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"""
This module provides quantum-inspired optimization algorithms for enhanced performance.
"""
try:
import numpy as np
except Exception:
np = None
import math
from typing import List, Dict, Any, Callable, Optional, Tuple
class QuantumInspiredOptimizer:
def __init__(self):
self.population_size = 50
self.num_qubits = 32
self.max_iterations = 100
self.optimization_history = []
self.best_solution = None
self.best_fitness = float('-inf')
def optimize(self, objective_function: Callable[[np.ndarray], float],
constraints: Optional[List[Dict[str, Any]]] = None) -> Dict[str, Any]:
"""
Perform quantum-inspired optimization.
Args:
objective_function: The function to optimize
constraints: Optional list of constraint dictionaries
Returns:
Optimization results
"""
# Initialize quantum population
population = self._initialize_quantum_population()
for iteration in range(self.max_iterations):
# Measure quantum states
classical_solutions = self._measure_quantum_states(population)
# Apply constraints if any
if constraints:
classical_solutions = self._apply_constraints(classical_solutions, constraints)
# Evaluate fitness
fitness_values = [objective_function(solution) for solution in classical_solutions]
# Update best solution
if np is not None:
current_best_idx = int(np.argmax(fitness_values))
else:
current_best_idx = int(max(range(len(fitness_values)), key=lambda i: fitness_values[i]))
if fitness_values[current_best_idx] > self.best_fitness:
self.best_fitness = fitness_values[current_best_idx]
self.best_solution = classical_solutions[current_best_idx]
# Apply quantum gates
population = self._apply_quantum_gates(population, fitness_values)
# Store iteration history
self.optimization_history.append({
"iteration": iteration,
"best_fitness": self.best_fitness,
"population_diversity": self._calculate_diversity(classical_solutions)
})
return {
"best_solution": self.best_solution,
"best_fitness": self.best_fitness,
"convergence": self.optimization_history,
"final_population": self._measure_quantum_states(population)
}
def _initialize_quantum_population(self) -> np.ndarray:
"""
Initialize the quantum population with superposition states.
"""
if np is not None:
# Create population of quantum individuals
population = np.zeros((self.population_size, self.num_qubits, 2), dtype=np.complex128)
# Initialize in superposition state
population[:, :, 0] = 1/np.sqrt(2) # amplitude for |0⟩
population[:, :, 1] = 1/np.sqrt(2) # amplitude for |1⟩
else:
# Fallback simple population representation (probabilities)
population = [[ [1/math.sqrt(2), 1/math.sqrt(2)] for _ in range(self.num_qubits)] for _ in range(self.population_size)]
return population
def _measure_quantum_states(self, population: np.ndarray) -> np.ndarray:
"""
Perform measurement on quantum states to get classical solutions.
"""
if np is not None:
classical_solutions = np.zeros((self.population_size, self.num_qubits))
for i in range(self.population_size):
# Calculate probabilities
probabilities = np.abs(population[i, :, 1])**2
# Perform measurement
classical_solutions[i] = np.random.random(self.num_qubits) < probabilities
return classical_solutions
else:
import random
classical_solutions = []
for i in range(self.population_size):
probs = [abs(complex(pair[1]))**2 for pair in population[i]]
classical_solutions.append([1 if random.random() < p else 0 for p in probs])
return classical_solutions
def _apply_quantum_gates(self, population: np.ndarray, fitness_values: List[float]) -> np.ndarray:
"""
Apply quantum gates to update the quantum states.
"""
# Normalize fitness values
if np is not None:
fitness_normalized = np.array(fitness_values)
fitness_normalized = (fitness_normalized - np.min(fitness_normalized)) / \
(np.max(fitness_normalized) - np.min(fitness_normalized) + 1e-10)
# Quantum rotation gate
theta = np.pi * fitness_normalized[:, np.newaxis] / 2
# Apply rotation
for i in range(self.population_size):
rotation_matrix = np.array([
[np.cos(theta[i]), -np.sin(theta[i])],
[np.sin(theta[i]), np.cos(theta[i])]
])
population[i] = np.einsum('ij,kj->ki', rotation_matrix, population[i])
else:
# fitness_normalized already computed by caller
theta = None
theta = [math.pi * f / 2 for f in fitness_normalized]
# Simple perturbation fallback
for i in range(self.population_size):
for q in range(self.num_qubits):
amp0, amp1 = population[i][q]
# rotate amplitudes slightly based on theta
t = theta[i]
new0 = amp0*math.cos(t) - amp1*math.sin(t)
new1 = amp0*math.sin(t) + amp1*math.cos(t)
population[i][q] = [new0, new1]
return population
def _apply_constraints(self, solutions: np.ndarray, constraints: List[Dict[str, Any]]) -> np.ndarray:
"""
Apply constraints to classical solutions.
"""
constrained_solutions = solutions.copy()
for constraint in constraints:
constraint_type = constraint.get("type", "")
if constraint_type == "bound":
lower = constraint.get("lower", 0)
upper = constraint.get("upper", 1)
constrained_solutions = np.clip(constrained_solutions, lower, upper)
elif constraint_type == "sum":
target_sum = constraint.get("target", 1)
current_sums = np.sum(constrained_solutions, axis=1)
for i in range(len(constrained_solutions)):
if current_sums[i] != 0: # Avoid division by zero
constrained_solutions[i] *= target_sum / current_sums[i]
return constrained_solutions
def _calculate_diversity(self, population: np.ndarray) -> float:
"""
Calculate diversity of the population.
"""
return np.mean([
np.mean(np.abs(p1 - p2))
for i, p1 in enumerate(population)
for p2 in population[i+1:]
])
def get_optimization_history(self) -> List[Dict[str, Any]]:
"""
Get the history of optimization progress.
"""
return self.optimization_history
def reset(self):
"""
Reset the optimizer state.
"""
self.optimization_history = []
self.best_solution = None
self.best_fitness = float('-inf')
def get_quantum_state(self) -> Dict[str, Any]:
"""
Get the current quantum state information.
"""
if not self.optimization_history:
return {"status": "not_initialized"}
return {
"iterations_completed": len(self.optimization_history),
"current_best_fitness": self.best_fitness,
"convergence_trend": [h["best_fitness"] for h in self.optimization_history],
"diversity_trend": [h["population_diversity"] for h in self.optimization_history]
} |