灰狼优化算法求解车间调度问题 代码python

以下是使用灰狼优化算法求解车间调度问题的 Python 代码：

import numpy as np

# 车间调度问题的目标函数
def makespan(schedule, n_jobs, n_machines, processing_times):
    start_times = np.zeros(n_jobs)
    end_times = np.zeros(n_jobs)
    machine_times = np.zeros(n_machines)
    for i in schedule:
        machine = np.argmin(machine_times)
        start_times[i] = machine_times[machine]
        machine_times[machine] += processing_times[i][machine]
        end_times[i] = machine_times[machine]
    return max(end_times)

# 灰狼优化算法
def grey_wolf_optimizer(obj_func, lb, ub, dim, n_pop, n_iter):
    alpha = np.zeros(dim)
    beta = np.zeros(dim)
    delta = np.zeros(dim)
    best_wolf = np.zeros(dim)
    best_fitness = float('inf')
    wolves = np.random.uniform(lb, ub, (n_pop, dim))

    for i in range(n_iter):
        for j in range(n_pop):
            fitness = obj_func(wolves[j])
            if fitness < best_fitness:
                best_fitness = fitness
                best_wolf = wolves[j]

            a = 2 - 2 * (i / n_iter)  # alpha 值逐渐减小
            r1 = np.random.uniform()
            r2 = np.random.uniform()
            A = 2 * a * r1 - a
            C = 2 * r2
            D = np.abs(C * best_wolf - wolves[j])
            X1 = best_wolf - A * D

            r1 = np.random.uniform()
            r2 = np.random.uniform()
            A = 2 * a * r1 - a
            C = 2 * r2
            D = np.abs(C * alpha - wolves[j])
            X2 = alpha - A * D

            r1 = np.random.uniform()
            r2 = np.random.uniform()
            A = 2 * a * r1 - a
            C = 2 * r2
            D = np.abs(C * beta - wolves[j])
            X3 = beta - A * D

            wolves[j] = (X1 + X2 + X3) / 3

            # 更新 alpha, beta, delta
            if fitness < obj_func(alpha):
                alpha = wolves[j]
            if obj_func(alpha) < fitness < obj_func(beta):
                beta = wolves[j]
            if obj_func(alpha) < obj_func(delta) < obj_func(beta):
                delta = wolves[j]

    return best_wolf

# 测试
n_jobs = 5
n_machines = 3
processing_times = np.array([[4, 7, 3], [2, 4, 5], [9, 3, 6], [8, 2, 1], [5, 5, 5]])

def obj_func(x):
    schedule = np.argsort(x)
    return makespan(schedule, n_jobs, n_machines, processing_times)

lb = np.zeros(n_jobs)
ub = n_machines * np.ones(n_jobs)
dim = n_jobs
n_pop = 30
n_iter = 100
best_wolf = grey_wolf_optimizer(obj_func, lb, ub, dim, n_pop, n_iter)
print(best_wolf)

代码中使用了 NumPy 库来方便地进行矩阵运算。在测试部分，我们定义了一个 5 个工件和 3 个机器的车间调度问题，并通过灰狼优化算法求解最小化的完工时间。最终输出的是最优解对应的工件调度顺序。