cumprod fuction in GA

I want to calculate the following formula in GA.

syms Nb Nv K n Tb Hb t Sb F Sv Hv...
D P Cj j r q
Tb=1.2;
Hb=[2.8 2.2 1.7 1.2 0.8 0.6 0 0];
Sb=[25 28 32 36 35 38 0 0];
F=[70 50 48 55 80 65 0 0];
Sv=[0 280 200 320 360 380 420 0];
Hv=[0 2.5 1.9 1.4 1 0.7 0.5 0];
D=[180000 200000 240000 300000 350000 400000 0 0];
P=[0 200000 240000 300000 350000 400000 450000 0];
q=[1 1 1 1 1 1 0 0];
u=[0.009 0.0064 0.0054 0.0072 0.01 0.008 0 0];
t=[0.015 0.01 0.009 0.012 0.016 0.014 0 0];
w=[0.005 0.004 0.003 0.004 0.006 0.004 0 0];
Se=[29 32 38 42 37 40 0 0];

n=[1 0.9 0.75 0.6 0.51 0.45];
p=[3.2 2.6 2.1 1.6 1.2 0.9 0 0];
%
Nb=[1 1 1 1 1 1 0 0];
Nv=[0 3 2 1 1 1 1 0];
K=[0 26 14 12 8 5 5 0];
m=[0.0095 0.0078 0.0072 0.0092 0.0116 0.0104 0 0];
%
idx = 1:6;
Nvc = cumprod(Nv(idx+1));
Nvb = cumprod(Nv(idx));
s = sum(n(idx).*Tb.*Hb(idx).*D(idx).*(m(idx)-u(idx))+...
        (n(idx)*Tb).^2./(Nvc.*K(idx+1)).* ...
        (D(idx)/2.*(Hb(idx)+Hv(idx+1)-2*Hv(idx+1).*(1-D(idx)./P(idx+1))))+ ...
        Nvc.*K(idx+1).*(Se(idx).*(t(idx)-m(idx)).^3.*(t(idx)+3*m(idx)-4*w(idx)) ...
        ./(t(idx)-w(idx)).^4 +(Hb(idx)+p(idx)).*D(idx).*(t(idx)-m(idx)).^5.*(2*t(idx)+3*m(idx)-5*w(idx)) ...
        ./(5*(t(idx)-w(idx)).^4)+F(idx))+Nvc.*Sv(idx+1)+...
        (n(idx)*Tb).^2./Nvc.*(Hv(idx+1).*D(idx)/2.*(1-D(idx)./P(idx+1)))...
        + Nvb.*Nb(idx).*Sb(idx))

so I put it in the Algorithm

tic
syms Nb Nv K n Tb Hb t Sb F Sv Hv...
D P Cj j r q
options = optimoptions( ...
             'ga', ...                                 
             'PopulationSize', 30, ...                   
             'MaxGenerations', 1000, ...                  
             'CrossoverFraction', 0.8, ...              
             'Display', 'iter');                         
             % 'PlotFcn', {@gaplotbestf, @my_plot}, ...     

Tb=1.2;
Hb=[2.8 2.2 1.7 1.2 0.8 0.6 0 0];
Sb=[25 28 32 36 35 38 0 0];
F=[70 50 48 55 80 65 0 0];
Sv=[0 280 200 320 360 380 420 0];
Hv=[0 2.5 1.9 1.4 1 0.7 0.5 0];
D=[180000 200000 240000 300000 350000 400000 0 0];
P=[0 200000 240000 300000 350000 400000 450000 0];
q=[1 1 1 1 1 1 0 0];
u=[0.009 0.0064 0.0054 0.0072 0.01 0.008 0 0];
t=[0.015 0.01 0.009 0.012 0.016 0.014 0 0];
w=[0.005 0.004 0.003 0.004 0.006 0.004 0 0];
Se=[29 32 38 42 37 40 0 0];
n=[1 0.9 0.75 0.6 0.51 0.45];
p=[3.2 2.6 2.1 1.6 1.2 0.9 0 0];


[x, fval] = ga(@FitnessFcn,x(1),x(2),x(3), 3, [], [], [], [], [1, 1], [40, 40], ...
    [w(idx)<= m(idx)<= t(idx)], [Nv,K,m], options);


function Z = FitnessFcn(x)

    Nv = x(1);
    K = x(2);
    m = x(3);

    idx = 1:6;
    Nvc = cumprod(Nv(idx+1));
    Nvb = cumprod(Nv(idx));

    Z = sum(n(idx).*Tb.*Hb(idx).*D(idx).*(m(idx)-u(idx))+...
        (n(idx)*Tb).^2./(Nvc.*K(idx+1)).* ...
        (D(idx)/2.*(Hb(idx)+Hv(idx+1)-2*Hv(idx+1).*(1-D(idx)./P(idx+1))))+ ...
        Nvc.*K(idx+1).*(Se(idx).*(t(idx)-m(idx)).^3.*(t(idx)+3*m(idx)-4*w(idx)) ...
        ./(t(idx)-w(idx)).^4 +(Hb(idx)+p(idx)).*D(idx).*(t(idx)-m(idx)).^5.*(2*t(idx)+3*m(idx)-5*w(idx)) ...
        ./(5*(t(idx)-w(idx)).^4)+F(idx))+Nvc.*Sv(idx+1)+...
        (n(idx)*Tb).^2./Nvc.*(Hv(idx+1).*D(idx)/2.*(1-D(idx)./P(idx+1)))...
        + Nvb.*Nb(idx).*Sb(idx))

Display Z Nv K m
toc
end

error

Unrecognized function or variable 'x'.

and it also can't seem to use cumprod in algorithm.

Nv,K,m are positive integers.

In addition, I would also like to ask if there is a three-variable drawing method based on the above problem. The information found so far only applies to two-variable equations.

Please help me fix the code so that I can get the result from algorithm, thank you for taking the time to answer.

[Torsten]

Your call to ga is wrong:

x(1), x(2) and x(3) do not belong there, idx is undefined, lb and ub have 2 elements instead of 3, [Nv,K,m] don't belong there.

In the fitness function:

Nv, K and m are single numbers, but you reference Nv, K and m as 7-element vectors in your sum expression.

Further, all your arrays Tb, Hb, Sb,... are not visible in the fitness function because you defined them in the script part, but don't transfer them to the function.

[HSUAN]

I really hope to use the algorithm to find the seven solutions of Nv, K and m. Based on this, how should I modify the code?

So I don't need to list the values ​​of Tb, Hb, Sb,...?

Answer 1

[Torsten]

Note that Nb was not defined in your code - I added it to the known arrays.

rng("default")
t=[0.015 0.01 0.009 0.012 0.016 0.014 0 0];
w=[0.005 0.004 0.003 0.004 0.006 0.004 0 0];
options = optimoptions( ...
    'ga', ...                                 
    'PopulationSize', 30, ...                   
    'MaxGenerations', 1000, ...                  
    'CrossoverFraction', 0.8, ...              
    'Display', 'iter');    
nvars = 7 + 7 + 6;
lb = [ones(7,1);ones(7,1);w(1:6).'];
ub = [40*ones(7,1);40*ones(7,1);t(1:6).'];
intcon = 1:(7+7);
[x, fval, exitflag,output] = ga(@FitnessFcn,nvars,[],[],[],[],lb,ub,[],intcon,options)

Single objective optimization:
20 Variables
14 Integer variables

Options:
CreationFcn:       @gacreationuniformint
CrossoverFcn:      @crossoverlaplace
SelectionFcn:      @selectiontournament
MutationFcn:       @mutationpower

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
    1               60        1.68e+06        3.57e+10        0
    2               85        1.68e+06       9.663e+09        1
    3              110        1.68e+06       2.437e+10        2
    4              135        1.68e+06       5.923e+09        3
    5              160       1.009e+06       2.529e+09        0
    6              185       6.031e+05       5.922e+09        0
    7              210       5.848e+05       1.109e+10        0
    8              235       2.733e+05       8.217e+08        0
    9              260       2.733e+05        4.51e+08        1
   10              285       2.733e+05       4.148e+10        2
   11              310       2.733e+05       2.086e+09        3
   12              335       2.733e+05       1.585e+09        4
   13              360       2.733e+05       4.752e+08        5
   14              385        2.45e+05       4.614e+08        0
   15              410       2.436e+05       1.445e+08        0
   16              435       2.005e+05       3.298e+09        0
   17              460       1.882e+05       1.945e+06        0
   18              485       1.882e+05       7.831e+09        1
   19              510       1.882e+05       1.714e+10        2
   20              535       1.882e+05         9.4e+08        3
   21              560       1.882e+05       1.885e+09        4
   22              585       1.826e+05       5.043e+09        0
   23              610       1.754e+05       2.931e+09        0
   24              635       1.687e+05       2.339e+05        0
   25              660       1.586e+05       4.432e+09        0
   26              685       1.586e+05       2.565e+09        1
   27              710        1.56e+05        2.19e+09        0
   28              735        1.56e+05       6.232e+08        1
   29              760       1.558e+05       3.814e+09        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
   30              785       1.531e+05       1.965e+05        0
   31              810       1.496e+05       2.147e+08        0
   32              835       1.491e+05       1.315e+09        0
   33              860       1.462e+05       8.205e+09        0
   34              885       1.437e+05       2.051e+09        0
   35              910       1.425e+05       4.477e+09        0
   36              935       1.381e+05       1.559e+05        0
   37              960       1.381e+05       8.978e+08        1
   38              985       1.347e+05       1.471e+05        0
   39             1010       1.341e+05       1.428e+05        0
   40             1035       1.323e+05       1.519e+05        0
   41             1060       1.323e+05       1.424e+05        1
   42             1085       1.313e+05       2.168e+09        0
   43             1110       1.283e+05       1.495e+05        0
   44             1135       1.283e+05       2.649e+09        1
   45             1160       1.268e+05       1.531e+05        0
   46             1185       1.268e+05       2.209e+08        0
   47             1210       1.268e+05       9.499e+08        1
   48             1235       1.231e+05       6.079e+09        0
   49             1260       1.231e+05       1.171e+07        1
   50             1285       1.231e+05       3.111e+09        2
   51             1310       1.231e+05       1.069e+08        3
   52             1335       1.231e+05       2.577e+10        4
   53             1360       1.231e+05       4.676e+08        5
   54             1385       1.231e+05       1.346e+05        6
   55             1410       1.228e+05       6.251e+09        0
   56             1435       1.213e+05       1.149e+10        0
   57             1460       1.205e+05       1.705e+09        0
   58             1485       1.205e+05       1.354e+05        1
   59             1510       1.205e+05       9.981e+08        2

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
   60             1535       1.205e+05       1.505e+05        3
   61             1560       1.205e+05       1.445e+05        4
   62             1585       1.205e+05       1.587e+10        5
   63             1610       1.199e+05        1.52e+05        0
   64             1635       1.194e+05       4.773e+08        0
   65             1660       1.193e+05       1.024e+10        0
   66             1685       1.193e+05       9.236e+09        0
   67             1710       1.192e+05       4.878e+06        0
   68             1735       1.179e+05        2.04e+10        0
   69             1760       1.179e+05       1.376e+05        1
   70             1785       1.179e+05       1.104e+10        2
   71             1810       1.179e+05       1.383e+05        3
   72             1835       1.179e+05       1.279e+05        4
   73             1860       1.178e+05       3.051e+08        0
   74             1885       1.178e+05       8.962e+09        1
   75             1910       1.178e+05        1.25e+05        2
   76             1935       1.176e+05       1.696e+10        0
   77             1960       1.175e+05       6.835e+08        0
   78             1985       1.175e+05       1.075e+11        1
   79             2010       1.174e+05       1.365e+08        0
   80             2035       1.173e+05         1.5e+09        0
   81             2060       1.169e+05       4.088e+09        0
   82             2085       1.166e+05       8.133e+10        0
   83             2110       1.163e+05       2.419e+08        0
   84             2135       1.156e+05       1.187e+05        0
   85             2160       1.154e+05       1.233e+05        0
   86             2185       1.153e+05       5.778e+08        0
   87             2210       1.149e+05       4.911e+08        0
   88             2235       1.141e+05       1.166e+05        0
   89             2260        1.14e+05       1.153e+05        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
   90             2285       1.138e+05       1.464e+10        0
   91             2310       1.135e+05       2.694e+08        0
   92             2335       1.135e+05       1.157e+05        1
   93             2360       1.134e+05       1.272e+05        0
   94             2385       1.134e+05        1.18e+05        1
   95             2410       1.133e+05       5.736e+09        0
   96             2435       1.131e+05       1.299e+09        0
   97             2460       1.131e+05       1.218e+05        1
   98             2485       1.131e+05       1.788e+09        0
   99             2510       1.131e+05       1.739e+09        1
  100             2535       1.131e+05       1.148e+05        2
  101             2560       1.128e+05       5.215e+09        0
  102             2585       1.124e+05       1.152e+05        0
  103             2610       1.123e+05       1.317e+05        0
  104             2635       1.123e+05       7.884e+09        1
  105             2660       1.123e+05       1.172e+05        2
  106             2685       1.123e+05       8.514e+09        3
  107             2710       1.123e+05       1.141e+05        4
  108             2735       1.123e+05       1.229e+05        5
  109             2760       1.122e+05       2.137e+09        0
  110             2785       1.122e+05       4.282e+09        1
  111             2810       1.122e+05       5.647e+08        2
  112             2835       1.122e+05        4.16e+08        3
  113             2860       1.122e+05       5.195e+08        0
  114             2885       1.122e+05       1.138e+05        0
  115             2910       1.122e+05       4.544e+09        1
  116             2935       1.121e+05       5.387e+08        0
  117             2960       1.121e+05       4.197e+09        0
  118             2985       1.121e+05       8.744e+08        0
  119             3010       1.121e+05        1.13e+05        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  120             3035       1.121e+05       1.169e+05        1
  121             3060       1.121e+05       3.956e+09        2
  122             3085       1.121e+05       1.163e+05        0
  123             3110       1.121e+05       5.443e+10        0
  124             3135       1.121e+05       1.173e+05        1
  125             3160       1.121e+05       1.159e+05        0
  126             3185       1.121e+05       1.034e+08        0
  127             3210       1.121e+05       1.144e+05        0
  128             3235       1.121e+05       3.852e+09        0
  129             3260       1.121e+05       6.047e+08        0
  130             3285       1.121e+05       1.154e+05        0
  131             3310       1.121e+05        1.14e+09        0
  132             3335       1.121e+05       1.476e+10        0
  133             3360       1.121e+05        4.08e+09        1
  134             3385       1.121e+05       1.129e+05        2
  135             3410       1.121e+05        8.66e+07        0
  136             3435       1.121e+05       1.166e+05        0
  137             3460       1.121e+05       2.594e+10        0
  138             3485       1.121e+05       5.404e+08        0
  139             3510       1.121e+05       2.081e+10        0
  140             3535       1.121e+05       6.659e+09        1
  141             3560       1.121e+05       1.138e+05        0
  142             3585       1.121e+05        1.15e+05        1
  143             3610       1.121e+05       5.924e+07        2
  144             3635       1.121e+05       4.099e+09        0
  145             3660       1.121e+05        6.75e+08        0
  146             3685       1.121e+05       7.468e+09        1
  147             3710       1.121e+05       1.322e+10        2
  148             3735       1.121e+05       1.167e+05        0
  149             3760       1.121e+05       1.133e+05        1

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  150             3785       1.121e+05       7.044e+09        2
  151             3810       1.121e+05       1.257e+08        3
  152             3835       1.121e+05       1.147e+05        0
  153             3860        1.12e+05       1.135e+05        0
  154             3885        1.12e+05       1.134e+05        1
  155             3910       1.117e+05        2.84e+08        0
  156             3935       1.115e+05       7.336e+10        0
  157             3960       1.115e+05       1.942e+10        1
  158             3985       1.115e+05       1.241e+09        2
  159             4010       1.115e+05       5.832e+06        3
  160             4035       1.115e+05       1.493e+08        0
  161             4060       1.115e+05       1.262e+09        1
  162             4085       1.115e+05        1.12e+05        2
  163             4110       1.115e+05       1.125e+05        3
  164             4135       1.115e+05       4.587e+09        4
  165             4160       1.115e+05       1.443e+05        5
  166             4185       1.115e+05       1.128e+05        6
  167             4210       1.115e+05       2.251e+09        7
  168             4235       1.115e+05       1.314e+09        0
  169             4260       1.115e+05       1.243e+05        0
  170             4285       1.115e+05       2.869e+09        0
  171             4310       1.115e+05       1.117e+05        1
  172             4335       1.115e+05       1.131e+05        2
  173             4360       1.115e+05       8.639e+09        0
  174             4385       1.115e+05       2.267e+09        1
  175             4410       1.115e+05       2.451e+10        2
  176             4435       1.115e+05       5.881e+08        0
  177             4460       1.115e+05       1.121e+05        0
  178             4485       1.115e+05        1.16e+05        0
  179             4510       1.115e+05       1.614e+09        1

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  180             4535       1.115e+05       1.436e+09        0
  181             4560       1.115e+05       1.731e+10        0
  182             4585       1.114e+05       3.974e+10        0
  183             4610       1.114e+05       1.129e+05        0
  184             4635       1.114e+05        2.83e+09        1
  185             4660       1.114e+05       2.044e+09        0
  186             4685       1.114e+05       9.661e+08        0
  187             4710       1.114e+05       8.422e+08        1
  188             4735       1.114e+05        5.73e+10        0
  189             4760       1.114e+05       2.253e+08        1
  190             4785       1.114e+05       4.512e+08        2
  191             4810       1.114e+05       4.174e+09        0
  192             4835       1.114e+05       1.699e+10        1
  193             4860       1.114e+05       1.119e+05        0
  194             4885       1.114e+05       6.666e+08        0
  195             4910       1.114e+05       5.871e+09        0
  196             4935       1.114e+05       2.716e+10        1
  197             4960       1.114e+05       6.854e+07        2
  198             4985       1.114e+05       2.017e+10        0
  199             5010       1.114e+05       1.149e+05        1
  200             5035       1.114e+05       1.138e+05        0
  201             5060       1.114e+05       4.336e+08        1
  202             5085       1.114e+05       6.012e+09        0
  203             5110       1.113e+05       1.142e+05        0
  204             5135       1.112e+05       1.143e+05        0
  205             5160       1.112e+05       1.118e+05        1
  206             5185       1.112e+05       1.174e+05        0
  207             5210       1.112e+05       3.051e+10        0
  208             5235       1.112e+05       2.053e+09        1
  209             5260       1.111e+05       4.557e+08        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  210             5285       1.111e+05       7.571e+08        1
  211             5310       1.111e+05       7.197e+09        2
  212             5335       1.111e+05       1.145e+05        3
  213             5360       1.111e+05       1.121e+05        0
  214             5385       1.111e+05       1.578e+10        1
  215             5410       1.111e+05       2.666e+07        0
  216             5435       1.111e+05       3.178e+07        0
  217             5460       1.111e+05       8.565e+09        1
  218             5485       1.111e+05       2.043e+10        2
  219             5510       1.111e+05       5.442e+09        0
  220             5535       1.111e+05       2.814e+08        1
  221             5560       1.111e+05       1.127e+05        0
  222             5585       1.111e+05       7.336e+08        0
  223             5610       1.111e+05       2.733e+10        1
  224             5635       1.111e+05       1.273e+05        2
  225             5660       1.111e+05       6.899e+09        3
  226             5685       1.111e+05       7.528e+08        0
  227             5710       1.111e+05       6.619e+08        1
  228             5735       1.111e+05       1.061e+10        0
  229             5760       1.111e+05       3.035e+09        1
  230             5785       1.111e+05       1.821e+09        2
  231             5810       1.111e+05       1.077e+10        0
  232             5835       1.111e+05       1.133e+05        0
  233             5860       1.111e+05       1.797e+08        0
  234             5885       1.111e+05        8.28e+08        1
  235             5910       1.111e+05        1.14e+05        0
  236             5935       1.111e+05       2.482e+10        0
  237             5960       1.111e+05       1.974e+09        0
  238             5985       1.111e+05       1.142e+05        1
  239             6010       1.111e+05       1.114e+05        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  240             6035       1.111e+05       1.307e+09        1
  241             6060       1.111e+05       1.154e+05        2
  242             6085       1.111e+05       9.023e+09        3
  243             6110       1.111e+05       1.163e+05        4
  244             6135       1.111e+05       2.702e+09        5
  245             6160       1.111e+05       2.276e+09        6
  246             6185       1.111e+05       8.233e+09        7
  247             6210       1.111e+05       1.156e+05        8
  248             6235       1.111e+05         7.4e+09        9
  249             6260       1.111e+05       1.133e+05       10
  250             6285       1.111e+05       1.049e+10       11
  251             6310       1.111e+05       1.298e+10       12
  252             6335       1.111e+05       1.297e+05       13
  253             6360       1.111e+05       1.121e+05       14
  254             6385       1.111e+05       1.164e+05       15
  255             6410       1.111e+05       3.452e+09       16
  256             6435       1.111e+05       1.152e+05       17
  257             6460       1.111e+05       1.028e+10       18
  258             6485       1.111e+05       1.215e+05       19
  259             6510       1.111e+05       7.092e+09       20
  260             6535        1.11e+05       1.138e+05        0
  261             6560        1.11e+05       6.835e+07        0
  262             6585        1.11e+05       6.281e+09        1
  263             6610        1.11e+05       1.139e+05        2
  264             6635        1.11e+05       2.119e+09        3
  265             6660        1.11e+05       1.128e+05        4
  266             6685        1.11e+05       1.501e+10        0
  267             6710        1.11e+05       6.156e+08        1
  268             6735        1.11e+05       1.196e+05        2
  269             6760        1.11e+05       1.317e+10        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  270             6785       1.109e+05       1.459e+10        0
  271             6810       1.109e+05       1.223e+05        0
  272             6835       1.109e+05       1.349e+07        0
  273             6860       1.109e+05       6.732e+09        0
  274             6885       1.109e+05       5.224e+10        1
  275             6910       1.109e+05       1.125e+05        2
  276             6935       1.109e+05       1.115e+05        3
  277             6960       1.109e+05        3.25e+08        4
  278             6985       1.109e+05       6.786e+07        5
  279             7010       1.109e+05       1.336e+10        0
  280             7035       1.109e+05       1.138e+05        1
  281             7060       1.109e+05       6.088e+08        2
  282             7085       1.109e+05        7.31e+09        0
  283             7110       1.109e+05       7.746e+08        1
  284             7135       1.109e+05       1.112e+05        0
  285             7160       1.109e+05       1.121e+05        1
  286             7185       1.109e+05       3.355e+09        0
  287             7210       1.109e+05       8.788e+08        0
  288             7235       1.109e+05       1.148e+05        1
  289             7260       1.109e+05       1.124e+05        0
  290             7285       1.109e+05       1.199e+05        0
  291             7310       1.109e+05       6.312e+09        1
  292             7335       1.109e+05       1.256e+10        0
  293             7360       1.109e+05       1.132e+05        0
  294             7385       1.109e+05       4.399e+09        1
  295             7410       1.109e+05       1.164e+05        0
  296             7435       1.109e+05       1.111e+05        0
  297             7460       1.109e+05       2.789e+08        1
  298             7485       1.109e+05       7.352e+08        0
  299             7510       1.109e+05       1.113e+05        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  300             7535       1.109e+05       1.188e+05        1
  301             7560       1.109e+05        1.12e+05        0
  302             7585       1.109e+05       1.203e+05        1
  303             7610       1.109e+05        1.28e+05        0
  304             7635       1.109e+05       1.447e+05        0
  305             7660       1.109e+05       1.202e+05        0
  306             7685       1.109e+05       1.125e+05        0
  307             7710       1.109e+05       1.364e+09        1
  308             7735       1.109e+05       1.254e+05        2
  309             7760       1.109e+05       2.357e+10        0
  310             7785       1.109e+05       1.119e+05        1
  311             7810       1.109e+05       5.921e+08        0
  312             7835       1.109e+05       3.144e+10        0
  313             7860       1.109e+05       7.998e+09        0
  314             7885       1.109e+05       1.117e+05        0
  315             7910       1.109e+05       1.839e+08        0
  316             7935       1.109e+05       1.124e+05        0
  317             7960       1.109e+05       5.483e+09        1
  318             7985       1.109e+05       2.871e+09        0
  319             8010       1.109e+05       1.163e+05        0
  320             8035       1.109e+05        5.51e+07        1
  321             8060       1.109e+05         5.6e+09        0
  322             8085       1.109e+05       1.156e+09        0
  323             8110       1.109e+05       1.382e+10        0
  324             8135       1.109e+05       9.655e+08        0
  325             8160       1.109e+05       1.427e+09        0
  326             8185       1.109e+05       1.112e+05        1
  327             8210       1.109e+05       1.203e+05        0
  328             8235       1.109e+05       7.335e+09        0
  329             8260       1.109e+05       1.861e+08        0

                                  Best          Mean         Stall
Generation      Func-count     Penalty         Penalty    Generations
  330             8285       1.109e+05       1.412e+10        0
  331             8310       1.109e+05       1.771e+08        0
  332             8335       1.109e+05       1.294e+05        0
  333             8360       1.109e+05       5.997e+10        0
  334             8385       1.109e+05        6.81e+09        0
  335             8410       1.109e+05        1.83e+09        0
  336             8435       1.109e+05       1.433e+08        1
ga stopped because the average change in the penalty function value is less than options.FunctionTolerance and 
the constraint violation is less than options.ConstraintTolerance.

x = 1x20

1.0000 1.0000 7.0000 1.0000 1.0000 1.0000 1.0000 17.0000 40.0000 12.0000 10.0000 7.0000 5.0000 4.0000 0.0063 0.0078 0.0071 0.0092 0.0121 0.0103

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fval = 1.1092e+05

exitflag = 1

output = struct with fields:
      problemtype: 'integerconstraints'
         rngstate: [1x1 struct]
      generations: 336
        funccount: 8436
          message: 'ga stopped because the average change in the penalty function value is less than options.FunctionTolerance and ...'
    maxconstraint: 0
       hybridflag: []

Nv = x(1:7)

Nv = 1x7

1 1 7 1 1 1 1

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<mw-icon class=""></mw-icon>

K = x(7+1:7+7)

K = 1x7

17 40 12 10 7 5 4

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<mw-icon class=""></mw-icon>

m = x(7+7+1:7+7+6)

m = 1x6

0.0063 0.0078 0.0071 0.0092 0.0121 0.0103

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<mw-icon class=""></mw-icon>

fval

fval = 1.1092e+05

FitnessFcn(x)

ans = 1.1092e+05

function Z = FitnessFcn(x)
  Nv = x(1:7);
  K = x(7+1:7+7);
  m = x(7+7+1:7+7+6);
  Tb=1.2;
  Hb=[2.8 2.2 1.7 1.2 0.8 0.6 0 0];
  Sb=[25 28 32 36 35 38 0 0];
  F=[70 50 48 55 80 65 0 0];
  Sv=[0 280 200 320 360 380 420 0];
  Hv=[0 2.5 1.9 1.4 1 0.7 0.5 0];
  D=[180000 200000 240000 300000 350000 400000 0 0];
  P=[0 200000 240000 300000 350000 400000 450000 0];
  q=[1 1 1 1 1 1 0 0];
  u=[0.009 0.0064 0.0054 0.0072 0.01 0.008 0 0];
  t=[0.015 0.01 0.009 0.012 0.016 0.014 0 0];
  w=[0.005 0.004 0.003 0.004 0.006 0.004 0 0];
  Se=[29 32 38 42 37 40 0 0];
  n=[1 0.9 0.75 0.6 0.51 0.45];
  p=[3.2 2.6 2.1 1.6 1.2 0.9 0 0];
  Nb=[1 1 1 1 1 1 0 0];
  idx = 1:6;
  Nvc = cumprod(Nv(idx+1));
  Nvb = cumprod(Nv(idx));
  Z = sum(n(idx).*Tb.*Hb(idx).*D(idx).*(m(idx)-u(idx))+...
          (n(idx)*Tb).^2./(Nvc.*K(idx+1)).* ...
          (D(idx)/2.*(Hb(idx)+Hv(idx+1)-2*Hv(idx+1).*(1-D(idx)./P(idx+1))))+ ...
          Nvc.*K(idx+1).*(Se(idx).*(t(idx)-m(idx)).^3.*(t(idx)+3*m(idx)-4*w(idx)) ...
          ./(t(idx)-w(idx)).^4 +(Hb(idx)+p(idx)).*D(idx).*(t(idx)-m(idx)).^5.*(2*t(idx)+3*m(idx)-5*w(idx)) ...
          ./(5*(t(idx)-w(idx)).^4)+F(idx))+Nvc.*Sv(idx+1)+...
          (n(idx)*Tb).^2./Nvc.*(Hv(idx+1).*D(idx)/2.*(1-D(idx)./P(idx+1)))...
          + Nvb.*Nb(idx).*Sb(idx));
end

[HSUAN]

Thank you for your answer but I have some more questions.

If I also want to minimize z and specify the number of iterations, do I need to add any instructions?

Just setting iter=1000 seems to have no effect.

[Torsten]

The code from above tries to minimize Z - so I don't know what you mean by: If I also want to minimize z

According to the exit flag (1 in your case), "ga" ended successfully. So no need to change anything in the options.

[HSUAN]

The part that specifies the number of iterations is like iter=100,200,300. I want to observe the results when the number of iterations is different.

[Torsten]

There is not equivalent to "iterations" in "ga" because "ga" doesn't iterate in the usual sense.

"MaxGenerations" is something similar - so make a loop over this options parameter, change it in the loop and call "ga" three times with the parameter changed accordingly.

[HSUAN]

But from the above example, as long as the number of iterations exceeds 336, nothing will change. That is, if you set a number above 336 in MaxGenerations, the results will not change. Am I right to understand this?

[Torsten]

Yes. But you wrote you want to use iter=100,200,300.

Here are the default options for "ga" - maybe of interest for you to know.

optimoptions(@ga)

ans = 
  ga options:

   Set properties:
     No options set.

   Default properties:
             ConstraintTolerance: 1.0000e-03
                     CreationFcn: []
                    CrossoverFcn: []
               CrossoverFraction: 0.8000
                         Display: 'final'
                      EliteCount: '0.05*PopulationSize'
                    FitnessLimit: -Inf
               FitnessScalingFcn: @fitscalingrank
               FunctionTolerance: 1.0000e-06
                       HybridFcn: []
         InitialPopulationMatrix: []
          InitialPopulationRange: []
             InitialScoresMatrix: []
                  MaxGenerations: '100*numberOfVariables'
             MaxStallGenerations: 50
                    MaxStallTime: Inf
                         MaxTime: Inf
                     MutationFcn: []
    NonlinearConstraintAlgorithm: 'auglag'
                       OutputFcn: []
                         PlotFcn: []
                  PopulationSize: '50 when numberOfVariables <= 5, else 200'
                  PopulationType: 'doubleVector'
                    SelectionFcn: []
                     UseParallel: 0
                   UseVectorized: 0

And if you want to change the seed of the random generator used in "ga", you can remove or modify the line "rng("default")" which serves the purpose to make the results obtained identical every time you run the code with the same inputs.

[HSUAN]

Thank you for your patient explanation, I learned a lot.