使用遗传算法求解多旅行商问题

DQN/dqn.py

@@ -40,54 +40,15 @@ class Agent:
         self.batch_size = 64
         self.optimizer = optim.Adam(self.eval_net.parameters(), lr=self.learning_rate)
         
-        # 离散化动作空间
-        self.v_cuts_actions = [1, 2, 3, 4, 5]  # 垂直切割数选项
-        self.h_cuts_actions = [1, 2, 3, 4, 5]  # 水平切割数选项
-        # self.rho_actions = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]  # 卸载率选项
-        
-    def discretize_action(self, q_values):
-        """将Q值转换为离散动作"""
-        action = []
-        
-        # 分别为三个维度选择动作
-        idx = 0
-        # 垂直切割数
-        v_cuts_q = q_values[idx:idx+len(self.v_cuts_actions)]
-        v_cuts_idx = torch.argmax(v_cuts_q).item()
-        action.append(self.v_cuts_actions[v_cuts_idx])
-        idx += len(self.v_cuts_actions)
-        
-        # 水平切割数
-        h_cuts_q = q_values[idx:idx+len(self.h_cuts_actions)]
-        h_cuts_idx = torch.argmax(h_cuts_q).item()
-        action.append(self.h_cuts_actions[h_cuts_idx])
-        idx += len(self.h_cuts_actions)
-        
-        # # 卸载率
-        # rho_q = q_values[idx:idx+len(self.rho_actions)]
-        # rho_idx = torch.argmax(rho_q).item()
-        # action.append(self.rho_actions[rho_idx])
-        
-        return np.array(action)
-    
-    def get_action_dim(self):
-        """获取离散化后的动作空间维度"""
-        return (len(self.v_cuts_actions) + 
-                len(self.h_cuts_actions))
-                # len(self.rho_actions))
-    
     def choose_action(self, state):
         if random.random() < self.epsilon:
             # 随机选择动作
-            v_cuts = random.choice(self.v_cuts_actions)
+            return random.randint(0, self.action_dim - 1)
-            h_cuts = random.choice(self.h_cuts_actions)
-            # rho = random.choice(self.rho_actions)
-            return np.array([v_cuts, h_cuts])
         else:
             # 根据Q值选择动作
             state = torch.FloatTensor(state).unsqueeze(0)
             q_values = self.eval_net(state)
-            return self.discretize_action(q_values[0])
+            return torch.argmax(q_values).item()
     
     def store_transition(self, state, action, reward, next_state, done):
         self.memory.append((state, action, reward, next_state, done))
@@ -99,13 +60,13 @@ class Agent:
         # 随机采样batch
         batch = random.sample(self.memory, self.batch_size)
         states = torch.FloatTensor([x[0] for x in batch])
-        actions = torch.FloatTensor([x[1] for x in batch])
+        actions = torch.LongTensor([x[1] for x in batch])
         rewards = torch.FloatTensor([x[2] for x in batch])
         next_states = torch.FloatTensor([x[3] for x in batch])
         dones = torch.FloatTensor([x[4] for x in batch])
         
         # 计算当前Q值
-        current_q_values = self.eval_net(states)
+        current_q_values = self.eval_net(states).gather(1, actions.unsqueeze(1))
         
         # 计算目标Q值
         next_q_values = self.target_net(next_states).detach()
@@ -113,7 +74,7 @@ class Agent:
         target_q_values = rewards + (1 - dones) * self.gamma * max_next_q
         
         # 计算损失
-        loss = nn.MSELoss()(current_q_values.mean(), target_q_values.mean())
+        loss = nn.MSELoss()(current_q_values.squeeze(), target_q_values)
         
         # 更新网络
         self.optimizer.zero_grad()
@@ -127,5 +88,7 @@ class Agent:
         if self.learn.counter % 100 == 0:
             self.target_net.load_state_dict(self.eval_net.state_dict())
         
+        self.learn.counter += 1
+    
     # 添加计数器属性
     learn.counter = 0

DQN/env_allocation.py

@@ -0,0 +1,140 @@
+import numpy as np
+import gym
+from gym import spaces
+
+class AllocationEnv(gym.Env):
+    """任务分配环境（第二层）"""
+    def __init__(self, subareas, num_systems):
+        super(AllocationEnv, self).__init__()
+        
+        self.subareas = subareas  # 子区域列表
+        self.num_systems = num_systems  # 系统数量
+        
+        # 时间系数
+        self.flight_time_factor = 3     # 每张照片飞行时间
+        self.comp_uav_factor = 5        # 无人机计算时间
+        self.trans_time_factor = 0.3    # 传输时间
+        self.car_move_time_factor = 100  # 汽车移动时间
+        self.comp_bs_factor = 5         # 机巢计算时间
+        
+        # 能量参数
+        self.flight_energy_factor = 0.05    # 飞行能耗
+        self.comp_energy_factor = 0.05      # 计算能耗
+        self.trans_energy_factor = 0.0025   # 传输能耗
+        self.battery_capacity = 30          # 电池容量
+        
+        # 动作空间：每个子区域分配给哪个系统
+        self.action_space = spaces.MultiDiscrete([num_systems] * len(subareas))
+        
+        # 状态空间：[各系统当前负载]
+        self.observation_space = spaces.Box(
+            low=np.zeros(num_systems),
+            high=np.ones(num_systems) * float('inf'),
+            dtype=np.float32
+        )
+        
+        self.state = None
+        self.current_step = 0
+        self.max_steps = 1000
+    
+    def calculate_rho(self, area):
+        """计算最优卸载率"""
+        rho_time_limit = (self.flight_time_factor - self.trans_time_factor) / \
+            (self.comp_uav_factor - self.trans_time_factor)
+        rho_energy_limit = (self.battery_capacity - self.flight_energy_factor * area - self.trans_energy_factor * area) / \
+            (self.comp_energy_factor * area - self.trans_energy_factor * area)
+        if rho_energy_limit < 0:
+            return None
+        return min(rho_time_limit, rho_energy_limit)
+    
+    def step(self, action):
+        self.current_step += 1
+        
+        # 初始化每个系统的任务列表
+        system_tasks = {i: [] for i in range(self.num_systems)}
+        
+        # 根据动作分配任务
+        for i, system_id in enumerate(action):
+            system_tasks[system_id].append(self.subareas[i])
+        
+        # 计算每个系统的完成时间
+        system_times = []
+        valid_allocation = True
+        
+        for system_id, tasks in system_tasks.items():
+            if not tasks:  # 如果系统没有分配任务
+                system_times.append(0)
+                continue
+                
+            # 调用第三层（路径规划）获取结果
+            from env_routing import RoutingEnv
+            route_env = RoutingEnv(tasks)
+            completion_time, valid = route_env.optimize()
+            
+            if not valid:
+                valid_allocation = False
+                break
+                
+            system_times.append(completion_time)
+        
+        total_time = max(system_times) if system_times else 0
+        
+        # 计算奖励
+        if not valid_allocation:
+            reward = -10000
+            done = True
+        else:
+            reward = -total_time
+            done = self.current_step >= self.max_steps
+        
+        # 更新状态（各系统的负载）
+        self.state = np.array([len(tasks) for tasks in system_tasks.values()])
+        
+        return self.state, reward, done, {}
+    
+    def reset(self):
+        self.state = np.zeros(self.num_systems)
+        self.current_step = 0
+        return self.state
+    
+    def render(self, mode='human'):
+        pass
+    
+    def optimize(self):
+        """使用DQN优化任务分配"""
+        from dqn import Agent
+        
+        state_dim = self.observation_space.shape[0]
+        action_dim = self.num_systems * len(self.subareas)
+        
+        agent = Agent(state_dim, action_dim)
+        
+        # 训练参数
+        episodes = 100  # 减少训练轮数，因为这是子问题
+        max_steps = 100
+        
+        best_reward = float('-inf')
+        best_time = float('inf')
+        valid_solution = False
+        
+        for episode in range(episodes):
+            state = self.reset()
+            episode_reward = 0
+            
+            for step in range(max_steps):
+                action = agent.choose_action(state)
+                next_state, reward, done, _ = self.step(action)
+                
+                agent.store_transition(state, action, reward, next_state, done)
+                agent.learn()
+                
+                episode_reward += reward
+                state = next_state
+                
+                if done:
+                    if reward != -10000:  # 如果是有效解
+                        valid_solution = True
+                        best_time = min(best_time, -reward)
+                    break
+        
+        return best_time, valid_solution

DQN/env_partition.py

@@ -0,0 +1,88 @@
+import numpy as np
+import gym
+from gym import spaces
+
+class PartitionEnv(gym.Env):
+    """区域划分环境（第一层）"""
+    def __init__(self):
+        super(PartitionEnv, self).__init__()
+        
+        # 环境参数
+        self.H = 20  # 区域高度
+        self.W = 25  # 区域宽度
+        self.k = 1   # 系统数量
+        
+        # 动作空间：[垂直切割数, 水平切割数]
+        self.action_space = spaces.Box(
+            low=np.array([1, 1]),
+            high=np.array([5, 5]),
+            dtype=np.float32
+        )
+        
+        # 状态空间：[当前垂直切割数, 当前水平切割数, 当前最大完成时间]
+        self.observation_space = spaces.Box(
+            low=np.array([1, 1, 0]),
+            high=np.array([5, 5, float('inf')]),
+            dtype=np.float32
+        )
+        
+        self.state = None
+        self.current_step = 0
+        self.max_steps = 1000
+    
+    def generate_subareas(self, v_cuts, h_cuts):
+        """生成子区域信息"""
+        v_boundaries = np.linspace(0, self.H, v_cuts + 1)
+        h_boundaries = np.linspace(0, self.W, h_cuts + 1)
+        
+        subareas = []
+        for i in range(len(v_boundaries) - 1):
+            for j in range(len(h_boundaries) - 1):
+                height = v_boundaries[i+1] - v_boundaries[i]
+                width = h_boundaries[j+1] - h_boundaries[j]
+                center_y = (v_boundaries[i] + v_boundaries[i+1]) / 2
+                center_x = (h_boundaries[j] + h_boundaries[j+1]) / 2
+                
+                subareas.append({
+                    'height': height,
+                    'width': width,
+                    'area': height * width,
+                    'center': (center_y, center_x)
+                })
+        return subareas
+    
+    def step(self, action):
+        self.current_step += 1
+        
+        # 解析动作
+        v_cuts = int(action[0])  # 垂直切割数
+        h_cuts = int(action[1])  # 水平切割数
+        
+        # 生成子区域
+        subareas = self.generate_subareas(v_cuts, h_cuts)
+        
+        # 调用第二层（任务分配）获取结果
+        from env_allocation import AllocationEnv
+        alloc_env = AllocationEnv(subareas, self.k)
+        total_time, valid = alloc_env.optimize()
+        
+        # 计算奖励
+        if not valid:
+            reward = -10000  # 惩罚无效方案
+            done = True
+        else:
+            reward = -total_time  # 负的完成时间作为奖励
+            done = self.current_step >= self.max_steps
+        
+        # 更新状态
+        self.state = np.array([v_cuts, h_cuts, total_time])
+        
+        return self.state, reward, done, {}
+    
+    def reset(self):
+        self.state = np.array([1, 1, 0])
+        self.current_step = 0
+        return self.state
+    
+    def render(self, mode='human'):
+        pass

DQN/env_routing.py

@@ -0,0 +1,152 @@
+import numpy as np
+import gym
+from gym import spaces
+
+class RoutingEnv(gym.Env):
+    """路径规划环境（第三层）"""
+    def __init__(self, tasks):
+        super(RoutingEnv, self).__init__()
+        
+        self.tasks = tasks  # 任务列表
+        self.H = 20  # 区域高度
+        self.W = 25  # 区域宽度
+        self.region_center = (self.H/2, self.W/2)
+        
+        # 时间系数
+        self.flight_time_factor = 3     # 每张照片飞行时间
+        self.comp_uav_factor = 5        # 无人机计算时间
+        self.trans_time_factor = 0.3    # 传输时间
+        self.car_move_time_factor = 100  # 汽车移动时间
+        self.comp_bs_factor = 5         # 机巢计算时间
+        
+        # 动作空间：选择下一个要访问的任务索引
+        self.action_space = spaces.Discrete(len(tasks))
+        
+        # 状态空间：[当前位置x, 当前位置y, 未访问任务的mask]
+        self.observation_space = spaces.Box(
+            low=np.array([0, 0] + [0] * len(tasks)),
+            high=np.array([self.H, self.W] + [1] * len(tasks)),
+            dtype=np.float32
+        )
+        
+        self.state = None
+        self.current_position = self.region_center
+        self.unvisited_mask = np.ones(len(tasks))
+        self.total_flight_time = 0
+        
+    def calculate_task_time(self, task):
+        """计算单个任务的执行时间"""
+        area = task['area']
+        
+        # 计算最优卸载率
+        rho_time_limit = (self.flight_time_factor - self.trans_time_factor) / \
+            (self.comp_uav_factor - self.trans_time_factor)
+        rho_energy_limit = (30 - self.flight_time_factor * area - self.trans_time_factor * area) / \
+            (self.comp_uav_factor * area - self.trans_time_factor * area)
+        if rho_energy_limit < 0:
+            return None, None
+        rho = min(rho_time_limit, rho_energy_limit)
+        
+        # 计算各阶段时间
+        flight_time = self.flight_time_factor * area
+        comp_time = self.comp_uav_factor * rho * area
+        trans_time = self.trans_time_factor * (1 - rho) * area
+        comp_bs_time = self.comp_bs_factor * (1 - rho) * area
+        
+        task_time = max(flight_time, comp_bs_time)
+        return task_time, rho
+    
+    def calculate_move_time(self, from_pos, to_pos):
+        """计算移动时间"""
+        dist = np.sqrt((from_pos[0] - to_pos[0])**2 + (from_pos[1] - to_pos[1])**2)
+        return dist * self.car_move_time_factor
+    
+    def step(self, action):
+        # 检查动作是否有效
+        if self.unvisited_mask[action] == 0:
+            return self.state, -10000, True, {}  # 惩罚选择已访问的任务
+        
+        # 获取选中的任务
+        task = self.tasks[action]
+        task_center = task['center']
+        
+        # 计算移动时间
+        move_time = self.calculate_move_time(self.current_position, task_center)
+        
+        # 计算任务执行时间
+        task_time, rho = self.calculate_task_time(task)
+        if task_time is None:  # 任务不可行
+            return self.state, -10000, True, {}
+        
+        # 更新状态
+        self.current_position = task_center
+        self.unvisited_mask[action] = 0
+        self.total_flight_time += task_time
+        
+        # 构建新状态
+        self.state = np.concatenate([
+            np.array(self.current_position),
+            self.unvisited_mask
+        ])
+        
+        # 检查是否所有任务都已完成
+        done = np.sum(self.unvisited_mask) == 0
+        
+        # 计算奖励（负的总时间）
+        total_time = max(self.total_flight_time, move_time)
+        reward = -total_time if done else -move_time
+        
+        return self.state, reward, done, {}
+    
+    def reset(self):
+        self.current_position = self.region_center
+        self.unvisited_mask = np.ones(len(self.tasks))
+        self.total_flight_time = 0
+        
+        self.state = np.concatenate([
+            np.array(self.current_position),
+            self.unvisited_mask
+        ])
+        return self.state
+    
+    def render(self, mode='human'):
+        pass
+    
+    def optimize(self):
+        """使用DQN优化路径规划"""
+        from dqn import Agent
+        
+        state_dim = self.observation_space.shape[0]
+        action_dim = len(self.tasks)
+        
+        agent = Agent(state_dim, action_dim)
+        
+        # 训练参数
+        episodes = 50  # 进一步减少训练轮数，因为这是最底层子问题
+        max_steps = len(self.tasks) + 1  # 最多访问所有任务+返回
+        
+        best_reward = float('-inf')
+        best_time = float('inf')
+        valid_solution = False
+        
+        for episode in range(episodes):
+            state = self.reset()
+            episode_reward = 0
+            
+            for step in range(max_steps):
+                action = agent.choose_action(state)
+                next_state, reward, done, _ = self.step(action)
+                
+                agent.store_transition(state, action, reward, next_state, done)
+                agent.learn()
+                
+                episode_reward += reward
+                state = next_state
+                
+                if done:
+                    if reward != -10000:  # 如果是有效解
+                        valid_solution = True
+                        best_time = min(best_time, -reward)
+                    break
+        
+        return best_time, valid_solution

DQN/run_hierarchical.py

@@ -0,0 +1,118 @@
+from env_partition import PartitionEnv
+from env_allocation import AllocationEnv
+from env_routing import RoutingEnv
+from dqn import Agent
+import numpy as np
+import matplotlib.pyplot as plt
+
+def train_hierarchical():
+    """训练分层强化学习系统"""
+    # 创建第一层环境（区域划分）
+    partition_env = PartitionEnv()
+    partition_state_dim = partition_env.observation_space.shape[0]
+    partition_action_dim = 10  # 5个垂直切割选项 + 5个水平切割选项
+    
+    partition_agent = Agent(partition_state_dim, partition_action_dim)
+    
+    # 训练参数
+    episodes = 1000
+    max_steps = 1000
+    
+    # 记录训练过程
+    rewards_history = []
+    best_reward = float('-inf')
+    best_solution = None
+    
+    # 开始训练
+    print("开始训练分层强化学习系统...")
+    
+    for episode in range(episodes):
+        state = partition_env.reset()
+        episode_reward = 0
+        
+        for step in range(max_steps):
+            # 选择动作
+            action = partition_agent.choose_action(state)
+            
+            # 执行动作（这会触发第二层和第三层的优化）
+            next_state, reward, done, _ = partition_env.step(action)
+            
+            # 存储经验
+            partition_agent.store_transition(state, action, reward, next_state, done)
+            
+            # 学习
+            partition_agent.learn()
+            
+            episode_reward += reward
+            state = next_state
+            
+            if done:
+                break
+        
+        # 记录每个episode的总奖励
+        rewards_history.append(episode_reward)
+        
+        # 更新最佳解
+        if episode_reward > best_reward:
+            best_reward = episode_reward
+            best_solution = {
+                'vertical_cuts': int(action[0]),
+                'horizontal_cuts': int(action[1]),
+                'total_time': -reward if reward != -10000 else float('inf'),
+                'episode': episode
+            }
+        
+        # 打印训练进度
+        if (episode + 1) % 10 == 0:
+            avg_reward = np.mean(rewards_history[-10:])
+            print(f"Episode {episode + 1}, Average Reward: {avg_reward:.2f}")
+    
+    return best_solution, rewards_history
+
+def plot_training_results(rewards_history):
+    plt.figure(figsize=(10, 5))
+    plt.plot(rewards_history)
+    plt.title('Hierarchical DQN Training Progress')
+    plt.xlabel('Episode')
+    plt.ylabel('Total Reward')
+    plt.grid(True)
+    plt.show()
+
+def print_solution(solution):
+    print("\n最佳解决方案:")
+    print(f"在第 {solution['episode']} 轮找到")
+    print(f"垂直切割数: {solution['vertical_cuts']}")
+    print(f"水平切割数: {solution['horizontal_cuts']}")
+    print(f"总完成时间: {solution['total_time']:.2f} 秒")
+
+def visualize_partition(solution):
+    """可视化区域划分结果"""
+    H, W = 20, 25
+    v_cuts = solution['vertical_cuts']
+    h_cuts = solution['horizontal_cuts']
+    
+    plt.figure(figsize=(10, 8))
+    
+    # 绘制网格
+    for i in range(v_cuts + 1):
+        y = i * (H / v_cuts)
+        plt.axhline(y=y, color='b', linestyle='-', alpha=0.5)
+    
+    for i in range(h_cuts + 1):
+        x = i * (W / h_cuts)
+        plt.axvline(x=x, color='b', linestyle='-', alpha=0.5)
+    
+    plt.title('Area Partition Visualization')
+    plt.xlabel('Width')
+    plt.ylabel('Height')
+    plt.grid(True, alpha=0.3)
+    plt.show()
+
+if __name__ == "__main__":
+    # 训练模型
+    best_solution, rewards_history = train_hierarchical()
+    
+    # 显示结果
+    plot_training_results(rewards_history)
+    print_solution(best_solution)
+    visualize_partition(best_solution)

ga.py

@@ -0,0 +1,369 @@
+import math
+import random
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+import plot_util
+
+
+class GA(object):
+    def __init__(self, num_drones, num_city, num_total, data, to_process_idx, rectangles):
+        self.num_drones = num_drones
+        self.num_city = num_city
+        self.num_total = num_total
+        self.scores = []
+        # self.iteration = iteration
+        self.location = data
+        self.to_process_idx = to_process_idx
+        self.rectangles = rectangles
+        self.epochs = 3000
+        self.ga_choose_ratio = 0.2
+        self.mutate_ratio = 0.05
+        # fruits中存每一个个体是下标的list
+        self.dis_mat = self.compute_dis_mat(num_city, data)
+        # self.fruits = self.greedy_init(self.dis_mat, num_total, num_city)
+        self.fruits = self.random_init(num_total, num_city)
+        # 显示初始化后的最佳路径
+        scores = self.compute_adp(self.fruits)
+        sort_index = np.argsort(-scores)
+        init_best = self.fruits[sort_index[0]]
+        init_best = self.location[init_best]
+
+
+        # 存储每个iteration的结果，画出收敛图
+        self.iter_x = [0]
+        self.iter_y = [1.0 / scores[sort_index[0]]]
+
+    def random_init(self, num_total, num_city):
+        tmp = [x for x in range(num_city)]
+        result = []
+        for i in range(num_total):
+            random.shuffle(tmp)
+            result.append(tmp.copy())
+        # print("Lens:", len(result), len(result[0]))
+        return result
+
+    def greedy_init(self, dis_mat, num_total, num_city):
+        start_index = 0
+        result = []
+        for i in range(num_total):
+            rest = [x for x in range(0, num_city)]
+            # 所有起始点都已经生成了
+            if start_index >= num_city:
+                start_index = np.random.randint(0, num_city)
+                result.append(result[start_index].copy())
+                continue
+            current = start_index
+            rest.remove(current)
+            # 找到一条最近邻路径
+            result_one = [current]
+            while len(rest) != 0:
+                tmp_min = math.inf
+                tmp_choose = -1
+                for x in rest:
+                    # print("---", current, x, dis_mat[current][x])
+                    if dis_mat[current][x] < tmp_min:
+                        tmp_min = dis_mat[current][x]
+                        tmp_choose = x
+                if tmp_choose == -1:  # 此种情况仅可能发生在剩的都是基地点
+                    tmp_choose = rest[0]
+                    # print("tmp_choose:", tmp_choose)
+                current = tmp_choose
+                result_one.append(tmp_choose)
+                # print(current, rest)
+                rest.remove(tmp_choose)
+                # print(rest)
+            result.append(result_one)
+            start_index += 1
+        # print(len(result), len(result[0]))
+        return result
+
+    # 计算不同城市之间的距离
+    def compute_dis_mat(self, num_city, location):
+        dis_mat = np.zeros((num_city, num_city))
+        for i in range(num_city):
+            for j in range(num_city):
+                if i == j:
+                    dis_mat[i][j] = np.inf
+                    continue
+                a = location[i]
+                b = location[j]
+                tmp = np.sqrt(sum([(x[0] - x[1]) ** 2 for x in zip(a, b)]))
+                dis_mat[i][j] = tmp
+
+        for i in self.to_process_idx:
+            for j in self.to_process_idx:
+                # print("processing:", i, j, dis_mat[i][j])
+                dis_mat[i][j] = np.inf
+
+        return dis_mat
+
+    # 计算路径长度
+    def compute_pathlen(self, tmp_path, dis_mat):
+        path = tmp_path.copy()
+        if path[0] not in self.to_process_idx:
+            path.insert(0, 0)
+
+        if path[-1] not in self.to_process_idx:
+            path.append(0)
+
+        try:
+            a = path[0]
+            b = path[-1]
+        except:
+            import pdb
+
+            pdb.set_trace()
+
+        car_infos = []
+        # 计算各系统的任务分配
+        found_start_points_indices = []
+        for i in range(len(path)):
+            if path[i] in self.to_process_idx:
+                found_start_points_indices.append(i)
+        car_paths = []
+        for j in range(len(found_start_points_indices) - 1):
+            from_index = found_start_points_indices[j]
+            end_index = found_start_points_indices[j + 1]
+            car_path = []
+            for k in range(from_index, end_index + 1):
+                car_path.append(path[k])
+            car_paths.append(car_path)
+        
+        # 计算各系统的车辆移动距离
+        for car_path in car_paths:
+            car_time = 0
+            for i in range(len(car_path) - 1):
+                a = car_path[i]
+                b = car_path[i + 1]
+                if a in self.to_process_idx and b in self.to_process_idx:
+                    car_time += 0
+                else:
+                    car_time += dis_mat[a][b] * 100 # TODO 这里要换成对应参数
+            car_move_info = {'car_path': car_path, 'car_time': car_time}
+            car_infos.append(car_move_info)
+
+        sorted_car_infos = sorted(car_infos, key=lambda x: x['car_time'])
+
+        # 处理任务分配为num_drones + 1的情况，合并列表前两个元素
+        if len(car_paths) == self.num_drones + 1:
+            first = sorted_car_infos[0]
+            second = sorted_car_infos[1]
+            merged_path = first['car_path'] + second['car_path']
+            merged_time = first['car_time'] + second['car_time']
+            merged_dict = {'car_path': merged_path, 'car_time': merged_time}
+            sorted_car_infos = [merged_dict] + sorted_car_infos[3:]
+
+        # 计算各系统的总时间max(飞行时间+车的时间, 机巢计算时间)
+        T_k_list = []
+        for car_info in sorted_car_infos:
+            flight_time = 0
+            bs_time = 0
+            for point in car_info['car_path']:
+                if point in self.to_process_idx:
+                    continue
+                else:
+                    flight_time += self.rectangles[point - 1]['flight_time'] # 注意，这里要减一！！！
+                    bs_time += self.rectangles[point - 1]['comp_bs_time']
+            system_time = max(flight_time + car_info['car_time'], bs_time)
+            T_k_list.append(system_time)
+        T_max = max(T_k_list)
+        
+        return T_max
+
+    # 计算种群适应度
+    def compute_adp(self, fruits):
+        adp = []
+        for fruit in fruits:
+            if isinstance(fruit, int):
+                import pdb
+
+                pdb.set_trace()
+            length = self.compute_pathlen(fruit, self.dis_mat)
+            adp.append(1.0 / length)
+        return np.array(adp)
+
+    def swap_part(self, list1, list2):
+        index = len(list1)
+        list = list1 + list2
+        list = list[::-1]
+        return list[:index], list[index:]
+
+    def ga_cross(self, x, y):
+        len_ = len(x)
+        assert len(x) == len(y)
+        path_list = [t for t in range(len_)]
+        order = list(random.sample(path_list, 2))
+        order.sort()
+        start, end = order
+
+        # 找到冲突点并存下他们的下标,x中存储的是y中的下标,y中存储x与它冲突的下标
+        tmp = x[start:end]
+        x_conflict_index = []
+        for sub in tmp:
+            index = y.index(sub)
+            if not (index >= start and index < end):
+                x_conflict_index.append(index)
+
+        y_confict_index = []
+        tmp = y[start:end]
+        for sub in tmp:
+            index = x.index(sub)
+            if not (index >= start and index < end):
+                y_confict_index.append(index)
+
+        assert len(x_conflict_index) == len(y_confict_index)
+
+        # 交叉
+        tmp = x[start:end].copy()
+        x[start:end] = y[start:end]
+        y[start:end] = tmp
+
+        # 解决冲突
+        for index in range(len(x_conflict_index)):
+            i = x_conflict_index[index]
+            j = y_confict_index[index]
+            y[i], x[j] = x[j], y[i]
+
+        assert len(set(x)) == len_ and len(set(y)) == len_
+        return list(x), list(y)
+
+    def ga_parent(self, scores, ga_choose_ratio):
+        sort_index = np.argsort(-scores).copy()
+        sort_index = sort_index[0 : int(ga_choose_ratio * len(sort_index))]
+        parents = []
+        parents_score = []
+        for index in sort_index:
+            parents.append(self.fruits[index])
+            parents_score.append(scores[index])
+        return parents, parents_score
+
+    def ga_choose(self, genes_score, genes_choose):
+        sum_score = sum(genes_score)
+        score_ratio = [sub * 1.0 / sum_score for sub in genes_score]
+        rand1 = np.random.rand()
+        rand2 = np.random.rand()
+        index1, index2 = 0, 0
+        for i, sub in enumerate(score_ratio):
+            if rand1 >= 0:
+                rand1 -= sub
+                if rand1 < 0:
+                    index1 = i
+            if rand2 >= 0:
+                rand2 -= sub
+                if rand2 < 0:
+                    index2 = i
+            if rand1 < 0 and rand2 < 0:
+                break
+        return list(genes_choose[index1]), list(genes_choose[index2])
+
+    def ga_mutate(self, gene):
+        path_list = [t for t in range(len(gene))]
+        order = list(random.sample(path_list, 2))
+        start, end = min(order), max(order)
+        tmp = gene[start:end]
+        # np.random.shuffle(tmp)
+        tmp = tmp[::-1]
+        gene[start:end] = tmp
+        return list(gene)
+
+    def ga(self):
+        # 获得优质父代
+        scores = self.compute_adp(self.fruits)
+        # 选择部分优秀个体作为父代候选集合
+        parents, parents_score = self.ga_parent(scores, self.ga_choose_ratio)
+        tmp_best_one = parents[0]
+        tmp_best_score = parents_score[0]
+        # 新的种群fruits
+        fruits = parents.copy()
+        # 生成新的种群
+        while len(fruits) < self.num_total:
+            # 轮盘赌方式对父代进行选择
+            gene_x, gene_y = self.ga_choose(parents_score, parents)
+            # 交叉
+            gene_x_new, gene_y_new = self.ga_cross(gene_x, gene_y)
+            # 变异
+            if np.random.rand() < self.mutate_ratio:
+                gene_x_new = self.ga_mutate(gene_x_new)
+            if np.random.rand() < self.mutate_ratio:
+                gene_y_new = self.ga_mutate(gene_y_new)
+            x_adp = 1.0 / self.compute_pathlen(gene_x_new, self.dis_mat)
+            y_adp = 1.0 / self.compute_pathlen(gene_y_new, self.dis_mat)
+            # 将适应度高的放入种群中
+            if x_adp > y_adp and (not gene_x_new in fruits):
+                fruits.append(gene_x_new)
+            elif x_adp <= y_adp and (not gene_y_new in fruits):
+                fruits.append(gene_y_new)
+
+        self.fruits = fruits
+
+        return tmp_best_one, tmp_best_score
+
+    def run(self):
+        BEST_LIST = None
+        best_score = -math.inf
+        self.best_record = []
+        early_stop_cnt = 0
+        for i in range(self.epochs):
+            tmp_best_one, tmp_best_score = self.ga()
+            self.iter_x.append(i)
+            self.iter_y.append(1.0 / tmp_best_score)
+            if tmp_best_score > best_score:
+                best_score = tmp_best_score
+                BEST_LIST = tmp_best_one
+                early_stop_cnt = 0
+            else:
+                early_stop_cnt += 1
+            if early_stop_cnt == 50:  # 若连续50次没有性能提升，则早停
+                break
+            self.best_record.append(1.0 / best_score)
+            best_length = 1.0 / best_score
+            # print(f"Epoch {i:3}: {best_length:.3f}")
+        # print(1.0 / best_score)
+        return tmp_best_one, 1.0 / best_score
+
+if __name__ == '__main__':
+    seed = 42
+    num_drones = 6
+    num_city = 12
+    epochs = 3000
+
+    # 固定随机数
+    np.random.seed(seed)
+    random.seed(seed)
+
+
+    ## 初始化坐标 (第一个点是基地的起点，起点的坐标是 0,0 )
+    data = [[0, 0]]
+    for i in range(num_city - 1):
+        while True:
+            x = np.random.randint(-250, 250)
+            y = np.random.randint(-250, 250)
+            if x != 0 or y != 0:
+                break
+        data.append([x, y])
+
+    data = np.array(data)
+
+    # 关键：有N架无人机，则再增加N-1个`点` (坐标是起始点)，这些点之间的距离是inf
+    for d in range(num_drones - 1):
+        data = np.vstack([data, data[0]])
+        num_city += 1  # 增加欺骗城市
+
+    to_process_idx = [0]
+    # print("start point:", location[0])
+    for d in range(1, num_drones):  # 1, ... drone-1
+        # print("added base point:", location[num_city - d])
+        to_process_idx.append(num_city - d)
+
+    model = GA(num_city=data.shape[0], num_total=20, data=data.copy())
+    Best_path, Best = model.run()
+    print(Best_path)
+    iterations = model.iter_x
+    best_record = model.iter_y
+
+    # print(Best_path)
+
+    print(f"Best Path Length: {Best:.3f}")
+    plot_util.plot_results(Best_path, iterations, best_record)

hybrid_solver.py

@@ -0,0 +1,172 @@
+import random
+import math
+import matplotlib.pyplot as plt
+import matplotlib.patches as patches
+import numpy as np
+from ga import GA
+import plot_util
+
+# 固定随机种子，便于复现
+random.seed(42)
+
+# ---------------------------
+# 参数设置
+# ---------------------------
+H = 20         # 区域高度，网格点之间的距离为25m（单位距离）
+W = 25         # 区域宽度
+k = 1           # 系统数量（车-巢-机系统个数）
+num_iterations = 10000  # 蒙特卡洛模拟迭代次数
+
+# 时间系数（单位：秒，每个网格一张照片）
+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
+comp_uav_factor = 5    # 无人机上每张照片计算时间，5s
+trans_time_factor = 0.3    # 每张照片传输时间，0.3s
+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
+comp_bs_factor = 5    # 机巢上每张照片计算时间
+
+# 其他参数
+flight_energy_factor = 0.05     # 单位：分钟/张
+comp_energy_factor = 0.05    # 计算能耗需要重新估计
+trans_energy_factor = 0.0025
+battery_capacity = 10  # 无人机只进行飞行，续航为30分钟
+# bs_energy_factor =
+# car_energy_factor =
+
+# ---------------------------
+# 蒙特卡洛模拟，寻找最佳方案
+# ---------------------------
+best_T = float('inf')
+best_solution = None
+
+for iteration in range(num_iterations):
+    # 随机生成分区的行分段数与列分段数
+    R = random.randint(1, 5)  # 行分段数
+    C = random.randint(1, 5)  # 列分段数
+
+    # 生成随机的行、列分割边界
+    row_boundaries = sorted(random.sample(range(1, H), R - 1))
+    row_boundaries = [0] + row_boundaries + [H]
+    col_boundaries = sorted(random.sample(range(1, W), C - 1))
+    col_boundaries = [0] + col_boundaries + [W]
+
+    # ---------------------------
+    # 根据分割边界生成所有矩形任务
+    # ---------------------------
+    rectangles = []
+    valid_partition = True  # 标记此分区是否满足所有约束
+    for i in range(len(row_boundaries) - 1):
+        for j in range(len(col_boundaries) - 1):
+            r1 = row_boundaries[i]
+            r2 = row_boundaries[i + 1]
+            c1 = col_boundaries[j]
+            c2 = col_boundaries[j + 1]
+            d = (r2 - r1) * (c2 - c1)  # 任务的照片数量（矩形面积）
+
+            # 求解rho
+            rho_time_limit = (flight_time_factor - trans_time_factor) / \
+                (comp_uav_factor - trans_time_factor)
+            rho_energy_limit = (battery_capacity - flight_energy_factor * d - trans_energy_factor * d) / \
+                (comp_energy_factor * d - trans_energy_factor * d)
+            if rho_energy_limit < 0:
+                valid_partition = False
+                break
+            rho = min(rho_time_limit, rho_energy_limit)
+            # print(rho)
+            flight_time = flight_time_factor * d
+            comp_time = comp_uav_factor * rho * d
+            trans_time = trans_time_factor * (1 - rho) * d
+            comp_bs_time = comp_bs_factor * (1 - rho) * d
+
+            # 计算任务矩形中心，用于后续车辆移动时间计算
+            center_r = (r1 + r2) / 2.0
+            center_c = (c1 + c2) / 2.0
+
+            rectangles.append({
+                'r1': r1, 'r2': r2, 'c1': c1, 'c2': c2,
+                'd': d,
+                'rho': rho,
+                'flight_time': flight_time,
+                'comp_time': comp_time,
+                'trans_time': trans_time,
+                'comp_bs_time': comp_bs_time,
+                'center': [center_r, center_c]
+            })
+        if not valid_partition:
+            break
+
+    # 如果有中存在任务不满足电池约束，则跳过这种分区
+    if not valid_partition:
+        continue
+
+    # ---------------------------
+    # 使用遗传算法，寻找最佳方案
+    # ---------------------------
+    num_city = len(rectangles) + 1    # 划分好的区域中心点+整个区域的中心
+    epochs = 3000
+
+    # 初始化坐标 (第一个点是整个区域的中心)
+    center_data = [[H / 2.0, W / 2.0]]
+    for rec in rectangles:
+        center_data.append(rec['center'])
+    center_data = np.array(center_data)
+
+    # 关键：有k架无人机，则再增加N-1个`点` (坐标是起始点)，这些点之间的距离是inf
+    for d in range(k - 1):
+        center_data = np.vstack([center_data, center_data[0]])
+        num_city += 1  # 增加欺骗城市
+
+    to_process_idx = [0]
+    # print("start point:", location[0])
+    for d in range(1, k):  # 1, ... drone-1
+        # print("added base point:", location[num_city - d])
+        to_process_idx.append(num_city - d)
+
+    model = GA(num_drones=k, num_city=center_data.shape[0], num_total=20, data=center_data.copy(), to_process_idx=to_process_idx, rectangles=rectangles)
+    Best_path, Best = model.run()
+
+    # 根据最佳路径计算各系统任务分配
+    if Best_path[0] not in to_process_idx:
+        Best_path.insert(0, 0)
+
+    if Best_path[-1] not in to_process_idx:
+        Best_path.append(0)
+
+    # 计算各系统的任务分配
+    system_tasks = []
+    found_start_points_indices = []
+    for i in range(len(Best_path)):
+        if Best_path[i] in to_process_idx:
+            found_start_points_indices.append(i)
+    for j in range(len(found_start_points_indices) - 1):
+        from_index = found_start_points_indices[j]
+        end_index = found_start_points_indices[j + 1]
+        system_task = []
+        for k in range(from_index, end_index + 1):
+            if Best_path[k] not in to_process_idx:
+                system_task.append(rectangles[Best_path[k] - 1])
+        system_tasks.append(system_task)
+    
+    if Best < best_T:
+        best_T = Best
+        best_solution = {
+            'system_tasks': system_tasks,
+            # 'T_k_list': T_k_list,
+            'best_T': best_T,
+            'iteration': iteration,
+            'R': R,
+            'C': C,
+            'row_boundaries': row_boundaries,
+            'col_boundaries': col_boundaries
+        }
+
+# ---------------------------
+# 输出最佳方案
+# ---------------------------
+if best_solution is not None:
+    print("最佳 T (各系统中最长的完成时间):", best_solution['best_T'])
+    for i in range(k):
+        num_tasks = len(best_solution['system_tasks'][i])
+        print(
+            f"系统 {i}: 飞行任务数量: {num_tasks}")
+else:
+    print("在给定的模拟次数内未找到满足所有约束的方案。")

mtkl_sovler.py

@@ -0,0 +1,306 @@
+import random
+import math
+import matplotlib.pyplot as plt
+import matplotlib.patches as patches
+
+# 固定随机种子，便于复现
+random.seed(42)
+
+# ---------------------------
+# 参数设置
+# ---------------------------
+H = 20         # 区域高度，网格点之间的距离为25m（单位距离）
+W = 25         # 区域宽度
+k = 1           # 系统数量（车-巢-机系统个数）
+num_iterations = 1000000  # 蒙特卡洛模拟迭代次数
+
+# 时间系数（单位：秒，每个网格一张照片）
+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
+comp_uav_factor = 5    # 无人机上每张照片计算时间，5s
+trans_time_factor = 0.3    # 每张照片传输时间，0.3s
+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
+comp_bs_factor = 5    # 机巢上每张照片计算时间
+
+# 其他参数
+flight_energy_factor = 0.05     # 单位：分钟/张
+comp_energy_factor = 0.05    # 计算能耗需要重新估计
+trans_energy_factor = 0.0025
+battery_capacity = 10  # 无人机只进行飞行，续航为30分钟
+# bs_energy_factor =
+# car_energy_factor =
+
+# ---------------------------
+# 蒙特卡洛模拟，寻找最佳方案
+# ---------------------------
+best_T = float('inf')
+best_solution = None
+
+for iteration in range(num_iterations):
+    # 随机生成分区的行分段数与列分段数
+    R = random.randint(1, 5)  # 行分段数
+    C = random.randint(1, 5)  # 列分段数
+
+    # 生成随机的行、列分割边界
+    row_boundaries = sorted(random.sample(range(1, H), R - 1))
+    row_boundaries = [0] + row_boundaries + [H]
+    col_boundaries = sorted(random.sample(range(1, W), C - 1))
+    col_boundaries = [0] + col_boundaries + [W]
+
+    # ---------------------------
+    # 根据分割边界生成所有矩形任务
+    # ---------------------------
+    rectangles = []
+    valid_partition = True  # 标记此分区是否满足所有约束
+    for i in range(len(row_boundaries) - 1):
+        for j in range(len(col_boundaries) - 1):
+            r1 = row_boundaries[i]
+            r2 = row_boundaries[i + 1]
+            c1 = col_boundaries[j]
+            c2 = col_boundaries[j + 1]
+            d = (r2 - r1) * (c2 - c1)  # 任务的照片数量（矩形面积）
+
+            # # 每个任务随机生成卸载比率 ρ ∈ [0,1]
+            # rho = random.random()
+            # # rho = 0.1
+
+            # # 计算各个阶段时间
+            # flight_time = flight_time_factor * d
+            # comp_time = comp_uav_factor * rho * d
+            # trans_time = trans_time_factor * (1 - rho) * d
+            # comp_bs_time = comp_bs_factor * (1 - rho) * d
+
+            # # 检查无人机电池约束：
+            # # 飞行+计算+传输能耗需不超过电池容量
+            # flight_energy = flight_energy_factor * d
+            # comp_energy = comp_energy_factor * rho * d
+            # trans_energy = trans_energy_factor * (1 - rho) * d
+            # total_uav_energy = flight_energy + comp_energy + trans_energy
+            # # 无人机计算与传输时间不超过飞行时间
+            # if (total_uav_energy > battery_capacity) or (comp_time + trans_time > flight_time):
+            #     # 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
+            #     valid_partition = False
+            #     break
+
+            # 求解rho
+            rho_time_limit = (flight_time_factor - trans_time_factor) / \
+                (comp_uav_factor - trans_time_factor)
+            rho_energy_limit = (battery_capacity - flight_energy_factor * d - trans_energy_factor * d) / \
+                (comp_energy_factor * d - trans_energy_factor * d)
+            if rho_energy_limit < 0:
+                valid_partition = False
+                break
+            rho = min(rho_time_limit, rho_energy_limit)
+            print(rho)
+            flight_time = flight_time_factor * d
+            comp_time = comp_uav_factor * rho * d
+            trans_time = trans_time_factor * (1 - rho) * d
+            comp_bs_time = comp_bs_factor * (1 - rho) * d
+
+            # 计算任务矩形中心，用于后续车辆移动时间计算
+            center_r = (r1 + r2) / 2.0
+            center_c = (c1 + c2) / 2.0
+
+            rectangles.append({
+                'r1': r1, 'r2': r2, 'c1': c1, 'c2': c2,
+                'd': d,
+                'rho': rho,
+                'flight_time': flight_time,
+                'comp_time': comp_time,
+                'trans_time': trans_time,
+                'comp_bs_time': comp_bs_time,
+                'center': (center_r, center_c)
+            })
+        if not valid_partition:
+            break
+
+    # 如果分区中存在任务不满足电池约束，则跳过该分区
+    if not valid_partition:
+        continue
+
+    # ---------------------------
+    # 随机将所有矩形任务分配给 k 个系统（车-机-巢）
+    # ---------------------------
+    system_tasks = {i: [] for i in range(k)}
+    for rect in rectangles:
+        system = random.randint(0, k - 1)
+        system_tasks[system].append(rect)
+
+    # ---------------------------
+    # 对于每个系统，计算该系统的总完成时间 T_k：
+    # T_k = 所有任务的飞行时间之和 + 车辆的移动时间
+    # 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）
+    # ---------------------------
+    region_center = (H / 2.0, W / 2.0)
+    T_k_list = []
+    for i in range(k):
+        tasks = system_tasks[i]
+        tasks.sort(key=lambda r: math.hypot(r['center'][0] - region_center[0],
+                                            r['center'][1] - region_center[1]))
+        total_flight_time = sum(task['flight_time'] for task in tasks)
+        if tasks:
+            # 车辆从区域中心到第一个任务中心
+            car_time = math.hypot(tasks[0]['center'][0] - region_center[0],
+                                  tasks[0]['center'][1] - region_center[1]) * car_move_time_factor
+            # 依次经过任务中心
+            for j in range(1, len(tasks)):
+                prev_center = tasks[j - 1]['center']
+                curr_center = tasks[j]['center']
+                car_time += math.hypot(curr_center[0] - prev_center[0],
+                                       curr_center[1] - prev_center[1]) * car_move_time_factor
+        else:
+            car_time = 0
+
+        # 机巢的计算时间
+        total_bs_time = sum(task['comp_bs_time'] for task in tasks)
+        T_k = max(total_flight_time + car_time, total_bs_time)
+        T_k_list.append(T_k)
+
+    T_max = max(T_k_list)  # 整体目标 T 为各系统中最大的 T_k
+
+    # TODO 没有限制系统的总能耗
+
+    if T_max < best_T:
+        best_T = T_max
+        best_solution = {
+            'system_tasks': system_tasks,
+            'T_k_list': T_k_list,
+            'T_max': T_max,
+            'iteration': iteration,
+            'R': R,
+            'C': C,
+            'row_boundaries': row_boundaries,
+            'col_boundaries': col_boundaries
+        }
+
+# ---------------------------
+# 输出最佳方案
+# ---------------------------
+if best_solution is not None:
+    print("最佳 T (各系统中最长的完成时间):", best_solution['T_max'])
+    for i in range(k):
+        num_tasks = len(best_solution['system_tasks'][i])
+        print(
+            f"系统 {i}: 完成时间 T = {best_solution['T_k_list'][i]}, 飞行任务数量: {num_tasks}")
+else:
+    print("在给定的模拟次数内未找到满足所有约束的方案。")
+
+# 在输出最佳方案后添加详细信息
+if best_solution is not None:
+    print("\n各系统详细信息:")
+    region_center = (H / 2.0, W / 2.0)
+
+    for system_id, tasks in best_solution['system_tasks'].items():
+        print(f"\n系统 {system_id} 的任务详情:")
+
+        # 按距离区域中心的距离排序任务
+        tasks_sorted = sorted(tasks, key=lambda r: math.hypot(r['center'][0] - region_center[0],
+                                                              r['center'][1] - region_center[1]))
+
+        if tasks_sorted:
+            print(
+                f"轨迹路线: 区域中心({region_center[0]:.1f}, {region_center[1]:.1f})", end="")
+            current_pos = region_center
+            total_car_time = 0
+            total_flight_time = 0
+            total_flight_energy = 0
+            total_comp_energy = 0
+            total_trans_energy = 0
+
+            for i, task in enumerate(tasks_sorted, 1):
+                # 计算车辆移动时间
+                car_time = math.hypot(task['center'][0] - current_pos[0],
+                                      task['center'][1] - current_pos[1]) * car_move_time_factor
+                total_car_time += car_time
+
+                # 更新当前位置
+                current_pos = task['center']
+                print(
+                    f" -> 任务{i}({current_pos[0]:.1f}, {current_pos[1]:.1f})", end="")
+
+                # 累加各项数据
+                total_flight_time += task['flight_time']
+                total_flight_energy += flight_energy_factor * task['d']
+                total_comp_energy += comp_energy_factor * \
+                    task['rho'] * task['d']
+                total_trans_energy += trans_energy_factor * \
+                    (1 - task['rho']) * task['d']
+
+            print("\n")
+            print(f"任务数量: {len(tasks_sorted)}")
+            print(f"车辆总移动时间: {total_car_time:.2f} 秒")
+            print(f"无人机总飞行时间: {total_flight_time:.2f} 秒")
+            print(f"能耗统计:")
+            print(f"  - 飞行能耗: {total_flight_energy:.2f} 分钟")
+            print(f"  - 计算能耗: {total_comp_energy:.2f} 分钟")
+            print(f"  - 传输能耗: {total_trans_energy:.2f} 分钟")
+            print(
+                f"  - 总能耗: {(total_flight_energy + total_comp_energy + total_trans_energy):.2f} 分钟")
+
+            print("\n各任务详细信息:")
+            for i, task in enumerate(tasks_sorted, 1):
+                print(f"\n任务{i}:")
+                print(
+                    f"  位置: ({task['center'][0]:.1f}, {task['center'][1]:.1f})")
+                print(f"  照片数量: {task['d']}")
+                print(f"  卸载比率(ρ): {task['rho']:.2f}")
+                print(f"  飞行时间: {task['flight_time']:.2f} 秒")
+                print(f"  计算时间: {task['comp_time']:.2f} 秒")
+                print(f"  传输时间: {task['trans_time']:.2f} 秒")
+                print(f"  -- 飞行能耗: {task['d'] * flight_energy_factor:.2f} 分钟")
+                print(f"  -- 计算能耗: {task['d'] * comp_energy_factor:.2f} 分钟")
+                print(f"  -- 传输能耗: {task['d'] * trans_energy_factor:.2f} 分钟")
+                print(f"  基站计算时间: {task['comp_bs_time']:.2f} 秒")
+        else:
+            print("该系统没有分配任务")
+        print("-" * 50)
+
+if best_solution is not None:
+    plt.rcParams['font.family'] = ['sans-serif']
+    plt.rcParams['font.sans-serif'] = ['SimHei']
+    fig, ax = plt.subplots()
+    ax.set_xlim(0, W)
+    ax.set_ylim(0, H)
+    ax.set_title("区域划分与车-机-巢系统覆盖")
+    ax.set_xlabel("区域宽度")
+    ax.set_ylabel("区域高度")
+
+    # 定义若干颜色以区分不同系统（系统编号从0开始）
+    colors = ['red', 'blue', 'green', 'orange', 'purple', 'cyan', 'magenta']
+
+    # 绘制区域中心
+    region_center = (W / 2.0, H / 2.0)  # 注意：x对应宽度，y对应高度
+    ax.plot(region_center[0], region_center[1],
+            'ko', markersize=8, label="区域中心")
+
+    # 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
+    for system_id, tasks in best_solution['system_tasks'].items():
+        # 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）
+        tasks_sorted = sorted(tasks, key=lambda task: math.hypot(
+            (task['c1'] + (task['c2'] - task['c1']) / 2.0) - region_center[0],
+            (task['r1'] + (task['r2'] - task['r1']) / 2.0) - region_center[1]
+        ))
+
+        for i, task in enumerate(tasks_sorted, 1):
+            # 绘制矩形：左下角坐标为 (c1, r1)，宽度为 (c2 - c1)，高度为 (r2 - r1)
+            rect = patches.Rectangle((task['c1'], task['r1']),
+                                     task['c2'] - task['c1'],
+                                     task['r2'] - task['r1'],
+                                     linewidth=2,
+                                     edgecolor=colors[system_id % len(colors)],
+                                     facecolor='none')
+            ax.add_patch(rect)
+            # 计算矩形中心
+            center_x = task['c1'] + (task['c2'] - task['c1']) / 2.0
+            center_y = task['r1'] + (task['r2'] - task['r1']) / 2.0
+            # 在矩形中心标注：系统编号、执行顺序和卸载比率 ρ
+            ax.text(center_x, center_y, f"S{system_id}-{i}\nρ={task['rho']:.2f}",
+                    color=colors[system_id % len(colors)],
+                    ha='center', va='center', fontsize=10, fontweight='bold')
+
+    # 添加图例
+    ax.legend()
+    # 反转 y 轴使得行号从上到下递增（如需，可取消）
+    ax.invert_yaxis()
+    plt.show()
+else:
+    print("没有找到满足约束条件的方案，无法进行可视化。")

plot_util.py

@@ -0,0 +1,93 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+# from matplotlib import colors as mcolors
+
+# matplotlib_colors = list(dict(mcolors.BASE_COLORS, **mcolors.CSS4_COLORS).keys())
+
+matplotlib_colors = [
+    "black",
+    "red",
+    "yellow",
+    "grey",
+    "brown",
+    "darkred",
+    "peru",
+    "darkorange",
+    "darkkhaki",
+    "steelblue",
+    "blue",
+    "cyan",
+    "green",
+    "navajowhite",
+    "lightgrey",
+    "lightcoral",
+    "mediumblue",
+    "midnightblue",
+    "blueviolet",
+    "violet",
+    "fuchsia",
+    "mediumvioletred",
+    "hotpink",
+    "crimson",
+    "lightpink",
+    "slategray",
+    "lime",
+    "springgreen",
+    "teal",
+    "beige",
+    "olive",
+]
+
+
+def find_indices(list_to_check, item_to_find):
+    indices = []
+    for idx, value in enumerate(list_to_check):
+        if np.array_equal(value, item_to_find):
+            indices.append(idx)
+    return indices
+
+
+def plot_results(Best_path, iterations, best_record):
+    # print(find_indices(Best_path, [0, 0]))
+
+    # Best_path = np.vstack([Best_path, Best_path[0]])
+    # Best_path = np.vstack([Best_path[0], Best_path])
+    # print(Best_path[0], Best_path[-1])
+
+    if not np.array_equal(Best_path[0], [0, 0]):
+        Best_path = np.vstack([[0, 0], Best_path])
+    if not np.array_equal(Best_path[-1], [0, 0]):
+        Best_path = np.vstack([Best_path, [0, 0]])
+    # print(Best_path)
+
+    found_start_points_indices = find_indices(Best_path, [0, 0])
+    result_paths = []
+
+    for j in range(len(found_start_points_indices) - 1):
+        from_index = found_start_points_indices[j]
+        end_index = found_start_points_indices[j + 1]
+        path = []
+        for k in range(from_index, end_index + 1):
+            path.append(Best_path[k])
+        path = np.array(path)
+        result_paths.append(path)
+
+    # print(Best_path)
+    # print(result_paths)
+
+    fig, axs = plt.subplots(1, 2, sharex=False, sharey=False)
+    axs[0].scatter(Best_path[:, 0], Best_path[:, 1])
+
+    for ix, path in enumerate(result_paths):
+        axs[0].plot(path[:, 0], path[:, 1], color=matplotlib_colors[ix], alpha=0.8)
+    # axs[0].plot(Best_path[:, 0], Best_path[:, 1], color="green", alpha=0.1)
+
+    # Draw start point
+    axs[0].plot([0], [0], marker="*", markersize=20, color="red")
+
+    axs[0].set_title("Searched Best Solution")
+
+    axs[1].plot(iterations, best_record)
+    axs[1].set_title("Convergence Curve")
+    plt.show()