差分进化算法python代码

差分进化算法（Differential Evolution，DE）是一种常用的全局优化算法，适用于连续优化问题。下面是一个简单的差分进化算法的 Python 代码实现：

import random
import numpy as np

def differential_evolution(fobj, bounds, popsize=20, mut=0.8, crossp=0.7, maxiter=100):
    """
    Differential evolution optimization algorithm.
    
    Parameters:
    -----------
    fobj : function
        The objective function to be minimized.
    bounds : list of tuples
        The bounds of the design variables.
    popsize : int, optional
        The population size. Default is 20.
    mut : float, optional
        The mutation factor. Default is 0.8.
    crossp : float, optional
        The crossover probability. Default is 0.7.
    maxiter : int, optional
        The maximum number of iterations. Default is 100.
        
    Returns:
    --------
    best : array_like
        The best solution found.
    """
    
    # Initialize the population randomly within the bounds
    pop = np.random.rand(popsize, len(bounds))
    min_b, max_b = np.asarray(bounds).T
    diff = np.fabs(min_b - max_b)
    pop_denorm = min_b + pop * diff
    
    # Evaluate the initial population
    fitness = np.asarray([fobj(ind) for ind in pop_denorm])
    
    # Find the best individual and its fitness value
    best_idx = np.argmin(fitness)
    best = pop_denorm[best_idx]
    
    # Iterate until the maximum number of iterations is reached
    for i in range(maxiter):
        for j in range(popsize):
            # Select three random individuals, excluding the current one
            idxs = [idx for idx in range(popsize) if idx != j]
            a, b, c = pop[np.random.choice(idxs, 3, replace=False)]
            
            # Mutation
            mutant = np.clip(a + mut * (b - c), 0, 1)
            
            # Crossover
            cross_points = np.random.rand(len(bounds)) < crossp
            if not np.any(cross_points):
                cross_points[np.random.randint(0, len(bounds))] = True
            trial = np.where(cross_points, mutant, pop[j])
            
            # Denormalize trial solution
            trial_denorm = min_b + trial * diff
            
            # Evaluate trial solution
            f = fobj(trial_denorm)
            
            # Update the population if the trial solution is better
            if f < fitness[j]:
                fitness[j] = f
                pop[j] = trial
                if f < fitness[best_idx]:
                    best_idx = j
                    best = trial_denorm
        
        # Print the current best fitness value every 10 iterations
        if i % 10 == 0:
            print("Iteration {}: Best fitness value = {}".format(i, fitness[best_idx]))
    
    return best

其中，fobj 是目标函数，bounds 是设计变量的上下界，popsize 是种群大小，mut 是变异因子，crossp 是交叉概率，maxiter 是最大迭代次数。函数返回最优解。