307 lines
13 KiB
Python
307 lines
13 KiB
Python
import random
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import math
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import matplotlib.pyplot as plt
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import matplotlib.patches as patches
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# 固定随机种子，便于复现
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random.seed(42)
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# ---------------------------
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# 参数设置
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# ---------------------------
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H = 20 # 区域高度，网格点之间的距离为25m（单位距离）
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W = 25 # 区域宽度
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k = 1 # 系统数量（车-巢-机系统个数）
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num_iterations = 1000000 # 蒙特卡洛模拟迭代次数
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# 时间系数（单位：秒，每个网格一张照片）
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flight_time_factor = 3 # 每张照片对应的飞行时间，无人机飞行速度为9.5m/s，拍摄照片的时间间隔为3s
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comp_uav_factor = 5 # 无人机上每张照片计算时间，5s
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trans_time_factor = 0.3 # 每张照片传输时间，0.3s
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car_move_time_factor = 2 * 50 # TODO 汽车每单位距离的移动时间，2s，加了一个放大因子
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comp_bs_factor = 5 # 机巢上每张照片计算时间
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# 其他参数
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flight_energy_factor = 0.05 # 单位：分钟/张
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comp_energy_factor = 0.05 # 计算能耗需要重新估计
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trans_energy_factor = 0.0025
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battery_capacity = 10 # 无人机只进行飞行，续航为30分钟
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# bs_energy_factor =
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# car_energy_factor =
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# ---------------------------
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# 蒙特卡洛模拟，寻找最佳方案
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# ---------------------------
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best_T = float('inf')
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best_solution = None
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for iteration in range(num_iterations):
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# 随机生成分区的行分段数与列分段数
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R = random.randint(1, 5) # 行分段数
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C = random.randint(1, 5) # 列分段数
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# 生成随机的行、列分割边界
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row_boundaries = sorted(random.sample(range(1, H), R - 1))
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row_boundaries = [0] + row_boundaries + [H]
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col_boundaries = sorted(random.sample(range(1, W), C - 1))
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col_boundaries = [0] + col_boundaries + [W]
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# ---------------------------
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# 根据分割边界生成所有矩形任务
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# ---------------------------
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rectangles = []
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valid_partition = True # 标记此分区是否满足所有约束
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for i in range(len(row_boundaries) - 1):
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for j in range(len(col_boundaries) - 1):
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r1 = row_boundaries[i]
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r2 = row_boundaries[i + 1]
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c1 = col_boundaries[j]
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c2 = col_boundaries[j + 1]
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d = (r2 - r1) * (c2 - c1) # 任务的照片数量（矩形面积）
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# # 每个任务随机生成卸载比率 ρ ∈ [0,1]
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# rho = random.random()
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# # rho = 0.1
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# # 计算各个阶段时间
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# flight_time = flight_time_factor * d
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# comp_time = comp_uav_factor * rho * d
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# trans_time = trans_time_factor * (1 - rho) * d
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# comp_bs_time = comp_bs_factor * (1 - rho) * d
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# # 检查无人机电池约束：
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# # 飞行+计算+传输能耗需不超过电池容量
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# flight_energy = flight_energy_factor * d
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# comp_energy = comp_energy_factor * rho * d
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# trans_energy = trans_energy_factor * (1 - rho) * d
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# total_uav_energy = flight_energy + comp_energy + trans_energy
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# # 无人机计算与传输时间不超过飞行时间
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# if (total_uav_energy > battery_capacity) or (comp_time + trans_time > flight_time):
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# # TODO 时间约束的rho上界是个常数0.57，如果区域划分定了，rho直接取上界即可，可以数学证明
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# valid_partition = False
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# break
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# 求解rho
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rho_time_limit = (flight_time_factor - trans_time_factor) / \
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(comp_uav_factor - trans_time_factor)
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rho_energy_limit = (battery_capacity - flight_energy_factor * d - trans_energy_factor * d) / \
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(comp_energy_factor * d - trans_energy_factor * d)
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if rho_energy_limit < 0:
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valid_partition = False
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break
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rho = min(rho_time_limit, rho_energy_limit)
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print(rho)
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flight_time = flight_time_factor * d
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comp_time = comp_uav_factor * rho * d
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trans_time = trans_time_factor * (1 - rho) * d
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comp_bs_time = comp_bs_factor * (1 - rho) * d
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# 计算任务矩形中心，用于后续车辆移动时间计算
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center_r = (r1 + r2) / 2.0
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center_c = (c1 + c2) / 2.0
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rectangles.append({
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'r1': r1, 'r2': r2, 'c1': c1, 'c2': c2,
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'd': d,
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'rho': rho,
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'flight_time': flight_time,
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'comp_time': comp_time,
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'trans_time': trans_time,
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'comp_bs_time': comp_bs_time,
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'center': (center_r, center_c)
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})
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if not valid_partition:
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break
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# 如果分区中存在任务不满足电池约束，则跳过该分区
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if not valid_partition:
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continue
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# ---------------------------
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# 随机将所有矩形任务分配给 k 个系统（车-机-巢）
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# ---------------------------
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system_tasks = {i: [] for i in range(k)}
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for rect in rectangles:
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system = random.randint(0, k - 1)
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system_tasks[system].append(rect)
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# ---------------------------
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# 对于每个系统，计算该系统的总完成时间 T_k：
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# T_k = 所有任务的飞行时间之和 + 车辆的移动时间
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# 车辆移动时间：车辆从区域中心出发，依次经过各任务中心（顺序采用距离区域中心的启发式排序）
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# ---------------------------
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region_center = (H / 2.0, W / 2.0)
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T_k_list = []
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for i in range(k):
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tasks = system_tasks[i]
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tasks.sort(key=lambda r: math.hypot(r['center'][0] - region_center[0],
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r['center'][1] - region_center[1]))
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total_flight_time = sum(task['flight_time'] for task in tasks)
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if tasks:
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# 车辆从区域中心到第一个任务中心
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car_time = math.hypot(tasks[0]['center'][0] - region_center[0],
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tasks[0]['center'][1] - region_center[1]) * car_move_time_factor
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# 依次经过任务中心
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for j in range(1, len(tasks)):
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prev_center = tasks[j - 1]['center']
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curr_center = tasks[j]['center']
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car_time += math.hypot(curr_center[0] - prev_center[0],
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curr_center[1] - prev_center[1]) * car_move_time_factor
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else:
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car_time = 0
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# 机巢的计算时间
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total_bs_time = sum(task['comp_bs_time'] for task in tasks)
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T_k = max(total_flight_time + car_time, total_bs_time)
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T_k_list.append(T_k)
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T_max = max(T_k_list) # 整体目标 T 为各系统中最大的 T_k
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# TODO 没有限制系统的总能耗
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if T_max < best_T:
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best_T = T_max
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best_solution = {
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'system_tasks': system_tasks,
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'T_k_list': T_k_list,
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'T_max': T_max,
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'iteration': iteration,
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'R': R,
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'C': C,
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'row_boundaries': row_boundaries,
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'col_boundaries': col_boundaries
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}
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# ---------------------------
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# 输出最佳方案
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# ---------------------------
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if best_solution is not None:
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print("最佳 T (各系统中最长的完成时间):", best_solution['T_max'])
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for i in range(k):
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num_tasks = len(best_solution['system_tasks'][i])
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print(
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f"系统 {i}: 完成时间 T = {best_solution['T_k_list'][i]}, 飞行任务数量: {num_tasks}")
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else:
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print("在给定的模拟次数内未找到满足所有约束的方案。")
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# 在输出最佳方案后添加详细信息
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if best_solution is not None:
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print("\n各系统详细信息:")
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region_center = (H / 2.0, W / 2.0)
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for system_id, tasks in best_solution['system_tasks'].items():
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print(f"\n系统 {system_id} 的任务详情:")
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# 按距离区域中心的距离排序任务
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tasks_sorted = sorted(tasks, key=lambda r: math.hypot(r['center'][0] - region_center[0],
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r['center'][1] - region_center[1]))
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if tasks_sorted:
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print(
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f"轨迹路线: 区域中心({region_center[0]:.1f}, {region_center[1]:.1f})", end="")
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current_pos = region_center
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total_car_time = 0
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total_flight_time = 0
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total_flight_energy = 0
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total_comp_energy = 0
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total_trans_energy = 0
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for i, task in enumerate(tasks_sorted, 1):
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# 计算车辆移动时间
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car_time = math.hypot(task['center'][0] - current_pos[0],
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task['center'][1] - current_pos[1]) * car_move_time_factor
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total_car_time += car_time
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# 更新当前位置
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current_pos = task['center']
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print(
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f" -> 任务{i}({current_pos[0]:.1f}, {current_pos[1]:.1f})", end="")
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# 累加各项数据
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total_flight_time += task['flight_time']
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total_flight_energy += flight_energy_factor * task['d']
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total_comp_energy += comp_energy_factor * \
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task['rho'] * task['d']
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total_trans_energy += trans_energy_factor * \
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(1 - task['rho']) * task['d']
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print("\n")
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print(f"任务数量: {len(tasks_sorted)}")
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print(f"车辆总移动时间: {total_car_time:.2f} 秒")
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print(f"无人机总飞行时间: {total_flight_time:.2f} 秒")
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print(f"能耗统计:")
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print(f" - 飞行能耗: {total_flight_energy:.2f} 分钟")
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print(f" - 计算能耗: {total_comp_energy:.2f} 分钟")
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print(f" - 传输能耗: {total_trans_energy:.2f} 分钟")
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print(
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f" - 总能耗: {(total_flight_energy + total_comp_energy + total_trans_energy):.2f} 分钟")
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print("\n各任务详细信息:")
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for i, task in enumerate(tasks_sorted, 1):
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print(f"\n任务{i}:")
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print(
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f" 位置: ({task['center'][0]:.1f}, {task['center'][1]:.1f})")
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print(f" 照片数量: {task['d']}")
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print(f" 卸载比率(ρ): {task['rho']:.2f}")
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print(f" 飞行时间: {task['flight_time']:.2f} 秒")
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print(f" 计算时间: {task['comp_time']:.2f} 秒")
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print(f" 传输时间: {task['trans_time']:.2f} 秒")
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print(f" -- 飞行能耗: {task['d'] * flight_energy_factor:.2f} 分钟")
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print(f" -- 计算能耗: {task['d'] * comp_energy_factor:.2f} 分钟")
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print(f" -- 传输能耗: {task['d'] * trans_energy_factor:.2f} 分钟")
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print(f" 基站计算时间: {task['comp_bs_time']:.2f} 秒")
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else:
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print("该系统没有分配任务")
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print("-" * 50)
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if best_solution is not None:
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plt.rcParams['font.family'] = ['sans-serif']
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plt.rcParams['font.sans-serif'] = ['SimHei']
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fig, ax = plt.subplots()
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ax.set_xlim(0, W)
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ax.set_ylim(0, H)
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ax.set_title("区域划分与车-机-巢系统覆盖")
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ax.set_xlabel("区域宽度")
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ax.set_ylabel("区域高度")
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# 定义若干颜色以区分不同系统（系统编号从0开始）
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colors = ['red', 'blue', 'green', 'orange', 'purple', 'cyan', 'magenta']
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# 绘制区域中心
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region_center = (W / 2.0, H / 2.0) # 注意：x对应宽度，y对应高度
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ax.plot(region_center[0], region_center[1],
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'ko', markersize=8, label="区域中心")
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# 绘制每个任务区域（矩形）及在矩形中心标注系统编号与卸载比率 ρ
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for system_id, tasks in best_solution['system_tasks'].items():
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# 重新按车辆行驶顺序排序（启发式：以任务中心距离区域中心的距离排序）
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tasks_sorted = sorted(tasks, key=lambda task: math.hypot(
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(task['c1'] + (task['c2'] - task['c1']) / 2.0) - region_center[0],
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(task['r1'] + (task['r2'] - task['r1']) / 2.0) - region_center[1]
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))
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for i, task in enumerate(tasks_sorted, 1):
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# 绘制矩形：左下角坐标为 (c1, r1)，宽度为 (c2 - c1)，高度为 (r2 - r1)
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rect = patches.Rectangle((task['c1'], task['r1']),
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task['c2'] - task['c1'],
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task['r2'] - task['r1'],
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linewidth=2,
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edgecolor=colors[system_id % len(colors)],
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facecolor='none')
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ax.add_patch(rect)
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# 计算矩形中心
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center_x = task['c1'] + (task['c2'] - task['c1']) / 2.0
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center_y = task['r1'] + (task['r2'] - task['r1']) / 2.0
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# 在矩形中心标注：系统编号、执行顺序和卸载比率 ρ
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ax.text(center_x, center_y, f"S{system_id}-{i}\nρ={task['rho']:.2f}",
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color=colors[system_id % len(colors)],
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ha='center', va='center', fontsize=10, fontweight='bold')
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# 添加图例
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ax.legend()
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# 反转 y 轴使得行号从上到下递增（如需，可取消）
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ax.invert_yaxis()
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plt.show()
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else:
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print("没有找到满足约束条件的方案，无法进行可视化。")
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