"Error in running optimization. Not enough input arguments" while running ga

I am using following objective function:

function Length_Sum = objective_function( l1,l2,l3 )

Length_Sum = l1 + l2 + l3; 

end

With constraints function given below:

function [c, ceq] = simple_constraint(l1,l2,l3)

c(1) = l3^2 + 200*l3*cos(30) + 10000 - (l1 + l2)^2;
c(2) = (100- l3*cos(30))^2 + (100*sin(30))^2 - (l1-l2)^2;

thetas = inverse_kinematics(l1,l2,l3);

c(3) = thetas(4,1) - 160;
c(4) = thetas(4,2) - 160;
c(5) = thetas(4,3) - 160;

c(6) = 20 - thetas(4,1);
c(7) = 20 - thetas(4,2);
c(8) = 20 - thetas(4,3);

c(9) = thetas(5,1) - 340;
c(10) = thetas(5,2) - 340;
c(11) = thetas(5,3) - 340;

c(12) = 200 - thetas(5,1);
c(13) = 200 - thetas(5,2);
c(14) = 200 - thetas(5,3);

c(15) = thetas(6,1) - 340;
c(16) = thetas(6,2) - 340;
c(17) = thetas(6,3) - 340;

c(18) = 200 - thetas(6,1);
c(19) = 200 - thetas(6,2);
c(20) = 200 - thetas(6,3);

ceq = [];

end

constraint function uses another function for generating values of thetas, the function is given below:

function thetas = inverse_kinematics(l1,l2,l3)
    x = 100;
    y = 0;
    phi = 210*pi/180:60*pi/180:330*pi/180;

      x1 = x - (l3*cos(phi));
      y1 = y - (l3*sin(phi));
      a = sqrt(x1.^2 + y1.^2);
      y2 = -y1./a;
      x2 = -x1./a;
      gamma = atan2(y2,x2);
      c = (- x1.^2 - y1.^2 - l1^2 + l2^2)./(2*l1*a);
      d = acos(c);

      theta1 = gamma + d;
      if theta1 < 0
          theta1 = theta1 + 2*pi;
      end

      theta4 = gamma - d;
      if theta4 < 0
         theta4 = theta4 + 2*pi;
      end

      e = (y1 - l1*sin(theta1))/l2;
      f = (x1 - l1*cos(theta1))/l2;

      theta2 = atan2(e,f) - theta1;
      if theta2 < 0
          theta2 = theta2 + 2*pi;
      end

      g = (y1 - l1*sin(theta4))/l2;
      h = (x1 - l1*cos(theta4))/l2;

      theta5 = atan2(g,h) - theta4;
      if theta5 < 0
          theta5 = theta5 + 2*pi;
      end

      theta3 = (phi)- (theta1 + theta2);
      if theta3 < 0
          theta3 = theta3 + 2*pi;
      end

      theta6 = (phi)- (theta4 + theta5);
      if theta6 < 0
          theta6 = theta6 + 2*pi;
      end

      thetas = [theta1;theta2;theta3;theta4;theta5;theta6].*180/pi;

end

After running this code using ga toolbox, with lower bounds [20 20 20] and upper bounds [100 100 100] and rest parameters set to default, I am getting "Error in running optimization. Not enough input arguments" error. Can someone help?

Answer 1

[Alan Weiss]

You need to have ONE variable as your decision variable. Something like

function Length_Sum = objective_function(x)
l1 = x(1);
l2 = x(2);
l3 = x(3);
Length_Sum = l1 + l2 + l3; % or just use sum(x)

See Compute Objective Function.

Similarly, pass just one variable to simple_constraint, and extract l1, l2, and l3 inside the function.

Alan Weiss

MATLAB mathematical toolbox documentation

[siddhesh rane]

@Alan Thanks. I am having problem with the constraint function if c(1) and c(2) are not satisfied inverse_kinematic() function gives an error. How can ensure that c(1) and c(2) are satisfied before running inverse_kinematics function? Is it allowed to use if condition in constraint function?

[Alan Weiss]

Your constraint functions can have any statements you like, including if.

Alan Weiss

MATLAB mathematical toolbox documentation

[siddhesh rane]

Do I need to set values of constraints c(3) to c(20) to very high positive value when c(1) and c(2) are not satisfied ? Otherwise wouldn't c(3) to c(20) have values from previous iteration which might mislead the GA and converge to non-feasible solution?

[Alan Weiss]

I believe that, if inverse_kinematic() would return an error, then you don't have to run it at all. Just return NaN for each of the constraints that would be calculated by that function, or, if you like, set the returned values to an arbitrary large value, as you say.

No, ga would NOT take values from a previous iteration.

Allow me to make two comments on your code:

1. You have a statement including cos(30). Are you expecting to calculate in degrees instead of radians? If so, use the cosd function, not cos.
2. Generally, patternsearch is a faster and more robust optimizer than ga. I heartily suggest that you give it a try. If you want to start patternsearch from a variety of initial points to search for a global solution, try

x0 = lb + rand(size(lb)).*(ub - lb);

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[siddhesh rane]

@Alan: Thank you for the answer and pointing out the cos(30) error. I will try using pattern search.

[siddhesh rane]

@Alan: I tried putting NaN values for constraints and using pattern search as well as ga, I am getting an error "Constraint function must return real value."

[Alan Weiss]

Well, try using 1e100 instead as each constraint value when the constraint is not defined. I thought that patternsearch, at least, would do OK with NaN values, but I guess not. Sorry.

Alan Weiss

MATLAB mathematical toolbox documentation

[siddhesh rane]

Thanks @Alan its working now

Answer 2

[Priya Venugopal]

how can we include the constraint Ax>=b as objective fuction....pl help