### 改进粒子群算法求解传感器覆盖优化问题的Python实现 改进粒子群算法（PSO）在无线传感器网络（WSN）节点优化部署中具有广泛应用。通过调整学习因子、惯性权重等参数，可以显著提高算法的收敛速度和全局搜索能力[^1]。此外，结合传感器覆盖优化问题的特点，可以通过定义适应度函数来评估节点部署的覆盖率[^3]。 以下是一个基于改进粒子群算法求解传感器覆盖优化问题的Python实现示例： ```python import numpy as np import matplotlib.pyplot as plt # 参数初始化 def init_parameters(): pop_size = 30 # 种群规模 dim = 2 # 搜索空间维度 (x, y) max_iter = 100 # 最大迭代次数 c1, c2 = 2.0, 2.0 # 学习因子 w_min, w_max = 0.4, 0.9 # 惯性权重范围 search_range = (-100, 100) # 搜索范围 sensor_radius = 10 # 传感器感知半径 area_size = 200 # 覆盖区域大小 return pop_size, dim, max_iter, c1, c2, w_min, w_max, search_range, sensor_radius, area_size # 计算覆盖率的适应度函数 def fitness_function(positions, area_size, sensor_radius): grid_resolution = 1 # 网格分辨率 grid_x = np.arange(0, area_size, grid_resolution) grid_y = np.arange(0, area_size, grid_resolution) grid_points = np.array(np.meshgrid(grid_x, grid_y)).T.reshape(-1, 2) covered = np.zeros(len(grid_points)) for pos in positions: distances = np.linalg.norm(grid_points - pos, axis=1) covered += (distances <= sensor_radius).astype(int) coverage_rate = np.sum(covered >= 1) / len(grid_points) return coverage_rate # 改进粒子群算法主程序 def improved_pso(pop_size, dim, max_iter, c1, c2, w_min, w_max, search_range, sensor_radius, area_size): # 初始化种群位置和速度 particles = np.random.uniform(search_range[0], search_range[1], (pop_size, dim)) velocities = np.zeros_like(particles) pbest_positions = particles.copy() pbest_fitness = np.array([fitness_function(p, area_size, sensor_radius) for p in particles]) gbest_position = particles[np.argmax(pbest_fitness)] gbest_fitness = np.max(pbest_fitness) # 迭代优化 for iteration in range(max_iter): w = w_max - (w_max - w_min) * iteration / max_iter # 动态惯性权重 for i in range(pop_size): r1, r2 = np.random.rand(), np.random.rand() velocities[i] = w * velocities[i] + c1 * r1 * (pbest_positions[i] - particles[i]) + c2 * r2 * (gbest_position - particles[i]) particles[i] += velocities[i] particles[i] = np.clip(particles[i], search_range[0], search_range[1]) current_fitness = np.array([fitness_function(p, area_size, sensor_radius) for p in particles]) better_indices = current_fitness > pbest_fitness pbest_positions[better_indices] = particles[better_indices] pbest_fitness[better_indices] = current_fitness[better_indices] new_gbest_index = np.argmax(pbest_fitness) if pbest_fitness[new_gbest_index] > gbest_fitness: gbest_position = pbest_positions[new_gbest_index] gbest_fitness = pbest_fitness[new_gbest_index] print(f"Iteration {iteration + 1}: Best Fitness = {gbest_fitness:.4f}") return gbest_position, gbest_fitness # 主程序运行 if __name__ == "__main__": pop_size, dim, max_iter, c1, c2, w_min, w_max, search_range, sensor_radius, area_size = init_parameters() best_position, best_fitness = improved_pso(pop_size, dim, max_iter, c1, c2, w_min, w_max, search_range, sensor_radius, area_size) print(f"Optimal Sensor Positions: {best_position}") print(f"Coverage Rate: {best_fitness:.4f}") # 可视化结果 plt.figure(figsize=(6, 6)) plt.scatter(best_position[:, 0], best_position[:, 1], c='red', label='Sensor Nodes') circle = plt.Circle((area_size / 2, area_size / 2), sensor_radius, color='blue', fill=False, linestyle='--', label='Coverage Radius') plt.gca().add_artist(circle) plt.xlim(0, area_size) plt.ylim(0, area_size) plt.legend() plt.title("Sensor Coverage Optimization") plt.show() ``` 上述代码实现了改进粒子群算法求解传感器覆盖优化问题的过程。其中，`fitness_function`用于计算传感器节点部署的覆盖率，`improved_pso`为改进粒子群算法的核心部分，动态调整惯性权重以平衡全局搜索和局部搜索能力[^1]。