10 202 2037 8.589037e-01 0.000e+00 1.528e+01 2.200e-10 203 2047 8.589037e-01 0.000e+00 1.528e+01 2.200e-10 204 2057 8.589037e-01 0.000e+00 1.528e+01 2.200e-10 205 2067 8.589037e-01 0.000e+00 1.528e+01 2.200e-10 206 2077 8.589036e-01 0.000e+00 1.528e+01 2.200e-10 207 2087 8.589036e-01 0.000e+00 1.528e+01 2.200e-10 208 2097 8.589036e-01 0.000e+00 1.528e+01 2.200e-10 209 2107 8.589036e-01 0.000e+00 1.528e+01 2.200e-10 210 2117 8.589036e-01 0.000e+00 1.528e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 211 2127 8.589035e-01 0.000e+00 1.528e+01 2.200e-10 212 2137 8.589035e-01 0.000e+00 1.528e+01 2.200e-10 213 2147 8.589035e-01 0.000e+00 1.528e+01 2.200e-10 214 2157 8.589035e-01 0.000e+00 1.528e+01 2.200e-10 215 2167 8.589035e-01 0.000e+00 1.528e+01 2.200e-10 216 2177 8.589034e-01 0.000e+00 1.528e+01 2.200e-10 217 2187 8.589034e-01 0.000e+00 1.528e+01 2.200e-10 218 2197 8.589034e-01 0.000e+00 1.528e+01 2.200e-10 219 2207 8.589034e-01 0.000e+00 1.528e+01 2.200e-10 220 2217 8.589033e-01 0.000e+00 1.528e+01 2.200e-10 221 2227 8.589033e-01 0.000e+00 1.528e+01 2.200e-10 222 2237 8.589033e-01 0.000e+00 1.528e+01 2.200e-10 223 2247 8.589033e-01 0.000e+00 1.528e+01 2.200e-10 224 2257 8.589033e-01 0.000e+00 1.528e+01 2.200e-10 225 2267 8.589032e-01 0.000e+00 1.528e+01 2.200e-10 226 2277 8.589032e-01 0.000e+00 1.528e+01 2.200e-10 227 2287 8.589032e-01 0.000e+00 1.528e+01 2.200e-10 228 2297 8.589032e-01 0.000e+00 1.528e+01 2.200e-10 229 2307 8.589032e-01 0.000e+00 1.528e+01 2.200e-10 230 2317 8.589031e-01 0.000e+00 1.528e+01 2.200e-10 231 2327 8.589031e-01 0.000e+00 1.528e+01 2.200e-10 232 2337 8.589031e-01 0.000e+00 1.528e+01 2.200e-10 233 2347 8.589031e-01 0.000e+00 1.528e+01 2.200e-10 234 2357 8.589030e-01 0.000e+00 1.528e+01 2.200e-10 235 2367 8.589030e-01 0.000e+00 1.528e+01 2.200e-10 236 2377 8.589030e-01 0.000e+00 1.528e+01 2.200e-10 237 2387 8.589030e-01 0.000e+00 1.528e+01 2.200e-10 238 2397 8.589030e-01 0.000e+00 1.528e+01 2.200e-10 239 2407 8.589029e-01 0.000e+00 1.528e+01 2.200e-10 240 2417 8.589029e-01 0.000e+00 1.528e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 241 2427 8.589029e-01 0.000e+00 1.528e+01 2.200e-10 242 2437 8.589029e-01 0.000e+00 1.528e+01 2.200e-10 243 2447 8.589029e-01 0.000e+00 1.528e+01 2.200e-10 244 2457 8.589028e-01 0.000e+00 1.528e+01 2.200e-10 245 2467 8.589028e-01 0.000e+00 1.528e+01 2.200e-10 246 2477 8.589028e-01 0.000e+00 1.528e+01 2.200e-10 247 2487 8.589028e-01 0.000e+00 1.528e+01 2.200e-10 248 2497 8.589027e-01 0.000e+00 1.528e+01 2.200e-10 249 2507 8.589027e-01 0.000e+00 1.528e+01 2.200e-10 250 2517 8.589027e-01 0.000e+00 1.528e+01 2.200e-10 251 2527 8.589027e-01 0.000e+00 1.528e+01 2.200e-10 252 2537 8.589027e-01 0.000e+00 1.528e+01 2.200e-10 253 2547 8.589026e-01 0.000e+00 1.528e+01 2.200e-10 254 2557 8.589026e-01 0.000e+00 1.528e+01 2.200e-10 255 2567 8.589026e-01 0.000e+00 1.528e+01 2.200e-10 256 2577 8.589026e-01 0.000e+00 1.528e+01 2.200e-10 257 2587 8.589026e-01 0.000e+00 1.528e+01 2.200e-10 258 2597 8.589025e-01 0.000e+00 1.528e+01 2.200e-10 259 2607 8.589025e-01 0.000e+00 1.528e+01 2.200e-10 260 2617 8.589025e-01 0.000e+00 1.528e+01 2.200e-10 261 2627 8.589025e-01 0.000e+00 1.528e+01 2.200e-10 262 2637 8.589024e-01 0.000e+00 1.528e+01 2.200e-10 263 2647 8.589024e-01 0.000e+00 1.528e+01 2.200e-10 264 2657 8.589024e-01 0.000e+00 1.528e+01 2.200e-10 265 2667 8.589024e-01 0.000e+00 1.528e+01 2.200e-10 266 2677 8.589024e-01 0.000e+00 1.528e+01 2.200e-10 267 2687 8.589023e-01 0.000e+00 1.528e+01 2.200e-10 268 2697 8.589023e-01 0.000e+00 1.528e+01 2.200e-10 269 2707 8.589023e-01 0.000e+00 1.528e+01 2.200e-10 270 2717 8.589023e-01 0.000e+00 1.528e+01 2.200e-10 First-order Norm of Iter F-count f(x) Feasibility optimality step 271 2727 8.589023e-01 0.000e+00 1.528e+01 2.200e-10 272 2737 8.589022e-01 0.000e+00 1.528e+01 2.200e-10 273 2747 8.589022e-01 0.000e+00 1.528e+01 2.200e-10 274 2757 8.589022e-01 0.000e+00 1.528e+01 2.200e-10 275 2767 8.589022e-01 0.000e+00 1.528e+01 2.200e-10 276 2777 8.589021e-01 0.000e+00 1.528e+01 2.200e-10 277 2787 8.589021e-01 0.000e+00 1.528e+01 2.200e-10 278 2797 8.589021e-01 0.000e+00 1.528e+01 2.200e-10 279 2807 8.589021e-01 0.000e+00 1.528e+01 2.200e-10 280 2817 8.589021e-01 0.000e+00 1.528e+01 2.200e-10 281 2827 8.589020e-01 0.000e+00 1.528e+01 2.200e-10 282 2837 8.589020e-01 0.000e+00 1.528e+01 2.200e-10 283 2847 8.589020e-01 0.000e+00 1.528e+01 2.200e-10 284 2857 8.589020e-01 0.000e+00 1.528e+01 2.200e-10 285 2867 8.589020e-01 0.000e+00 1.528e+01 2.200e-10 286 2877 8.589019e-01 0.000e+00 1.528e+01 2.200e-10 287 2887 8.589019e-01 0.000e+00 1.528e+01 2.200e-10 288 2897 8.589019e-01 0.000e+00 1.528e+01 2.200e-10 289 2907 8.589019e-01 0.000e+00 1.528e+01 2.200e-10 290 2917 8.589018e-01 0.000e+00 1.528e+01 2.200e-10 291 2927 8.589018e-01 0.000e+00 1.528e+01 2.200e-10 292 2937 8.589018e-01 0.000e+00 1.528e+01 2.200e-10 293 2947 8.589018e-01 0.000e+00 1.528e+01 2.200e-10 294 2957 8.589018e-01 0.000e+00 1.528e+01 2.200e-10 295 2967 8.589017e-01 0.000e+00 1.528e+01 2.200e-10 296 2977 8.589017e-01 0.000e+00 1.528e+01 2.200e-10 297 2987 8.589017e-01 0.000e+00 1.528e+01 2.200e-10 298 2997 8.589017e-01 0.000e+00 1.528e+01 2.200e-10 Solver stopped prematurely. fmincon stopped because it exceeded the function evaluation limit, options.MaxFunctionEvaluations = 3.000000e+03. Optimal value of d1: 0.020019 mm Optimal value of t1: 0.0010257 mm Optimal value of d2: 0.0010639 mm Optimal value of t2: 0.0011383mm Optimal value of f: 0.8589 kg
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Wheelchair
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Wheelchair
% clc;
clear all; close all;
dp=design_parameters; % Generate structure variable containing all design parameters
f=@(x)objective_function(x,dp); % Objective function handle
nonlcon=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
x0=[25e-3;1.5e-3;20e-3;1e-3]; % Initial design point
A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
b=[-1,-1,1,-1,1,-1,1,-1,1];
% Minimization using fmincon and the specified options:
options=optimoptions('fmincon','Display','iter','OptimalityTolerance',1e-12,'ConstraintTolerance',1e-6,'StepTolerance',1e-12);
[x,fval]=fmincon(f,x0,A,b,[],[],lb,ub,nonlcon,options);
% Display of the optimal design results:
disp(['Optimal value of d1: ',num2str(x(1)),' mm']);
disp(['Optimal value of t1: ',num2str(x(2)),' mm']);
disp(['Optimal value of d2: ',num2str(x(3)),' mm']);
disp(['Optimal value of t2: ',num2str(x(4)),'mm']);
disp(['Optimal value of f: ',num2str(fval),' kg']);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function dp=design_parameters
dp.L1=0.82; %(m)
dp.L2=0.691; %(m)
dp.L3=0.270; %(m)
dp.L4=0.04; %(m)
dp.L5=1.59; %(m)
dp.L6=0.627; %(m)
dp.L7=0.568;
dp.Lad=0.601;
dp.Lss=0.4;
dp.mb=150;
dp.Rho=2700;
dp.g=10;
dp.db=6e-3;
dp.sigmau=110e6;
dp.E=70e9;
dp.K=2.1;
dp.deltamax=1e-3;
dp.X1_min=20e-3; dp.X1_max=30e-3; %
dp.X2_min=1e-3; dp.X2_max=2e-3; %
dp.X3_min=1e-3; dp.X3_max=22e-3; %
dp.X4_min=0.8e-3; dp.X4_max=1.5e-3;
end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;
f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); %
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;
c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
ceq=[]; % There are no nonlinear equality constraints
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Elmira Jafari
Elmira Jafari on 15 Dec 2021
Thanks. yes I. changed its location now it works correctly. I dont know what wrong was with it
Elmira Jafari
Elmira Jafari on 15 Dec 2021
Edited: Walter Roberson on 15 Dec 2021
sorry but I got the same error for solving by GA, Would you run this one as well?
function wheel
clc; clear all; close all;
global ccc
rng('shuffle');
dp=design_parameters; % Generate structure variable containing all design parameters
f=@(x)objective_function(x,dp); % Objective function handle
g=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
nvars=4; % Number of design variables
lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
b=[-1,-1,1,-1,1,-1,1,-1,1];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialization of figure used to illustrate individuals within
% design space:
% figure(1); hold on; grid on; box on; view(3);
%axis([dp.x(1)_min dp.d_max dp.D_min dp.D_max dp.N_min dp.N_max]);
%xlabel('d'); ylabel('D'); zlabel('N');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Defining various GA options:
options=optimoptions('ga','PopulationSize',200,...
'EliteCount',5,...
'MaxGenerations',200,...
'MutationFcn',@mutationadaptfeasible,...
'CrossoverFcn',{@crossoverintermediate,1.5},...
'FunctionTolerance',1e-12,...
'ConstraintTolerance',1e-6,...
'HybridFcn','fmincon',...
'Display','iter',...
'PlotFcn',{@gaplotbestf,@gaplotrange},...
'OutputFcn',@custom_output);
% Call to the 'ga' function:
[x,fval,exitflag,output,population,scores]=ga(f,nvars,A,b,[],[],lb,ub,g,options);
disp(['Optimal value of d1: ',num2str(x(1)),' mm']);
disp(['Optimal value of t1: ',num2str(x(2)),' mm']);
disp(['Optimal value of d2: ',num2str(x(3)),' mm']);
disp(['Optimal value of t2: ',num2str(x(4)),'mm']);
disp(['Optimal value of f: ',num2str(fval),' kg']);
figure(1);
plot3(x(1),x(2),x(3),x(4),'b.','Markersize',20);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function dp=design_parameters
dp.L1=0.82; %(m)
dp.L2=0.691; %(m)
dp.L3=0.270; %(m)
dp.L4=0.04; %(m)
dp.L5=1.59; %(m)
dp.L6=0.627; %(m)
dp.L7=0.568;
dp.Lad=0.601;
dp.Lss=0.4;
dp.mb=150;
dp.Rho=2700;
dp.g=10;
dp.db=6e-3;
dp.sigmau=110e6;
dp.E=70e9;
dp.K=2.1;
dp.deltamax=1e-3;
dp.X1_min=20e-3; dp.X1_max=30e-3; %
dp.X2_min=1e-3; dp.X2_max=2e-3; %
dp.X3_min=1e-3; dp.X3_max=22e-3; %
dp.X4_min=0.8e-3; dp.X4_max=1.5e-3;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;
f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); %
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;
c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
ceq=[]; % There are no nonlinear equality constraints
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function [state,options,optchanged]=custom_output(options,state,flag)
global ccc
title(['Current generation: ',num2str(state.Generation)]);
if ~isempty(ccc)
delete(ccc);
end
figure(1)
ccc=plot3(state.Population(:,1),state.Population(:,2),state.Population(:,3),'r.','Markersize',10);
pause(0.01);
optchanged = false;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Walter Roberson
Walter Roberson on 15 Dec 2021
That works for me as well, until the very end. You have
plot3(x(1),x(2),x(3),x(4),'b.','Markersize',20);
plot3() requires that the number of data arguments is a multiple of 3, whereas you have 4 data arguments.
If you had been using plot() instead of plot3() then you would have plotted two points.
I would suggest to you that plotting two points would be a bit difficult to understand unless perhaps you had a legend() that told you which point was which.
Torsten
Torsten on 16 Dec 2021
Note that the inequality constraints in the function "nonlinear_constraints" must be indexed starting with 1:
c(1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(2)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
Walter Roberson
Walter Roberson on 16 Dec 2021
@Torsten
While indexing from 1 is a good idea for clarity, it is not necessary. As usual when you first store into a matrix starting at an index other than 1, all elements from 1 to just before where you wrote are filled with 0. But for the purposes of constraints, 0 is fine: 0 satisfies the <= 0 test for nonlinear inequalities, and statisfies the == 0 for nonlinear equalities. So those entries c(1:9) being 0 are a small waste of time but do not affect convergence.

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Answers (2)

KSSV
KSSV on 15 Dec 2021

0 votes

You may use scatter3
figure(1);
scatter3(x(1),x(2),x(3),[],x(4),'filled');

3 Comments
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Elmira Jafari
Elmira Jafari on 15 Dec 2021
it works but as you said I have 4 variables, how can I have 2 plots , one of the 2 variable with objective function and the other with other 2 variables and objective function. would you guide me?
KSSV
KSSV on 15 Dec 2021
Then may you are expecting:
plot(x(1),x(2),'.b',x(3),x(4),'.r');
Elmira Jafari
Elmira Jafari on 15 Dec 2021
Edited: Walter Roberson on 15 Dec 2021
Ran in:
Ran in:
would you run this code?
wheel()
Could not find a feasible initial point.
Index exceeds the number of array elements. Index must not exceed 0.

Error in solution>wheel (line 43)
disp(['Optimal value of d1: ',num2str(x(1)),' mm']);
function wheel
clc; clear all; close all;
global ccc
rng('shuffle');
dp=design_parameters; % Generate structure variable containing all design parameters
f=@(x)objective_function(x,dp); % Objective function handle
g=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
nvars=4; % Number of design variables
lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
b=[-1,-1,1,-1,1,-1,1,-1,1];
figure(1); hold on; grid on; box on; view(3);
axis([dp.X1_min dp.X1_max dp.X2_min dp.X2_max dp.X3_min dp.X3_max]);
xlabel('d1'); ylabel('t1'); zlabel('d2');
options=optimoptions('ga','PopulationSize',200,...
'EliteCount',5,...
'MaxGenerations',200,...
'MutationFcn',@mutationadaptfeasible,...
'CrossoverFcn',{@crossoverintermediate,1.5},...
'FunctionTolerance',1e-12,...
'ConstraintTolerance',1e-6,...
'HybridFcn','fmincon',...
'Display','iter',...
'PlotFcn',{@gaplotbestf,@gaplotrange},...
'OutputFcn',@custom_output);
% Call to the 'ga' function:
[x,fval,exitflag,output,population,scores]=ga(f,nvars,A,b,[],[],lb,ub,g,options);
disp(['Optimal value of d1: ',num2str(x(1)),' mm']);
disp(['Optimal value of t1: ',num2str(x(2)),' mm']);
disp(['Optimal value of d2: ',num2str(x(3)),' mm']);
disp(['Optimal value of t2: ',num2str(x(4)),'mm']);
disp(['Optimal value of f: ',num2str(fval),' kg']);
figure(1);
plot3(x(1),x(2),x(3),'b.','Markersize',20);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function dp=design_parameters
dp.L1=0.82; %(m)
dp.L2=0.691; %(m)
dp.L3=0.270; %(m)
dp.L4=0.04; %(m)
dp.L5=1.59; %(m)
dp.L6=0.627; %(m)
dp.L7=0.568;
dp.Lad=0.601;
dp.Lss=0.4;
dp.mb=150;
dp.Rho=2700;
dp.g=10;
dp.db=6e-3;
dp.sigmau=110e6;
dp.E=70e9;
dp.K=2.1;
dp.deltamax=1e-3;
dp.X1_min=10e-3; dp.X1_max=20e-3; %
dp.X2_min=0.5e-3; dp.X2_max=1e-3; %
dp.X3_min=10e-3; dp.X3_max=20e-3; %
dp.X4_min=0.5e-3; dp.X4_max=1e-3;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;
f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); %
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;
c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
ceq=[]; % There are no nonlinear equality constraints
end
%%%%%%%%%%%%
function [state,options,optchanged]=custom_output(options,state,flag)
global ccc
title(['Current generation: ',num2str(state.Generation)]);
if ~isempty(ccc)
delete(ccc);
end
figure(1)
ccc=plot3(state.Population(:,1),state.Population(:,2),state.Population(:,3),'r.','Markersize',10);
pause(0.01);
optchanged = false;
end

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Elmira Jafari
Elmira Jafari on 15 Dec 2021
Edited: Walter Roberson on 15 Dec 2021

0 votes

I have a question, I run the same objective function, constraints, boundrie by GA and fmincon. fmincon gives me a logical answre but Ga cant solve it. what would be the reason? I have attached them. First one is by Ga and second one by fmincon. It is appreciated if help me as always.
GA
function wheel
clc; clear all; close all;
global ccc
rng('shuffle');
dp=design_parameters; % Generate structure variable containing all design parameters
f=@(x)objective_function(x,dp); % Objective function handle
g=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
nvars=4; % Number of design variables
lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
b=[-1,-1,1,-1,1,-1,1,-1,1];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialization of figure used to illustrate individuals within
% design space:
%figure(1); hold on; grid on; box on; view(3);
%axis([dp.X1_min dp.X1_max dp.X2_min dp.X2_max dp.X3_min dp.X3_max]);
%xlabel('d1'); ylabel('t1'); zlabel('d2');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Defining various GA options:
options=optimoptions('ga','PopulationSize',200,...
'EliteCount',5,...
'MaxGenerations',300,...
'MutationFcn',@mutationadaptfeasible,...
'CrossoverFcn',{@crossoverintermediate,1.5},...
'FunctionTolerance',1e-12,...
'ConstraintTolerance',1e-6,...
'HybridFcn','fmincon',...
'Display','iter',...
'PlotFcn',{@gaplotbestf,@gaplotrange},...
'OutputFcn',@custom_output);
% Call to the 'ga' function:
[x,fval,exitflag,output,population,scores]=ga(f,nvars,A,b,[],[],lb,ub,g,options);
disp(['Optimal value of d1: ',num2str(1000*x(1)),' mm']);
disp(['Optimal value of t1: ',num2str(1000*x(2)),' mm']);
disp(['Optimal value of d2: ',num2str(1000*x(3)),' mm']);
disp(['Optimal value of t2: ',num2str(1000*x(4)),'mm']);
disp(['Optimal value of f: ',num2str(fval),' kg']);
% figure(1);
% plot3(x(1),x(2),x(3),'.b');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function dp=design_parameters
dp.L1=0.82; %(m)
dp.L2=0.691; %(m)
dp.L3=0.270; %(m)
dp.L4=0.04; %(m)
dp.L5=1.59; %(m)
dp.L6=0.627; %(m)
dp.L7=0.568;
dp.Lad=0.601;
dp.Lss=0.4;
dp.mb=150;
dp.Rho=2700;
dp.g=10;
dp.db=6e-3;
dp.sigmau=110e6;
dp.E=70e9;
dp.K=2.1;
dp.deltamax=1e-3;
dp.X1_min=14e-3; dp.X1_max=20e-3; %
dp.X2_min=0.5e-3; dp.X2_max=1e-3; %
dp.X3_min=10e-3; dp.X3_max=16e-3; %
dp.X4_min=0.5e-3; dp.X4_max=1e-3;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;
f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); %
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;
c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
ceq=[]; % There are no nonlinear equality constraints
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [state,options,optchanged]=custom_output(options,state,flag)
global ccc
title(['Current generation: ',num2str(state.Generation)]);
if ~isempty(ccc)
delete(ccc);
end
figure(1)
ccc=plot3(state.Population(:,1),state.Population(:,2),state.Population(:,3),'r.','Markersize',10);
pause(0.01);
optchanged = false;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Wheelchair
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Wheelchair
% clc;
clear all; close all;
dp=design_parameters; % Generate structure variable containing all design parameters
f=@(x)objective_function(x,dp); % Objective function handle
nonlcon=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
x0=[25e-3;1.5e-3;20e-3;1e-3]; % Initial design point
A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
b=[-1,-1,1,-1,1,-1,1,-1,1];
% Minimization using fmincon and the specified options:
options=optimoptions('fmincon','Display','iter','OptimalityTolerance',1e-12,'ConstraintTolerance',1e-6,'StepTolerance',1e-12);
[x,fval]=fmincon(f,x0,A,b,[],[],lb,ub,nonlcon,options);
% Display of the optimal design results:
disp(['Optimal value of d1: ',num2str(1000*x(1)),' mm']);
disp(['Optimal value of t1: ',num2str(1000*x(2)),' mm']);
disp(['Optimal value of d2: ',num2str(1000*x(3)),' mm']);
disp(['Optimal value of t2: ',num2str(1000*x(4)),'mm']);
disp(['Optimal value of f: ',num2str(fval),' kg']);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function dp=design_parameters
dp.L1=0.82; %(m)
dp.L2=0.691; %(m)
dp.L3=0.270; %(m)
dp.L4=0.04; %(m)
dp.L5=1.59; %(m)
dp.L6=0.627; %(m)
dp.L7=0.568;
dp.Lad=0.601;
dp.Lss=0.4;
dp.mb=150;
dp.Rho=2700;
dp.g=10;
dp.db=6e-3;
dp.sigmau=110e6;
dp.E=68e9;
dp.K=2.1;
dp.deltamax=1e-3;
dp.X1_min=14e-3; dp.X1_max=20e-3; % Minimum/maximum length of rectangular (mm)
dp.X2_min=0.5e-3; dp.X2_max=1.1e-3; %
dp.X3_min=10e-3; dp.X3_max=15e-3; %
dp.X4_min=0.5e-3; dp.X4_max=1.1e-3;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;
f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); %
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;
c(10,1)=0.2*dp.mb*dp.g*100-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; %
ceq=[]; % There are no nonlinear equality constraints
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

4 Comments
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Walter Roberson
Walter Roberson on 15 Dec 2021
You are not asking them to solve the same problem.
GA:
dp.E=70e9;
dp.X2_min=0.5e-3; dp.X2_max=1e-3; %
dp.X3_min=10e-3; dp.X3_max=16e-3; %
dp.X4_min=0.5e-3; dp.X4_max=1e-3;
fmincon:
dp.E=68e9;
dp.X2_min=0.5e-3; dp.X2_max=1.1e-3; %
dp.X3_min=10e-3; dp.X3_max=15e-3; %
dp.X4_min=0.5e-3; dp.X4_max=1.1e-3;
Walter Roberson
Walter Roberson on 15 Dec 2021
Different constraints too.
GA:
c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
% ^^^^
fmincon:
c(10,1)=0.2*dp.mb*dp.g*100-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); %
% ^^^^^^^^
Elmira Jafari
Elmira Jafari on 15 Dec 2021
Thanks Robert your right but even I make them similar, my problem is not solved.
Walter Roberson
Walter Roberson on 15 Dec 2021
I broke all the functions out into separate files. I then edited wheel to call the functions you built for fmincon. It did not have any problem.
Single objective optimization:
4 Variable(s)
11 Nonlinear inequality constraint(s)
9 Linear inequality constraint(s)
Options:
CreationFcn: @gacreationlinearfeasible
CrossoverFcn: @crossoverintermediate
SelectionFcn: @selectionstochunif
MutationFcn: @mutationadaptfeasible
Best Max Stall
Generation Func-count f(x) Constraint Generations
1 10350 0.761147 0 0
2 20500 0.761047 0 0
3 38060 0.75681 0 0
4 64785 0.752895 0 0
5 95215 0.752255 0 0
6 131300 0.752225 0 0
Optimization terminated: average change in the fitness value less than options.FunctionTolerance
and constraint violation is less than options.ConstraintTolerance.
Switching to the hybrid optimization algorithm (FMINCON).
FMINCON terminated.
Optimal value of d1: 14 mm
Optimal value of t1: 1.0029 mm
Optimal value of d2: 10 mm
Optimal value of t2: 0.50061mm
Optimal value of f: 0.75222 kg

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Asked:

Elmira Jafari
Elmira Jafari
on 15 Dec 2021

Commented:

Walter Roberson
Walter Roberson
on 16 Dec 2021

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