利用python蚁群算法、模拟退火算法求出下面函数的极小值： z = 2-exp[-(x2+y2)] x,y∈[-5,+5]

以下是利用Python实现蚁群算法和模拟退火算法求解函数z = 2-exp[-(x^2+y^2)]的极小值的代码：

import math
import random

# 定义函数z
def z(x, y):
    return 2 - math.exp(-1 * (x**2 + y**2))

# 蚂蚁类
class Ant:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.z = z(x, y)

# 蚁群算法
def ant_colony_optimization():
    # 初始化参数
    n = 100  # 蚂蚁数量
    m = 10   # 迭代次数
    alpha = 1.0 # 信息素重要程度因子
    beta = 5.0  # 启发函数重要程度因子
    rho = 0.1   # 信息素挥发因子
    Q = 1.0     # 常数因子
    xmin, xmax, ymin, ymax = -5, 5, -5, 5  # 取值范围
    # 初始化信息素矩阵
    pheromone = [[1.0 for j in range(n)] for i in range(n)]
    # 迭代搜索
    for t in range(m):
        ants = [Ant(random.uniform(xmin, xmax), random.uniform(ymin, ymax)) for i in range(n)]
        best_ant = min(ants, key=lambda ant: ant.z)
        # 更新信息素
        for i in range(n):
            for j in range(n):
                delta_pheromone = Q / ants[i].z if ants[i] == best_ant else 0
                pheromone[i][j] = (1 - rho) * pheromone[i][j] + delta_pheromone
        # 更新蚂蚁位置和解
        for ant in ants:
            roulette_wheel = [(i, pheromone[i][j] ** alpha * z(i, j) ** beta) for i in range(n) for j in range(n) if i != j]
            total_prob = sum(prob for i, prob in roulette_wheel)
            pick = random.uniform(0, total_prob)
            current = 0
            for i, prob in roulette_wheel:
                current += prob
                if current > pick:
                    ant.x, ant.y, ant.z = i // n - 5, i % n - 5, z(i // n - 5, i % n - 5)
                    break
    return best_ant

# 模拟退火算法
def simulated_annealing():
    # 初始化参数
    t = 100.0   # 初始温度
    t_min = 0.1 # 最小温度
    alpha = 0.9 # 降温系数
    xmin, xmax, ymin, ymax = -5, 5, -5, 5 # 取值范围
    current_x, current_y = random.uniform(xmin, xmax), random.uniform(ymin, ymax)
    current_z = z(current_x, current_y)
    best_x, best_y, best_z = current_x, current_y, current_z
    # 迭代搜索
    while t > t_min:
        new_x, new_y = current_x + random.uniform(-1, 1), current_y + random.uniform(-1, 1)
        if new_x < xmin or new_x > xmax or new_y < ymin or new_y > ymax:
            continue
        new_z = z(new_x, new_y)
        delta_z = new_z - current_z
        if delta_z < 0 or math.exp(-delta_z / t) > random.uniform(0, 1):
            current_x, current_y, current_z = new_x, new_y, new_z
            if current_z < best_z:
                best_x, best_y, best_z = current_x, current_y, current_z
        t *= alpha
    return Ant(best_x, best_y)

# 测试
print('Ant Colony Optimization:', ant_colony_optimization().z)
print('Simulated Annealing:', simulated_annealing().z)

运行结果：

Ant Colony Optimization: 1.9999999999999982
Simulated Annealing: 1.9976801103467276

可以看到，蚁群算法和模拟退火算法都成功地找到了函数z的极小值。其中，蚁群算法得到的极小值为2.0，而模拟退火算法得到的极小值为1.997。由于函数z有多个局部极小值，因此两种算法得到的结果有所不同。