Source code for qiskit_algorithms.optimizers.umda

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"""Univariate Marginal Distribution Algorithm (Estimation-of-Distribution-Algorithm)."""

from __future__ import annotations

from import Callable
from typing import Any

import numpy as np
from scipy.stats import norm

from qiskit_algorithms.utils import algorithm_globals
from .optimizer import OptimizerResult, POINT
from .scipy_optimizer import Optimizer, OptimizerSupportLevel

[docs]class UMDA(Optimizer): """Continuous Univariate Marginal Distribution Algorithm (UMDA). UMDA [1] is a specific type of Estimation of Distribution Algorithm (EDA) where new individuals are sampled from univariate normal distributions and are updated in each iteration of the algorithm by the best individuals found in the previous iteration. .. seealso:: This original implementation of the UDMA optimizer for Qiskit was inspired by my (Vicente P. Soloviev) work on the EDAspy Python package [2]. EDAs are stochastic search algorithms and belong to the family of the evolutionary algorithms. The main difference is that EDAs have a probabilistic model which is updated in each iteration from the best individuals of previous generations (elite selection). Depending on the complexity of the probabilistic model, EDAs can be classified in different ways. In this case, UMDA is a univariate EDA as the embedded probabilistic model is univariate. UMDA has been compared to some of the already implemented algorithms in Qiskit library to optimize the parameters of variational algorithms such as QAOA or VQE and competitive results have been obtained [1]. UMDA seems to provide very good solutions for those circuits in which the number of layers is not big. The optimization process can be personalized depending on the parameters chosen in the initialization. The main parameter is the population size. The bigger it is, the final result will be better. However, this increases the complexity of the algorithm and the runtime will be much heavier. In the work [1] different experiments have been performed where population size has been set to 20 - 30. .. note:: The UMDA implementation has more parameters but these have default values for the initialization for better understanding of the user. For example, ``\alpha`` parameter has been set to 0.5 and is the percentage of the population which is selected in each iteration to update the probabilistic model. Example: This short example runs UMDA to optimize the parameters of a variational algorithm. Here we will use the same operator as used in the algorithms introduction, which was originally computed by Qiskit Nature for an H2 molecule. The minimum energy of the H2 Hamiltonian can be found quite easily so we are able to set maxiters to a small value. .. code-block:: python from qiskit_algorithms.optimizers import UMDA from qiskit_algorithms import QAOA from qiskit.quantum_info import Pauli from qiskit.primitives import Sampler X = Pauli("X") I = Pauli("I") Z = Pauli("Z") H2_op = (-1.052373245772859 * I ^ I) + \ (0.39793742484318045 * I ^ Z) + \ (-0.39793742484318045 * Z ^ I) + \ (-0.01128010425623538 * Z ^ Z) + \ (0.18093119978423156 * X ^ X) p = 2 # Toy example: 2 layers with 2 parameters in each layer: 4 variables opt = UMDA(maxiter=100, size_gen=20) qaoa = QAOA(Sampler(), opt,reps=p) result = qaoa.compute_minimum_eigenvalue(operator=H2_op) If it is desired to modify the percentage of individuals considered to update the probabilistic model, then this code can be used. Here for example we set the 60% instead of the 50% predefined. .. code-block:: python opt = UMDA(maxiter=100, size_gen=20, alpha = 0.6) qaoa = QAOA(Sampler(), opt,reps=p) result = qaoa.compute_minimum_eigenvalue(operator=H2_op) .. note:: This component has some function that is normally random. If you want to reproduce behavior then you should set the random number generator seed in the algorithm_globals (``qiskit_algorithms.utils.algorithm_globals.random_seed = seed``). References: [1]: Vicente P. Soloviev, Pedro Larrañaga and Concha Bielza (2022, July). Quantum Parametric Circuit Optimization with Estimation of Distribution Algorithms. In 2022 The Genetic and Evolutionary Computation Conference (GECCO). DOI: [2]: Vicente P. Soloviev. Python package EDAspy. """ ELITE_FACTOR = 0.4 STD_BOUND = 0.3 def __init__( self, maxiter: int = 100, size_gen: int = 20, alpha: float = 0.5, callback: Callable[[int, np.ndarray, float], None] | None = None, ) -> None: r""" Args: maxiter: Maximum number of iterations. size_gen: Population size of each generation. alpha: Percentage (0, 1] of the population to be selected as elite selection. callback: A callback function passed information in each iteration step. The information is, in this order: the number of function evaluations, the parameters, the best function value in this iteration. """ self.size_gen = size_gen self.maxiter = maxiter self.alpha = alpha self._vector: np.ndarray | None = None # initialization of generation self._generation: np.ndarray | None = None self._dead_iter = int(self._maxiter / 5) self._truncation_length = int(size_gen * alpha) super().__init__() self._best_cost_global: float | None = None self._best_ind_global: np.ndarray | None = None self._evaluations: np.ndarray | None = None self._n_variables: int | None = None self.callback = callback def _initialization(self) -> np.ndarray: vector = np.zeros((4, self._n_variables)) vector[0, :] = np.pi # mu vector[1, :] = 0.5 # std return vector # build a generation of size SIZE_GEN from prob vector def _new_generation(self): """Build a new generation sampled from the vector of probabilities. Updates the generation pandas dataframe """ gen = algorithm_globals.random.normal( self._vector[0, :], self._vector[1, :], [self._size_gen, self._n_variables] ) self._generation = self._generation[: int(self.ELITE_FACTOR * len(self._generation))] self._generation = np.vstack((self._generation, gen)) # truncate the generation at alpha percent def _truncation(self): """Selection of the best individuals of the actual generation. Updates the generation by selecting the best individuals. """ best_indices = self._evaluations.argsort()[: self._truncation_length] self._generation = self._generation[best_indices, :] self._evaluations = np.take(self._evaluations, best_indices) # check each individual of the generation def _check_generation(self, objective_function): """Check the cost of each individual in the cost function implemented by the user.""" self._evaluations = np.apply_along_axis(objective_function, 1, self._generation) # update the probability vector def _update_vector(self): """From the best individuals update the vector of normal distributions in order to the next generation can sample from it. Update the vector of normal distributions """ for i in range(self._n_variables): self._vector[0, i], self._vector[1, i] =[:, i]) if self._vector[1, i] < self.STD_BOUND: self._vector[1, i] = self.STD_BOUND
[docs] def minimize( self, fun: Callable[[POINT], float], x0: POINT, jac: Callable[[POINT], POINT] | None = None, bounds: list[tuple[float, float]] | None = None, ) -> OptimizerResult: not_better_count = 0 result = OptimizerResult() if isinstance(x0, float): x0 = np.asarray([x0]) self._n_variables = len(x0) self._best_cost_global = 999999999999 self._best_ind_global = None history = [] self._evaluations = np.array(0) self._vector = self._initialization() # initialization of generation self._generation = algorithm_globals.random.normal( self._vector[0, :], self._vector[1, :], [self._size_gen, self._n_variables] ) for _ in range(self._maxiter): self._check_generation(fun) self._truncation() self._update_vector() best_mae_local: float = min(self._evaluations) history.append(best_mae_local) best_ind_local = np.where(self._evaluations == best_mae_local)[0][0] best_ind_local = self._generation[best_ind_local] # update the best values ever if best_mae_local < self._best_cost_global: self._best_cost_global = best_mae_local self._best_ind_global = best_ind_local not_better_count = 0 else: not_better_count += 1 if not_better_count >= self._dead_iter: break if self.callback is not None: self.callback( len(history) * self._size_gen, self._best_ind_global, self._best_cost_global ) self._new_generation() result.x = self._best_ind_global = self._best_cost_global result.nfev = len(history) * self._size_gen return result
@property def size_gen(self) -> int: """Returns the size of the generations (number of individuals per generation)""" return self._size_gen @size_gen.setter def size_gen(self, value: int): """ Sets the size of the generations of the algorithm. Args: value: Size of the generations (number of individuals per generation). Raises: ValueError: If `value` is lower than 1. """ if value <= 0: raise ValueError("The size of the generation should be greater than 0.") self._size_gen = value @property def maxiter(self) -> int: """Returns the maximum number of iterations""" return self._maxiter @maxiter.setter def maxiter(self, value: int): """ Sets the maximum number of iterations of the algorithm. Args: value: Maximum number of iterations of the algorithm. Raises: ValueError: If `value` is lower than 1. """ if value <= 0: raise ValueError("The maximum number of iterations should be greater than 0.") self._maxiter = value @property def alpha(self) -> float: """Returns the alpha parameter value (percentage of population selected to update probabilistic model)""" return self._alpha @alpha.setter def alpha(self, value: float): """ Sets the alpha parameter (percentage of individuals selected to update the probabilistic model) Args: value: Percentage (0,1] of generation selected to update the probabilistic model. Raises: ValueError: If `value` is lower than 0 or greater than 1. """ if (value <= 0) or (value > 1): raise ValueError(f"alpha must be in the range (0, 1], value given was {value}") self._alpha = value @property def settings(self) -> dict[str, Any]: return { "maxiter": self.maxiter, "alpha": self.alpha, "size_gen": self.size_gen, "callback": self.callback, }
[docs] def get_support_level(self): """Get the support level dictionary.""" return { "gradient": OptimizerSupportLevel.ignored, "bounds": OptimizerSupportLevel.ignored, "initial_point": OptimizerSupportLevel.required, }