Error using fmincon Too many input arguments

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]

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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Elmira Jafari]

Thanks. yes I. changed its location now it works correctly. I dont know what wrong was with it

[Elmira Jafari]

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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Walter Roberson]

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]

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]

@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.

Answer 1

[KSSV]

You may use scatter3

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

[Elmira Jafari]

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]

Then may you are expecting:

plot(x(1),x(2),'.b',x(3),x(4),'.r');

[Elmira Jafari]

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

Answer 2

[Elmira Jafari]

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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Walter Roberson]

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]

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]

Thanks Robert your right but even I make them similar, my problem is not solved.

[Walter Roberson]

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