Vectorization of a Non-Linear Fitness Function

Hi,

I have a set of targets, a 30x2 double, which I would like to 'hit' with a projectile. To do so, I would like to pass the vector of targets through a genetic algorithm which minimises the distance between projectile and target at some point during its trajectory.

However, when I have tried to vectorize my code, I get the following error:

"When 'Vectorized' is 'on', your fitness function must return a vector of length equal to the size of the population."

My original code, which works for a single input is as follows:

%Calling genetic algorithm solver for target (x,y)
    [xga,fga,flga,oga]=target(x,y);
Where:
    function [xga,fga,flga,oga]=target(target_x, target_y)
        %GA to minimise the distance to the target by changing the initial speed and angle of the 
        %projectile.         
        rng default
        object=@(initialSpeedAngle)objective(initialSpeedAngle,target_x,target_y);
        %Initial guess for speed and angle.
        startAtCentre=[450 45];
        %Defining a randomised initial population
        initpop=10*randn(20,2)+repmat(startAtCentre,20,1);
        %Defining GA options - initial population and function tolerance.
        optns=optimoptions('ga','InitialPopulationMatrix',initpop,'TolFun',0);
        %Running the GA
        [xga,fga,flga,oga]=ga(object,2,[],[],[],[],[100 10],[800 80],[],optns);
    end
And:
    function out=objective(initialSpeedAngle,target_x,target_y)
        %Projectile trajectory
        ode45solns=solve_ode45(initialSpeedAngle(1),initialSpeedAngle(2),0,0.01,100);
        %Initialising cell
        DistToTarget=zeros(size(ode45solns,1),3);
        %Column 1 is difference in x between trajectory and target, Column 2 difference in y. Column 3 is     
        %total 2D distance
        DistToTarget(:,1)=target_x-ode45solns(:,4);
        DistToTarget(:,2)=target_y-ode45solns(:,5);
        DistToTarget(:,3)=sqrt(DistToTarget(:,1).^2+DistToTarget(:,2).^2);
        out=min(DistToTarget(:,3));
    end

I have tried to vectorize the problem for x_targets=targets(:,1) and y_targets=targets(:,2), giving;

%Calling the genetic algorithm for a vector of targets:
    [xga,fga,flga,oga]=targetVectorized(x_targets,y_targets);
Where:
    function [xga,fga,flga,oga]=targetVectorized(target_x, target_y)
        %Using a genetic algorithm (GA) to minimise the distance to the target by changing the initial 
        %speed and angle of the projectile.
        rng default
        %Defining what the GA should change.
        object=@(initialSpeedAngle)objectiveVectorized(initialSpeedAngle, target_x(:,1),target_y(:,1));
        %Initial guess for speed and angle.
        startAtCentre=[450 45];
        %Defining a randomised initial population
        initpop=10*randn(size(20,1),2)+repmat(startAtCentre,size(20,1),1);
        %Defining GA options - initial population and function tolerance.
        optns=optimoptions('ga','InitialPopulationMatrix',initpop,'TolFun',0,'UseVectorized', true);
        %Running the GA
        [xga,fga,flga,oga]=ga(object,2,[],[],[],[],[100 10],[800 80],[],optns);
    end
And:
    function out=objective(initialSpeedAngle,target_x,target_y)

        %Projectile trajectory
        ode45solns=solve_ode45(initialSpeedAngle(1),initialSpeedAngle(2),0,0.01,...
            100);
        
        %Size of loop, initialising cells
        NumTargets=size(target_x,1);
        xDistToTarget=zeros(size(ode45solns,1),NumTargets);
        yDistToTarget=zeros(size(ode45solns,1),NumTargets);
        
        %Calculating differences between the target and ode45solns
        for ii=1:1:NumTargets
            
            %xDistToTarget difference in x between trajectory and target.
            xDistToTarget(:,ii)=target_x(ii)-ode45solns(:,4);
            
            %yDistToTarget difference in y between trajectory and target.
            yDistToTarget(:,ii)=target_y(ii)-ode45solns(:,5);
            
        end
        
        %totDistToTarget is total 2D distance.
        totDistToTarget=sqrt(xDistToTarget.^2+yDistToTarget.^2);
        
        %Smallest distance between target and projectile
        out=min(totDistToTarget)';

    end

Thanks in advance for any help!

Answer 1

[Jorge Martinez]

I had a similar issue, the problem is that I was using 'ga' with the vectorized fitness function. The actual function is 'gamultiobj'.

Matlab R2014a