PSO does not satisfy the nonlcon inequality constraint and gives solutions less than LB

Hello everyone,

I uses this pso code: https://www.mathworks.com/matlabcentral/fileexchange/25986-constrained-particle-swarm-optimization?s_tid=srchtitle

when running the pso with:

[best_solution, fval] = pso(objFcn,nVars,[],[],A_eq,B_eq,LB(ttt,:),UB(ttt,:),nonlcon,options_pso)

returns me solutions does not satisfy the nonlcon and some solutions have values lower than than the LB ?

here is the nonlcon function:

function [cneq, ceq] = myNonLinearConstraint(force_pop)
global ttt 
% compression and shear vectors directions
[a1, b1, c1, a2, b2, c2, a, b, c, d, e, f] = shear_comp_ratio_coef;

% GH reaction forces
R_gh_x = force_pop(55);
R_gh_y = force_pop(56);
R_gh_z = force_pop(57);

% shear forces
F_shear_1 = a1(ttt)*R_gh_x+b1(ttt)*R_gh_y+c1(ttt)*R_gh_z;
F_shear_2 = a2(ttt)*R_gh_x+b2(ttt)*R_gh_y+c2(ttt)*R_gh_z;

% angle between F_shear_1 (as x-dir) and F_shear_2 (as y-dir)
theta = atan2d(F_shear_2,F_shear_1);
if theta<0
    theta = theta+360;
end

% emprical shear_comp_ratio 
shear_comp_ratio_emprical = [0.51, 0.33, 0.29, 0.4, 0.56, 0.43, 0.3, 0.35, 0.51];
angle = 0:45:360;

% get the shear_comp_ratio_at the current angle theta using linear interpolation
shear_comp_ratio_at_theta = interp1(angle,shear_comp_ratio_emprical,theta);

% total shear force
F_shear = (a(ttt)*R_gh_x+b(ttt)*R_gh_y+c(ttt)*R_gh_z);

% compression force
F_comp = (d(ttt)*R_gh_x+e(ttt)*R_gh_y+f(ttt)*R_gh_z);

% cneq: not equality constraint 
cneq = abs(F_shear/F_comp)-shear_comp_ratio_at_theta;
% ceq: equality constraint not exist
ceq = [];

thanks in advance

[Matt J]

You rprobably need to demonstrate the problem.

[Taha]

the first problem: the cneq should be <=0 (to satisfy the nonlcon inequality constraints) but some times the pso solves the problem and gives the result with cneq>0 (larger than the ConstTol = 1e-6) (for example: cneq = 0.3)

the second problem: the pso returns solutions with values less than the LB (LB = zeros), but some variables have large negative values (larger than the ConstTol = 1e-6)

note: I used the same nonlcon function file with ga(), No issues found, the cneq<=0 and all solutions values between LB and UB (in my point of view: this means that the nonlcon function have been written correctly)

[Torsten]

And what are the exitflags from pso for the runs where you encounter the constraint violations ?

[Taha]

Here is a solution with the problem encountered:

part of the solution: Final best point: [-0.3753 13.9498 17.7519 18.4837 35.3622 80.2211 118.4277 117.5890 176.7455 39.6731 7.9237 52.9169 -33.2149] (values should >= LB, LB set to zeros for all variables)

cneq = 0.1143 (should to be <=0)

exitflag =

0

[Torsten]

Did you look up what exitflag = 0 means ? According to the documentation:

Exit FlagMeaning

1

Without nonlinear constraints — Average cumulative change in value of the fitness function over MaxStallGenerations generations is less than FunctionTolerance, and the constraint violation is less than ConstraintTolerance.

With nonlinear constraints — Magnitude of the complementarity measure (see Complementarity Measure) is less than sqrt(ConstraintTolerance), the subproblem is solved using a tolerance less than FunctionTolerance, and the constraint violation is less than ConstraintTolerance.

3

Value of the fitness function did not change in MaxStallGenerations generations and the constraint violation is less than ConstraintTolerance.

4

Magnitude of step smaller than machine precision and the constraint violation is less than ConstraintTolerance.

5

Minimum fitness limit FitnessLimit reached and the constraint violation is less than ConstraintTolerance.

0

Maximum number of generations MaxGenerations exceeded.

-1

Optimization terminated by an output function or plot function.

-2

No feasible point found.

-4

Stall time limit MaxStallTime exceeded.

-5

Time limit MaxTime exceeded.

So you should try increasing the value for "MaxGenerations" in the options setting for "pso" in order to get a feasible solution.

[Taha]

Okay, I will increase the MaxGenerations, but why pso returns infeasible solutions and don't indicates that by exitflag = -2 (Like ga())

[Taha]

the problem here:

when solving using pso, the result is:

exitflag = 3 (which means that: Value of the fitness function did not change in MaxStallGenerations generations and the constraint violation is less than ConstraintTolerance.)

and: cneq = 3.1556 (should be <=0 with ConstTol = 1e-6)

How pso says "the constraint violation is less than ConstraintTolerance." and actually the tolerance is 3.1556

[Torsten]

Without the code to reproduce the results, we cannot tell.

[Walter Roberson]

You did not post your full code and you did not attach your data, so we cannot test this for you.

Answer 1

[Steven Lord]

Have you considered using the particleswarm function in Global Optimization Toolbox, either as your main solver or to help you diagnose why the solver in the File Exchange submission doesn't give you the answers you expect?

[Taha]

The particleswarm function in Global Optimization Toolbox doesn't support linear and nonlinear constraints

[Taha]

Any way to use The particleswarm function in Global Optimization Toolbox with the linear and nonlinear constraints?

[Matt J]

Why not use ga()? Does particleswarm have some important property?

[Taha]

Yes, pso is faster than ga and the results are more smooth than ga. but when including the nonlcon in both algorithms, pso is not stable and gives me wrong solutions, but ga still gives correct and not smooth solutions

[Matt J]

If "correct" solutions exist that don't have the smoothness property that you want, it means the problem isn't properly regularized. You shouldn't be relying on the optimization solver to steer away from global solutions that aren't smooth. If a solution isn't smooth, it shouldn't be a solution.

[Taha]

these figures show what I meant by the smooth solutions.

The two solutions of ps and ga are solved for the same exact inputs for the two algorithms

here, pso have smooth solutions over the time frames (no large change in reaction force over the time),

but ga have large changes every time step

[Matt J]

But again, you shouldn't be allowing these 2 different solutions to exist. Add a roughness penalty or something to your objective function..

[Taha]

My problem is a redundant problem, 34 equations with 69 unknowns, mathematically there are infinite number of solutions , I used the optimization technique and the constraints to reach to the best solution. There is big difference in ga and ps results , but both have the same trend. The point of enforcing the ga() to get smooth solutions I think it's very hard to do that. Anyway, I will try in this way.