Ho to Constraint GA to Generate Population Within Design Space

Dear all,

I’m currently working on a genetic algorithm-based optimization and would like to constrain the GA to select design variables strictly within a predefined design space.

While I can set upper and lower bounds for the variables, my design space is more complex, and I’m working with a large population. I’m wondering if there’s a way to configure the GA so that it generates the populations entirely within the valid design space, rather than just filtering or penalizing out-of-bounds individuals afterward.

Attached is a simple sketch illustrating the shape of my design space.

Thanks in advance for your guidance!

Best regards,

Mirhan

Answer 1

[Matt J]

Yes, you can reparametrize the design vector x as,

x=t1*v1+t2*v2

where v1 and v2 are the direction vectors of the two rays bounding your cone,

v1=[cosd(150),sind(150)]
v2=[cosd(30), sind(30)]

The new design variables are t=[t1,t2], which only need simple positivity constraints to confine x to the cone.

[Mirhan]

Thank you very much for your quick and helpful response!

I was wondering—how can I implement this into a classical genetic algorithm? I'm not quite sure where exactly this type of constraint should be defined within the algorithm.

Thank you again!

Best regards,

Mirhan

LB = [0 0 0];    
UB = [10 10 10];             

%% Optimization Options
PopulationSize = 50*nvars;
Generations = 50;

% Set GA options
options = optimoptions( 'ga',...
                    'Display', 'iter',...
                    'TolFun', 1e-9,...
                    'TolCon', 1e-3,...
                    'PlotFcn',{@gaplotbestf,@gaplotdistance});


ObjectiveFunction = @(x) simple_objective (x);

% Run Genetic Algorithm
[x_opt, fval_opt] = ga(ObjectiveFunction, nvars, [], [], [], [], LB, UB, [], options);

[Matt J]

The code from your last comment is for a 3D problem, whereas your diagram was for a 2D problem. I will continue to assume the 2D problem whose design space is a cone at 30 degrees to the x-axis.

You need to reparametrize your fitness function in terms of t,

xoft=@(t) t(1)*v(1)+t(2)*v(2);

ObjectiveFunction = @(t) simple_objective( xoft(t));

% Run Genetic Algorithm
[t_opt, fval_opt] = ga(ObjectiveFunction, 2, [], [], [], [], [0,0], [], [], options);


x_opt =  xoft(t_opt)