利用差分进化求解SVP问题的python代码
时间: 2024-09-08 13:02:59 浏览: 25
差分进化算法是一种全局优化技术,用于寻找函数的全局最小值。在Python中,我们可以利用`deap`库来实现差分进化算法。下面是一个简单的例子,展示如何使用`deap`解决单变量优化问题(Single Variable Problem,SVP),假设我们要最小化一个函数`f(x)`:
```python
import numpy as np
from deap import base, creator, tools
# 假设我们有一个自定义的目标函数
def objective_function(x):
return x**2 + 10 * np.sin(x)
# 初始化DEAP模块
creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)
toolbox = base.Toolbox()
toolbox.register("attr_float", np.random.uniform, -100, 100)
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_float, n=1)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
# 差分进化设置
pop_size = 50
iter_num = 1000
mutation_factor = 0.8
cross_prob = 0.7
tolerance = 1e-4
def differential_evolution(population, toolbox):
pop = population[:] # Deep copy the population.
fits = [objective_function(ind) for ind in pop]
for g in range(iter_num):
offspring = toolbox.clone(pop)
# Mutation
for i in range(len(offspring)):
a, b, c = map(toolbox.choice, [offspring] * 3)
mutant = toolbox.clone(a)
mutant[0] = a[0] + mutation_factor * (b[0] - c[0])
if mutant[0] < pop[i][0]:
offspring[i] = mutant
# Crossover
for i in range(len(offspring)):
if np.random.random() < cross_prob:
a, b = map(toolbox.choice, [offspring] * 2)
offspring[i][0] = a[0] if np.random.random() < 0.5 else b[0]
# Update fit values and select next generation
new_pop = [(ind, fit) for ind, fit in zip(offspring, [objective_function(ind) for ind in offspring])]
fits = [fit for ind, fit in new_pop]
offspring = [ind for ind, fit in new_pop if fit < fits[best_i]]
# Check convergence
best_fit = min(fits)
if abs(best_fit - fits[best_i]) < tolerance:
break
pop[:] = offspring
best_ind = offspring[0]
return best_ind, best_fit
# 初始化并运行差分进化算法
population = toolbox.population(n=pop_size)
best_solution, best_cost = differential_evolution(population, toolbox)
print(f"Best solution found: {best_solution[0]} with cost {best_cost}")