利用PSO算法求函数f(ar, y)=3*cos(ay)＋a＋y2的最小值。其中，n∈ [-4，4] , y∈e [-4，4]。

好的，这是一个优化问题，可以使用PSO（粒子群优化）算法来求解。

首先，我们需要定义适应度函数，即要最小化的目标函数。根据题意，我们可以定义如下的适应度函数：

def fitness_function(x):
    a, y = x
    return 3 * math.cos(a * y) + a + y ** 2

其中，`x`是一个包含`a`和`y`的元组。

接下来，我们可以使用如下的代码来实现PSO算法：

import random
import math

class Particle:
    def __init__(self, bounds):
        self.particle_position = [random.uniform(bounds[i][0], bounds[i][1]) for i in range(len(bounds))]
        self.particle_velocity = [random.uniform(-1, 1) for _ in range(len(bounds))]
        self.local_best_particle_position = self.particle_position
        self.fitness_local_best_particle_position = float('inf')
        
    def update_velocity(self, global_best_particle_position, omega, phip, phig):
        for i in range(len(self.particle_position)):
            r1 = random.uniform(0, 1)
            r2 = random.uniform(0, 1)
            cognitive_velocity = phip * r1 * (self.local_best_particle_position[i] - self.particle_position[i])
            social_velocity = phig * r2 * (global_best_particle_position[i] - self.particle_position[i])
            self.particle_velocity[i] = omega * self.particle_velocity[i] + cognitive_velocity + social_velocity
            
    def update_position(self, bounds):
        for i in range(len(self.particle_position)):
            self.particle_position[i] += self.particle_velocity[i]
            if self.particle_position[i] < bounds[i][0]:
                self.particle_position[i] = bounds[i][0]
            elif self.particle_position[i] > bounds[i][1]:
                self.particle_position[i] = bounds[i][1]
                
    def evaluate_fitness(self, fitness_function):
        self.fitness_particle_position = fitness_function(self.particle_position)
        if self.fitness_particle_position < self.fitness_local_best_particle_position:
            self.local_best_particle_position = self.particle_position
            self.fitness_local_best_particle_position = self.fitness_particle_position

def particle_swarm_optimization(fitness_function, bounds, num_particles, max_iterations):
    omega = 0.5
    phip = 0.5
    phig = 0.5
    global_best_particle_position = None
    global_best_fitness = float('inf')
    swarm = [Particle(bounds) for _ in range(num_particles)]
    for i in range(max_iterations):
        for j in range(num_particles):
            swarm[j].evaluate_fitness(fitness_function)
            if swarm[j].fitness_particle_position < global_best_fitness:
                global_best_particle_position = swarm[j].particle_position
                global_best_fitness = swarm[j].fitness_particle_position
        for j in range(num_particles):
            swarm[j].update_velocity(global_best_particle_position, omega, phip, phig)
            swarm[j].update_position(bounds)
    return global_best_particle_position, global_best_fitness

最后，我们可以使用如下的代码来调用PSO算法，并求解目标函数的最小值：

bounds = [(-4, 4), (-4, 4)]
num_particles = 20
max_iterations = 100
best_position, best_fitness = particle_swarm_optimization(fitness_function, bounds, num_particles, max_iterations)
print('Best position:', best_position)
print('Best fitness:', best_fitness)

运行以上代码，就可以得到目标函数的最小值及其对应的参数`a`和`y`。