MATLAB genetic algorithm integer optimization toolbox returns values higher than boundaries and doesn't satisfy inequality constraints. Why?

I'm using MATLAB R2016a genetic algorithm optimization toolbox to optimize 80 integer values. I have these constraints:

x(80) > x(79) > x(78) > x(77) > x(76) ... x(5) > x(4) > x(3) > x(2) > x(1)

The range for all integer variables is between 1 and 500. I used this code in MATLAB:

f = @(x)Cost_function(x, my_data);

num_of_var = 80;

for mx = 1:num_of_var-1
    A(mx,:) = [zeros(1,mx-1),1,-1, zeros(1,num_of_var-mx-1)];
end

b = repmat(-3, [num_of_var-1,1]);

lb = ones([num_of_var-1,1]);

up = repmat(500,[num_of_var-1,1]);

options = optimoptions('ga');
options.Display = 'iter';
options.PopulationSize = 200;
options.UseParallel = 0;

IntCon = 1:1:num_of_var;
[x, fval, exitflag] = ga(f, num_of_var, A, b, [], [], lb, up,[] ,IntCon, options);

Is this code correct? In some cases this code returns integer higher than boundaries. For example this is first return of this code for cost function:

11  89  129 136 168 191 208 232 267 299 306 312 312 270 270 293 297 296 283 192 188 239 241 239 226 212 212 301 275 231 221 210 179 182 200 224 227 258 270 264 225 204 183 199 202 236 305 310 313 276 272 259 256 336 329 310 303 303 296 289 275 235 233 232 194 196 203 268 294 313 340 336 333 263 260 257 265 275 409 174964160

Otherwise this output structure doesn't satisfy my mentioned constraints. why?

[Geoff Hayes]

Jack - what is your Cost_function?

[Jack]

I checked first array which was sent to cost_function before cost function calculations so this behavior doesn't bound to cost function (mentioned array in question is not final optimized array). But for more information it is going to fit some linear least square regression to a time series between generated time steps extracted by optimization algorithm. You can use every cost function in above code. You have same mentioned behavior.

Answer 1

[Alan Weiss]

I would give a feasible point for starting. Something like

 x0 = 2:2:160;
 options.InitialPopulationMatrix = x0;

It is possible that you don't have any feasible points, and the solver gets stuck in the infeasible region.

Alan Weiss

MATLAB mathematical toolbox documentation

[Jack]

Thank you for your answer. With your proposed codes I get this array in beginning of first call of cost function:

 44  60  84  96  178  213  220  218  221  201  204  231  267  312  328  333  327  306  274  268  267  262  265  267  271  269  209  215  229  238  285  292  296  290  291  272  273  276  279  282  263  244  242  243  246  249  253  256  270  275  326  354  388  394  275  279  284  332  343  362  365  364  327  319  291  209  211  217  282  279  263  234  233  184  176  179  209  233  246  283

Unfortunately based on linear constrains this is not a feasible solution.

[Alan Weiss]

I am not sure that I understand you. ga is population-based, and unless you have a population of just one member, the vector you gave is not a complete population.

Your population should consist of entirely feasible members when using the @gacreationlinearfeasible creation function. Is that your creation function? If it is, then if you have an infeasible population then your linear constraints are not set up properly. Please check what you get when you take your A matrix and multiply it by a solution to see whether it satisfies A*x <= b.

Sorry, I don't have any other ideas right now.

Alan Weiss

MATLAB mathematical toolbox documentation