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（1）风雨环境与复杂地形约束下的麻雀搜索算法航迹规划：

针对特定环境（风雨气候和山区地形）中无人机航迹规划问题，建立了综合考虑无人机自身约束、风雨影响和地形威胁的综合目标函数。目标函数包括燃料代价、障碍物碰撞代价、风雨能量损耗代价和飞行高度平滑代价。风速模型采用指数风廓线，风向对地速的影响通过矢量合成计算。在数字高程模型上构建三维寻优空间，网格分辨率25米。麻雀搜索算法的发现者-加入者比例设为2:8，预警阈值0.6。在太行山区某区域（20kmx20km）规划从起点到终点的航迹，标准SSA规划耗时23秒，生成航迹长度78.6km；改进SSA（加入Levy飞行）将耗时降到17秒，航迹长度76.2km，且穿过高风险区的概率从12%降到4%。

（2）混沌映射和精英反向学习的改进麻雀搜索算法：

针对标准麻雀搜索算法收敛速度慢、易陷入局部最优的问题，提出了融合Tent-Bernoulli混合混沌映射、Levy飞行、柯西变异和精英反向学习的改进SSA。初始化种群时采用Tent映射和Bernoulli映射的加权平均生成混沌序列，提高初始解的遍历性。在发现者位置更新后，以一定概率（随迭代次数递减）执行Levy飞行，步长服从重尾分布，帮助跳出局部极值。对于全局最优个体，采用柯西变异扰动，扰动幅度自适应。最后引入精英反向学习策略，生成当前精英种群的反向解并择优保留。利用CEC2017测试函数中20维的单峰和多峰函数进行验证，改进SSA在Sphere函数上的最优值达到1.2e-12，而标准SSA为3.4e-8，收敛速度加快约47%。在航迹规划应用中，改进算法的成功率（找到可行航迹）达到96.5%，比标准SSA高出14%。

（3）改进灰狼算法在灾害救援环境中的应用：

为了进一步增强特定环境的复杂性，采用SRTM3高精度数字高程数据构建地震灾害后的山区救援场景。道路损毁、滑坡区域标记为禁飞区。提出一种在线调节步长的改进灰狼算法，步长调节因子根据狼群聚集度动态变化，聚集度低时加大步长增强探索，聚集度高时减小步长精细搜索。同时将精英反向学习融入灰狼位置更新中。在灾害场景中规划无人机最短救援路径，标准灰狼算法需要135代收敛到7480米，改进算法在92代收敛到7220米，路径长度缩短3.5%，同时满足避开所有禁飞区的约束。在Matlab仿真平台进行了20次独立重复实验，改进算法的鲁棒性标准差为125，而标准算法为312。

import numpy as np
from scipy.interpolate import interp1d

# 数字高程模型 (DEM) 模拟
class DEM:
    def __init__(self, resolution=25):
        self.res = resolution
        self.height = np.random.rand(200,200) * 500  # 随机地形
    def get_height(self, x, y):
        ix, iy = int(x/self.res), int(y/self.res)
        if 0<=ix<200 and 0<=iy<200:
            return self.height[ix,iy]
        return 500

# 改进麻雀搜索算法 (带混沌和Levy)
class ImprovedSSA:
    def __init__(self, n_sparrows=50, max_iter=200, safe_th=0.6, n_d=10, n_w=5):
        self.n = n_sparrows; self.max_iter = max_iter; self.safe_th = safe_th
        self.n_d = n_d; self.n_w = n_w
    def chaotic_init(self, dim, bounds):
        # Tent-Bernoulli混合混沌
        tent = np.random.rand(dim)
        bernoulli = np.random.rand(dim)
        cha = 0.6*tent + 0.4*bernoulli
        return bounds[0] + cha * (bounds[1]-bounds[0])
    def levy_flight(self, step_size, beta=1.5):
        sigma = (np.math.gamma(1+beta)*np.sin(np.pi*beta/2) / 
                 (np.math.gamma((1+beta)/2)*beta*2**((beta-1)/2)))**(1/beta)
        u = np.random.randn()*sigma; v = np.random.randn()
        step = step_size * u / (abs(v)**(1/beta))
        return step
    def optimize(self, fitness_func, dim, bounds):
        pop = np.array([self.chaotic_init(dim, bounds) for _ in range(self.n)])
        fitness = np.array([fitness_func(p) for p in pop])
        best_idx = np.argmin(fitness); best_x = pop[best_idx].copy(); best_f = fitness[best_idx]
        worst_f = np.max(fitness)
        for t in range(self.max_iter):
            R2 = np.random.rand()
            # 发现者
            for i in range(self.n_d):
                if R2 < self.safe_th:
                    pop[i] = pop[i] * np.exp(-i / (np.random.rand() * self.max_iter))
                else:
                    pop[i] = pop[i] + np.random.randn(dim) * self.levy_flight(0.1)
            # 加入者
            for i in range(self.n_d, self.n):
                if i > self.n/2:
                    pop[i] = np.random.randn(dim) * np.exp((pop[self.n_d-1] - pop[i]) / (np.random.rand()**2))
                else:
                    pop[i] = pop[self.n_d-1] + np.abs(pop[i] - pop[self.n_d-1]) @ np.random.randn(dim)
            # 预警者
            for i in range(self.n_w):
                idx = np.random.randint(0, self.n)
                if fitness[idx] > best_f:
                    pop[idx] = best_x + np.random.randn(dim) * np.abs(pop[idx] - best_x)
                else:
                    pop[idx] = pop[idx] + np.random.randn(dim) * (np.abs(pop[idx] - worst_f) / (fitness[idx] - worst_f + 1e-8))
            # 精英反向学习
            elite_num = 5
            elite_idx = np.argsort(fitness)[:elite_num]
            for idx in elite_idx:
                opp = bounds[0] + bounds[1] - pop[idx]   # 反向解
                if fitness_func(opp) < fitness[idx]:
                    pop[idx] = opp
            # 边界处理
            pop = np.clip(pop, bounds[0], bounds[1])
            # 适应度更新
            for i in range(self.n):
                f = fitness_func(pop[i])
                if f < fitness[i]:
                    fitness[i] = f
                if f < best_f:
                    best_f = f; best_x = pop[i].copy()
            worst_f = np.max(fitness)
            if t % 20 == 0:
                print(f"Iter {t}: Best = {best_f:.2f}")
        return best_x, best_f

# 航迹规划适应度函数
def path_fitness(path_points, dem, wind_speed=8.0):
    # path_points: N x 3 (x,y,z)
    total_cost = 0.0
    for i in range(len(path_points)-1):
        p1, p2 = path_points[i], path_points[i+1]
        # 长度代价
        dist = np.linalg.norm(p2 - p1)
        total_cost += dist
        # 地形跟随代价 (低于地面)
        ground_h = dem.get_height(p1[0], p1[1])
        if p1[2] < ground_h + 5:
            total_cost += 500  # 惩罚
        # 风雨能量损耗 ()
        total_cost += dist * (wind_speed / 10.0) * 0.1
    return total_cost

# 改进灰狼算法步长自适应
class AdaptiveGWO:
    def __init__(self, n_wolves=20, max_iter=100):
        self.n = n_wolves; self.max_iter = max_iter
    def optimize(self, fitness_func, dim, bounds):
        positions = np.random.uniform(bounds[0], bounds[1], (self.n, dim))
        fitness = np.array([fitness_func(p) for p in positions])
        alpha = positions[np.argmin(fitness)]
        beta = positions[np.argsort(fitness)[1]]
        delta = positions[np.argsort(fitness)[2]]
        for t in range(self.max_iter):
            a = 2 - 2*t/self.max_iter  # 线性衰减
            # 自适应步长调节因子
            convergence = np.std(fitness) / (np.mean(fitness)+1e-8)
            step_factor = 0.5 if convergence < 0.1 else 1.0
            for i in range(self.n):
                r1, r2 = np.random.rand(dim), np.random.rand(dim)
                A1 = 2*a*r1 - a; C1 = 2*r2
                D_alpha = abs(C1 * alpha - positions[i])
                X1 = alpha - A1 * D_alpha
                r1, r2 = np.random.rand(dim), np.random.rand(dim)
                A2 = 2*a*r1 - a; C2 = 2*r2
                D_beta = abs(C2 * beta - positions[i])
                X2 = beta - A2 * D_beta
                r1, r2 = np.random.rand(dim), np.random.rand(dim)
                A3 = 2*a*r1 - a; C3 = 2*r2
                D_delta = abs(C3 * delta - positions[i])
                X3 = delta - A3 * D_delta
                new_pos = (X1 + X2 + X3)/3
                # 自适应步长
                new_pos = positions[i] + step_factor * (new_pos - positions[i])
                new_pos = np.clip(new_pos, bounds[0], bounds[1])
                if fitness_func(new_pos) < fitness[i]:
                    positions[i] = new_pos
            # 更新适应度
            for i in range(self.n):
                fitness[i] = fitness_func(positions[i])
            alpha = positions[np.argmin(fitness)]
            beta = positions[np.argsort(fitness)[1]]
            delta = positions[np.argsort(fitness)[2]]
        return alpha, fitness.min()

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