Particle Swarm Optimisation (PSO)

A module for particle swarm optimisation with three different speed mechanisms.

Original papers:

  • Kennedy, J., Eberhart, R. (1995). Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks (Vol. 4, pp. 1942-1948), IEEE.

  • Kennedy, J., & Eberhart, R. C. (1997). A discrete binary version of the particle swarm algorithm. In: 1997 IEEE International conference on systems, man, and cybernetics. Computational cybernetics and simulation (Vol. 5, pp. 4104-4108), IEEE.

  • Clerc, M., Kennedy, J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE transactions on Evolutionary Computation, 6(1), 58-73.

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What can you use?

  • Multi processing: ✔️

  • Discrete spaces: ✔️

  • Continuous spaces: ✔️

  • Mixed Discrete/Continuous spaces: ✔️

Parameters

class neorl.evolu.pso.PSO(mode, bounds, fit, npar=50, c1=2.05, c2=2.05, speed_mech='constric', ncores=1, seed=None)[source]

Parallel Particle Swarm Optimisaion (PSO) module

Parameters

  • mode – (str) problem type, either “min” for minimization problem or “max” for maximization

  • bounds – (dict) input parameter type and lower/upper bounds in dictionary form. Example: bounds={'x1': ['int', 1, 4], 'x2': ['float', 0.1, 0.8], 'x3': ['float', 2.2, 6.2]}

  • fit – (function) the fitness function

  • npar – (int) number of particles in the swarm

  • c1 – (float) cognitive speed constant

  • c2 – (float) social speed constant

  • speed_mech – (str) type of speed mechanism to update particle velocity, choose between constric, timew, globw.

  • ncores – (int) number of parallel processors

  • seed – (int) random seed for sampling

evolute(ngen, x0=None, verbose=False, **kwargs)[source]

This function evolutes the PSO algorithm for number of generations.

Parameters

  • ngen – (int) number of generations to evolute

  • x0 – (list of lists) the initial position of the swarm particles

  • verbose – (bool) print statistics to screen

Returns

(tuple) (best individual, best fitness, and a list of fitness history)

Example

from neorl import PSO

#Define the fitness function
def FIT(individual):
    """Sphere test objective function.
                    F(x) = sum_{i=1}^d xi^2
                    d=1,2,3,...
                    Range: [-100,100]
                    Minima: 0
    """
    y=sum(x**2 for x in individual)
    return y

#Setup the parameter space (d=5)
nx=5
BOUNDS={}
for i in range(1,nx+1):
    BOUNDS['x'+str(i)]=['float', -100, 100]

#setup and evolute PSO
pso=PSO(mode='min', bounds=BOUNDS, fit=FIT, c1=2.05, c2=2.1, npar=50,
                speed_mech='constric', ncores=1, seed=1)
x_best, y_best, pso_hist=pso.evolute(ngen=100, verbose=1)

Notes

  • Always try the three speed mechanisms via speed_mech when you solve any problem.

  • Keep c1, c2 > 2.0 when using speed_mech='constric'.

  • speed_mech=timew uses a time-dependent inertia factor, where inertia w is annealed over PSO generations.

  • speed_mech=globw uses a ratio of swarm global position to local position to define inertia factor, and this factor is updated every generation.

  • Look for an optimal balance between npar and ngen, it is recommended to minimize particle size to allow for more generations.

  • Total number of cost evaluations for PSO is npar * (ngen + 1).