Algoritmo y Problema Personalizado

En este cuaderno, mostraremos como usar Algorithm y Problem para crear un algoritmo y problema personalizado. Aqui daremos un ejemplo de implementacion de un algoritmo PSO que resuelve el problema Sphere.

import torch

from evox.core import Algorithm, Mutable, Parameter, Problem
from evox.utils import clamp
from evox.workflows import EvalMonitor, StdWorkflow

Ejemplo de algoritmo: algoritmo PSO

La Optimizacion por Enjambre de Particulas (PSO) es un algoritmo metaheuristico basado en poblacion inspirado en el comportamiento social de las aves y los peces. Es ampliamente utilizado para resolver problemas de optimizacion continuos y discretos.

Aqui hay un ejemplo de implementacion del algoritmo PSO en EvoX:

def min_by(
    values,
    keys,
):
    """A helper function to find the minimum value in a list of values."""
    values = torch.cat(values, dim=0)
    keys = torch.cat(keys, dim=0)
    min_index = torch.argmin(keys)
    return values[min_index[None]][0], keys[min_index[None]][0]


class PSO(Algorithm):
    def __init__(
        self,
        pop_size: int,
        lb: torch.Tensor,
        ub: torch.Tensor,
        w: float = 0.6,
        phi_p: float = 2.5,
        phi_g: float = 0.8,
        device: torch.device | None = None,
    ):
        super().__init__()
        device = torch.get_default_device() if device is None else device
        assert lb.shape == ub.shape and lb.ndim == 1 and ub.ndim == 1 and lb.dtype == ub.dtype
        self.pop_size = pop_size
        self.dim = lb.shape[0]
        # Here, Parameter is used to indicate that these values are hyper-parameters
        # so that they can be correctly traced and vector-mapped
        self.w = Parameter(w, device=device)
        self.phi_p = Parameter(phi_p, device=device)
        self.phi_g = Parameter(phi_g, device=device)
        # setup
        lb = lb[None, :].to(device=device)
        ub = ub[None, :].to(device=device)
        length = ub - lb
        pop = torch.rand(self.pop_size, self.dim, device=device)
        pop = length * pop + lb
        velocity = torch.rand(self.pop_size, self.dim, device=device)
        velocity = 2 * length * velocity - length
        # write to self
        self.lb = lb
        self.ub = ub
        # mutable
        self.pop = Mutable(pop)
        self.velocity = Mutable(velocity)
        self.fit = Mutable(torch.full((self.pop_size,), torch.inf, device=device))
        self.local_best_location = Mutable(pop)
        self.local_best_fit = Mutable(torch.full((self.pop_size,), torch.inf, device=device))
        self.global_best_location = Mutable(pop[0])
        self.global_best_fit = Mutable(torch.tensor(torch.inf, device=device))

    def step(self):
        compare = self.local_best_fit > self.fit
        self.local_best_location = torch.where(compare[:, None], self.pop, self.local_best_location)
        self.local_best_fit = torch.where(compare, self.fit, self.local_best_fit)
        self.global_best_location, self.global_best_fit = min_by(
            [self.global_best_location.unsqueeze(0), self.pop],
            [self.global_best_fit.unsqueeze(0), self.fit],
        )
        rg = torch.rand(self.pop_size, self.dim, device=self.fit.device)
        rp = torch.rand(self.pop_size, self.dim, device=self.fit.device)
        velocity = (
            self.w * self.velocity
            + self.phi_p * rp * (self.local_best_location - self.pop)
            + self.phi_g * rg * (self.global_best_location - self.pop)
        )
        pop = self.pop + velocity
        self.pop = clamp(pop, self.lb, self.ub)
        self.velocity = clamp(velocity, self.lb, self.ub)
        self.fit = self.evaluate(self.pop)

    def init_step(self):
        """Perform the first step of the PSO optimization.

        See `step` for more details.
        """
        self.fit = self.evaluate(self.pop)
        self.local_best_fit = self.fit
        self.global_best_fit = torch.min(self.fit)

Ejemplo de problema: problema Sphere

El problema Sphere es un problema de optimizacion de referencia simple pero fundamental utilizado para probar algoritmos de optimizacion.

La funcion Sphere se define como:

$$ \min f(x)= \sum_{i=1}^{n} x_{i}^{2} $$ Aqui hay un ejemplo de implementacion del problema Sphere en EvoX:

class Sphere(Problem):
    def __init__(self):
        super().__init__()

    def evaluate(self, pop: torch.Tensor):
        return (pop**2).sum(-1)

Usar el algoritmo para resolver el problema

Iniciar el algoritmo, problema y monitor

algorithm = PSO(
    pop_size=100,
    lb=torch.tensor([-10.0]),
    ub=torch.tensor([10.0]),
    w=0.6,
    phi_p=2.5,
    phi_g=0.8,
)
problem = Sphere()
monitor = EvalMonitor()

Iniciar el flujo de trabajo y ejecutarlo

workflow = StdWorkflow(algorithm=algorithm, problem=problem, monitor=monitor)

for _ in range(100):
    workflow.step()

workflow.monitor.plot()