Extra documentation for custom objective function

[jmmcd]

I found it surprising that the objective function has to accept the entire population (not a single particle) and return one value per particle. My students found it surprising too. In most treatments of optimisation, we define an objective function as a function that accepts a single solution and returns a single real number.

I see that it's documented at https://pyswarms.readthedocs.io/en/latest/api/pyswarms.utils.functions.html#module-pyswarms.utils.functions.single_obj:

"All objective functions obj_func() must accept a (numpy.ndarray) with shape (n_particles, dimensions). Thus, each row represents a particle, and each column represents its position on a specific dimension of the search-space.

In this context, obj_func() must return an array j of size (n_particles, ) that contains all the computed fitness for each particle."

Ok, I understand that in PySwarms, we are using the vectorised version for speed. I don't disagree with this design decision! Instead, a small addition to the docs would help.

In all the tutorials https://pyswarms.readthedocs.io/en/latest/tutorials.html, the objective is one of the built-in ones, and so the new user is not confronted with the issue. They try to write their own objective function which accepts a single particle, and they don't see any error -- but the algorithm is now not correct! This code runs but only calculates a single objective value for the entire population. I guess that with Numpy broadcasting, the algorithm now operates as if all particles have the same objective value.

import numpy as np
import pyswarms as ps
def my_sphere(x):
    return np.sum(x**2)

options = {'c1': 0.5, 'c2': 0.3, 'w':0.9}
optimizer = ps.single.GlobalBestPSO(n_particles=10, dimensions=2, options=options)
cost, pos = optimizer.optimize(my_sphere, iters=1000)

In other cases, depending on the definition of the objective, the user may see a confusing Numpy error message.

Solutions

1. I would suggest to write a short section "Optimizing your own function" where the objective is hand-written, before the "Optimizing a function with bounds" tutorial section. It could mention this issue and basically use the above example, but show how to use axis=1 to fix the problem. I could do this and create a PR, what do you think?

2. Could PySwarms make a specific check that the return value from the objective has the expected shape, ie n_particles, and write out a user-friendly error message if not? I guess this would be in https://github.com/jmmcd/pyswarms/blob/master/pyswarms/backend/operators.py#L213.

[jmmcd]

I implemented these changes here: https://github.com/jmmcd/pyswarms/

Unfortunately I won't have time to setup tests, CI etc to make an official PR for the code (item 2). For the docs (item 1) I can if needed.

[ljvmiranda921]

Hi @jmmcd , thanks a lot for putting this together!

the objective is one of the built-in ones, and so the new user is not confronted with the issue. They try to write their own objective function which accepts a single particle, and they don't see any error -- but the algorithm is now not correct!

You're definitely right, the new user is not confronted with the issue when built-in ones are used. I also agree that the problem occurs one we start writing our own objective function. We do have a decorator for that, I guess that should be properly documented as well

Thanks for catching! I'll check with your fork and do the appropriate changes! There's a lot of things that I need to handle yet (including 3.6+ support, etc.). If you're interested to make a PR I'll appreciate that as well! 🙇

[jmmcd]

Hi @ljvmiranda921, I will just create the PR containing both the docs and the extra check. I won't have time to do tests etc so I will leave it in your hands :) Hope it helps.

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