$$ f=\alpha C_1L\sum_{k=1}^K{\frac{1}{t_k}}+\beta C_2\sum_{k=1}^K{\sum_{j=1}^J{\left( \frac{V_{kj}t_k}{2} \right)}} $$、$$ c\cdot \frac{\sum_{k=1}^K{\sum_{j=1}^J{V_{kj}}}}{\sum_{k=1}^K{\frac{1}{t_k}}}>c_1L $$，alpha、beta、c、c1、c2、L、K、J、V为自定义常量，t为K个元素的数组，5<t<30，用Python求最小值f多目标遗传算法代码

以下是用Python实现多目标遗传算法求解最小值f的代码：

import random
import numpy as np

# 自定义常量
alpha = 0.5
beta = 0.5
c = 1.0
c1 = 1.0
c2 = 1.0
L = 1.0
K = 10
J = 5
V = np.random.random((K, J))

# 定义解的类
class Solution:
    def __init__(self, t):
        self.t = t
        self.f1 = alpha * c1 * L * np.sum(1 / t) + beta * c2 * np.sum(V * t / 2)
        self.f2 = c * np.sum(V) / np.sum(1 / t)

# 初始化种群
def init_population(pop_size):
    population = []
    for i in range(pop_size):
        t = np.random.uniform(5, 30, size=K)
        population.append(Solution(t))
    return population

# 计算每个解的适应度值
def cal_fitness(solution):
    return solution.f1, solution.f2

# 计算种群中每个解的适应度值
def cal_pop_fitness(population):
    fitness = []
    for solution in population:
        fitness.append(cal_fitness(solution))
    return np.array(fitness)

# 选择操作
def selection(population, fitness, num_parents):
    parents = np.empty((num_parents, K))
    for i in range(num_parents):
        idx = np.random.choice(len(population), size=2, replace=False)
        if fitness[idx[0]][0] < fitness[idx[1]][0] and fitness[idx[0]][1] < fitness[idx[1]][1]:
            parents[i] = population[idx[0]].t
        elif fitness[idx[0]][0] > fitness[idx[1]][0] and fitness[idx[0]][1] > fitness[idx[1]][1]:
            parents[i] = population[idx[1]].t
        elif fitness[idx[0]][0] / fitness[idx[0]][1] < fitness[idx[1]][0] / fitness[idx[1]][1]:
            parents[i] = population[idx[0]].t
        else:
            parents[i] = population[idx[1]].t
    return parents

# 交叉操作
def crossover(parents, offspring_size):
    offspring = np.empty(offspring_size)
    for i in range(offspring_size[0]):
        idx = np.random.choice(len(parents), size=2, replace=False)
        crossover_point = np.random.randint(1, K - 1)
        offspring[i, 0:crossover_point] = parents[idx[0], 0:crossover_point]
        offspring[i, crossover_point:] = parents[idx[1], crossover_point:]
    return offspring

# 变异操作
def mutation(offspring_crossover, mutation_rate):
    for i in range(offspring_crossover.shape[0]):
        for j in range(offspring_crossover.shape[1]):
            if random.random() < mutation_rate:
                offspring_crossover[i, j] = np.random.uniform(5, 30)
    return offspring_crossover

# 多目标遗传算法
def mo_ga(pop_size, num_generations, num_parents, mutation_rate):
    population = init_population(pop_size)
    for generation in range(num_generations):
        fitness = cal_pop_fitness(population)
        parents = selection(population, fitness, num_parents)
        offspring_crossover = crossover(parents, (pop_size - num_parents, K))
        offspring_mutation = mutation(offspring_crossover, mutation_rate)
        population[0:num_parents] = parents
        population[num_parents:] = [Solution(t) for t in offspring_mutation]
    return population

# 测试
pop_size = 50
num_generations = 100
num_parents = 20
mutation_rate = 0.1
population = mo_ga(pop_size, num_generations, num_parents, mutation_rate)
fitness = cal_pop_fitness(population)
idx = np.argmin(fitness[:, 0] + fitness[:, 1])
print("最小值：", population[idx].f1, population[idx].f2)
print("对应的t：", population[idx].t)

其中，init_population()函数用于初始化种群，cal_fitness()函数用于计算每个解的适应度值，cal_pop_fitness()函数用于计算种群中每个解的适应度值，selection()函数用于进行选择操作，crossover()函数用于进行交叉操作，mutation()函数用于进行变异操作，mo_ga()函数用于实现多目标遗传算法的主体流程。最后，我们可以调用mo_ga()函数得到最优解的t值以及对应的最小值f。