用改进遗传算法编写代码求解一条高速公路上充电站的选址定容问题
时间: 2023-10-23 15:10:43 浏览: 86
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高速公路上充电站的选址定容问题可以通过遗传算法求解,以下是一种改进遗传算法的代码实现:
首先,我们需要定义基因和个体。在这个问题中,每个个体可以看做是一组充电站的选址方案,而每个基因则代表一个充电站的选址。我们可以将每个基因定义为一个二元组,其中第一个元素表示充电站的位置,第二个元素表示充电站的容量。例如,基因 (10, 50) 表示在距离起点 10 公里处建立一座容量为 50 的充电站。
接下来,我们需要定义适应度函数。在这个问题中,我们希望让选址方案满足以下两个条件:一是能够覆盖整个高速公路,即每个车辆都可以在某个充电站充电;二是所选的充电站数量尽可能少。因此,我们可以将适应度函数定义为两部分,一部分是覆盖率,另一部分是充电站数量。具体而言,我们可以用以下公式计算适应度:
fitness = coverage * (1 - num_stations / max_stations)
其中,coverage 表示覆盖率,即所有车辆在某个充电站充电的比例,可以用以下公式计算:
coverage = 1 - (num_uncovered_vehicles / total_vehicles)
其中,num_uncovered_vehicles 表示未被覆盖的车辆数量,total_vehicles 表示总车辆数量。
而 num_stations 表示选址方案中的充电站数量,max_stations 则表示最大充电站数量,可以根据实际情况来设定。在这个问题中,我们可以将 max_stations 定为一个较小的数,例如 10。
接下来,我们需要定义遗传算法的操作。在这个问题中,我们可以采用以下操作:
1. 初始化种群。我们可以随机生成一些个体作为初始种群。
2. 选择。我们可以采用轮盘赌算法对种群进行选择,选择适应度较高的个体。
3. 交叉。我们可以采用单点交叉的方法对个体进行交叉,即在某个位置将两个个体分别切割并拼接起来。
4. 变异。我们可以对个体进行变异,即随机改变基因的值。
5. 替换。我们可以将新生成的个体替换掉原来的个体,保留适应度较高的个体。
下面是代码实现的具体步骤:
```python
import random
# 定义基因和个体
class Gene:
def __init__(self, position, capacity):
self.position = position
self.capacity = capacity
class Individual:
def __init__(self, genes):
self.genes = genes
self.fitness = 0
# 定义适应度函数
def fitness_function(individual, vehicles, max_stations):
# 计算覆盖率
num_uncovered_vehicles = vehicles
for i in range(len(individual.genes)):
if individual.genes[i].capacity >= num_uncovered_vehicles:
num_uncovered_vehicles = 0
else:
num_uncovered_vehicles -= individual.genes[i].capacity
coverage = 1 - (num_uncovered_vehicles / vehicles)
# 计算充电站数量
num_stations = len(individual.genes)
# 计算适应度
individual.fitness = coverage * (1 - num_stations / max_stations)
return individual.fitness
# 定义遗传算法的操作
def initialize_population(population_size, highway_length, max_capacity, max_stations):
population = []
for i in range(population_size):
genes = []
while True:
position = random.randint(0, highway_length)
capacity = random.randint(1, max_capacity)
gene = Gene(position, capacity)
if gene not in genes:
genes.append(gene)
if len(genes) == max_stations or len(genes) == highway_length:
break
individual = Individual(genes)
fitness_function(individual, highway_length, max_stations)
population.append(individual)
return population
def selection(population):
total_fitness = sum([individual.fitness for individual in population])
probabilities = [individual.fitness / total_fitness for individual in population]
selected_population = []
for i in range(len(population)):
individual = random.choices(population, weights=probabilities)[0]
selected_population.append(individual)
return selected_population
def crossover(parent1, parent2):
point = random.randint(1, len(parent1.genes) - 1)
genes1 = parent1.genes[:point] + parent2.genes[point:]
genes2 = parent2.genes[:point] + parent1.genes[point:]
child1 = Individual(genes1)
child2 = Individual(genes2)
return child1, child2
def mutation(individual, highway_length, max_capacity):
for i in range(len(individual.genes)):
if random.random() < 0.1:
individual.genes[i].position = random.randint(0, highway_length)
individual.genes[i].capacity = random.randint(1, max_capacity)
def replacement(population, new_population):
combined_population = population + new_population
sorted_population = sorted(combined_population, key=lambda x: x.fitness, reverse=True)
return sorted_population[:len(population)]
# 运行遗传算法
def genetic_algorithm(population_size, highway_length, max_capacity, max_stations, generations):
# 初始化种群
population = initialize_population(population_size, highway_length, max_capacity, max_stations)
# 迭代进化
for i in range(generations):
# 选择
selected_population = selection(population)
# 交叉
new_population = []
for j in range(len(selected_population) // 2):
parent1 = selected_population[2 * j]
parent2 = selected_population[2 * j + 1]
child1, child2 = crossover(parent1, parent2)
new_population.append(child1)
new_population.append(child2)
# 变异
for individual in new_population:
mutation(individual, highway_length, max_capacity)
fitness_function(individual, highway_length, max_stations)
# 替换
population = replacement(population, new_population)
# 返回最优个体
best_individual = sorted(population, key=lambda x: x.fitness, reverse=True)[0]
return best_individual
```
接下来,我们可以使用该程序求解高速公路上充电站的选址定容问题。例如,假设高速公路长度为 100 公里,每辆车的最大续航里程为 50 公里,最大充电站数量为 5,最大容量为 20,初始种群大小为 50,迭代次数为 100,可以运行以下代码:
```python
population_size = 50
highway_length = 100
max_capacity = 20
max_stations = 5
generations = 100
vehicles = highway_length // max_capacity
best_individual = genetic_algorithm(population_size, highway_length, max_capacity, max_stations, generations)
print("Best individual:")
for i in range(len(best_individual.genes)):
print(f"Station {i}: position={best_individual.genes[i].position}, capacity={best_individual.genes[i].capacity}")
print(f"Fitness: {best_individual.fitness}")
```
该程序会输出最优充电站选址方案及其适应度。
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