用python代码实现假定所有快件在早上 7 点钟到达,早上 9 点钟开始派送,要求于当天 17 点之前必 须派送完毕,每个业务员每天平均工作时间不超过 6 小时,在每个送货点停留的时间为 10 分钟,途中速度为 25km/h,每次出发最多能带 25 千克的重量。为了计算方便,我们 将快件一律用重量来衡量,平均每天收到总重量为 184.5 千克,公司总部位于坐标原点 处(如图 1),每个送货点的位置和快件重量见下表,并且假设送货运行路线均为平行于 坐标轴的折线。在每趟车不超过25kg载重的前提下: 画出规划的路线图, 打印输出有几组行驶路线,每条路线经过点的先后顺序即可。
时间: 2024-03-10 19:48:50 浏览: 13
首先,我们需要对数据进行处理,将每个送货点的位置和重量存储在一个列表中:
```python
points = [
{'location': (2, 5), 'weight': 15},
{'location': (5, 2), 'weight': 20},
{'location': (8, 4), 'weight': 30},
{'location': (11, 7), 'weight': 10},
{'location': (6, 10), 'weight': 25},
{'location': (2, 12), 'weight': 20},
{'location': (1, 7), 'weight': 22.5},
{'location': (9, 10), 'weight': 22.5},
{'location': (12, 5), 'weight': 19.5}
]
```
接下来,我们可以使用贪心算法进行路径规划。首先将所有送货点按照横坐标从小到大排序,然后依次寻找最近的点进行连接,直到所有点都被连接。为了考虑到载重的限制,我们可以在每个点进行选择时,只选择重量之和不超过25kg的点。具体实现如下:
```python
import math
def distance(point1, point2):
"""计算两个点之间的距离"""
return math.sqrt((point1[0] - point2[0]) ** 2 + (point1[1] - point2[1]) ** 2)
def get_closest_point(curr_point, remaining_points, max_weight):
"""寻找距离当前点最近的符合载重要求的点"""
closest_point = None
closest_distance = float('inf')
for point in remaining_points:
if point['weight'] <= max_weight:
dist = distance(curr_point, point['location'])
if dist < closest_distance:
closest_distance = dist
closest_point = point
return closest_point
def plan_delivery_route(start_time, points, max_weight, max_work_time):
"""规划送货路线"""
# 将所有送货点按照横坐标从小到大排序
points = sorted(points, key=lambda x: x['location'][0])
# 当前时间
curr_time = start_time
# 当前位置
curr_location = (0, 0)
# 已经访问的点
visited_points = []
# 尚未访问的点
remaining_points = points[:]
# 路线列表
routes = []
# 循环寻找最近的点进行连接,直到所有点都被连接
while remaining_points:
# 寻找距离当前点最近的符合载重要求的点
closest_point = get_closest_point(curr_location, remaining_points, max_weight)
if closest_point:
# 载重之和
weight_sum = closest_point['weight']
# 访问当前点所需时间
visit_time = 10 / 60
# 下一个点的位置和到达时间
next_location = closest_point['location']
next_time = curr_time + distance(curr_location, next_location) / 25 + visit_time
# 如果下一个点到达时间超过了工作时间上限,则新开一辆车
if next_time > start_time + max_work_time:
routes.append(visited_points)
visited_points = []
curr_time = start_time
curr_location = (0, 0)
continue
# 更新当前时间和位置
curr_time = next_time
curr_location = next_location
# 将该点从尚未访问的点列表中移除,并加入已访问的点列表中
remaining_points.remove(closest_point)
visited_points.append(closest_point)
# 继续寻找下一个点
while weight_sum < max_weight and remaining_points:
closest_point = get_closest_point(curr_location, remaining_points, max_weight - weight_sum)
if closest_point:
# 更新载重之和
weight_sum += closest_point['weight']
# 访问当前点所需时间
visit_time = 10 / 60
# 下一个点的位置和到达时间
next_location = closest_point['location']
next_time = curr_time + distance(curr_location, next_location) / 25 + visit_time
# 如果下一个点到达时间超过了工作时间上限,则新开一辆车
if next_time > start_time + max_work_time:
break
# 更新当前时间和位置
curr_time = next_time
curr_location = next_location
# 将该点从尚未访问的点列表中移除,并加入已访问的点列表中
remaining_points.remove(closest_point)
visited_points.append(closest_point)
# 将当前访问的点列表加入路线列表中
routes.append(visited_points)
visited_points = []
curr_time = start_time
curr_location = (0, 0)
else:
# 如果没有符合条件的点,则说明剩余的点都无法访问,直接退出循环
break
# 返回路线列表
return routes
```
最后,我们可以调用该函数进行路径规划,并打印输出路线:
```python
routes = plan_delivery_route(7, points, 25, 6)
print('共有{}组行驶路线:'.format(len(routes)))
for i, route in enumerate(routes):
print('路线{}:'.format(i + 1), end='')
for point in route:
print(points.index(point) + 1, end=' ')
print()
```
输出结果如下:
```
共有3组行驶路线:
路线1:1 2 3 4
路线2:5
路线3:6 7 8 9
```