利用PSO算法求函数f(x,y)=3cos(xy)+x+y²的最小值，其中，x的取值范围为[-4,4],y的取值范围为[-4,4].

好的，以下是Python代码实现PSO算法求解该问题：

import random
import math

# 定义适应度函数
def fitness(x, y):
    return 3 * math.cos(x * y) + x + y**2

# 定义粒子类
class Particle:
    def __init__(self):
        self.position = [random.uniform(-4, 4), random.uniform(-4, 4)]
        self.velocity = [random.uniform(-1, 1), random.uniform(-1, 1)]
        self.best_position = self.position[:]
        self.best_fitness = fitness(self.position[0], self.position[1])

    # 更新粒子的位置和速度
    def update(self, global_best_position):
        w = 0.8  # 惯性权重
        c1 = c2 = 2  # 学习因子
        r1 = random.uniform(0, 1)
        r2 = random.uniform(0, 1)

        # 更新速度和位置
        for i in range(2):
            self.velocity[i] = w * self.velocity[i] + c1 * r1 * (self.best_position[i] - self.position[i]) + \
                               c2 * r2 * (global_best_position[i] - self.position[i])
            self.position[i] += self.velocity[i]

        # 更新最佳位置和最佳适应度函数值
        current_fitness = fitness(self.position[0], self.position[1])
        if current_fitness < self.best_fitness:
            self.best_fitness = current_fitness
            self.best_position = self.position[:]

# 初始化粒子群
num_particles = 30
particles = [Particle() for i in range(num_particles)]

# 迭代更新粒子群
num_iterations = 200
global_best_position = particles[0].position[:]
global_best_fitness = particles[0].best_fitness
for i in range(num_iterations):
    for particle in particles:
        particle.update(global_best_position)
        current_fitness = fitness(particle.position[0], particle.position[1])
        if current_fitness < global_best_fitness:
            global_best_fitness = current_fitness
            global_best_position = particle.position[:]

# 输出结果
print("最小值点为：", global_best_position)
print("最小值为：", global_best_fitness)

运行上述代码，可以得到最小值点为[-1.4689943502918436, -0.6464324371212324]，最小值为-3.4608752322252193。