数学建模-建模算法（4）
python虽然不是完全为数学建模而生的，但是它完整的库让它越来越适合建模了。
- 线性规划：使用scipy.optimize.linprog()函数
```python
from scipy.optimize import linprog
c = [-1, 4]
A = [[-3, 1], [1, 2]]
b = [6, 4]
x0_bounds = (None, None)
x1_bounds = (-3, None)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs')
print(res)
```
- 整数规划：使用scipy.optimize.linprog()函数，并将目标函数系数转换为整数
```python
from scipy.optimize import linprog
c = [-1, 4]
A = [[-3, 1], [1, 2]]
b = [6, 4]
x0_bounds = (None, None)
x1_bounds = (-3, None)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs', integer=True)
print(res)
```
- 多元规划：使用scipy.optimize.linprog()函数
```python
from scipy.optimize import linprog
c = [-1, 4]
A = [[-3, 1, 1], [1, 2, 3]]
b = [6, 4, 5]
x0_bounds = (None, None, None)
x1_bounds = (-3, -3, -3)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs')
print(res)
```
- 二次规划：使用scipy.optimize.linprog()函数，并将目标函数系数转换为平方项
```python
from scipy.optimize import linprog
c = [-1, 4]
A = [[-3, 1], [1, 2]]
b = [6, 4]
x0_bounds = (None, None)
x1_bounds = (-3, None)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs', square_root=True)
print(res)
```
- 遗传算法：使用DEAP库
```python
from deap import base, creator, tools, algorithms
import random
creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)
toolbox = base.Toolbox()
toolbox.register("attr_bool", random.randint, 0, 1)
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_bool, n=100)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
def evalOneMax(individual):
return sum(individual),
toolbox.register("evaluate", evalOneMax)
toolbox.register("mate", tools.cxTwoPoint)
toolbox.register("mutate", tools.mutFlipBit, indpb=0.05)
toolbox.register("select", tools.selTournament, tournsize=3)
population = toolbox.population(n=300)
algorithms.eaSimple(population, toolbox, cxpb=0.5, mutpb=0.2, ngen=40)
```
- 动态规划：使用scipy.optimize.linprog()函数，并将目标函数转换为动态规划问题
```python
from scipy.optimize import linprog
c = [-1, 4]
A = [[-3, 1], [1, 2]]
b = [6, 4]
x0_bounds = (None, None)
x1_bounds = (-3, None)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs')
print(res)
```
- 贪心算法：使用scipy.optimize.linprog()函数，并将目标函数转换为贪心策略
```python
from scipy.optimize import linprog
c = [-1, 4]
A = [[-3, 1], [1, 2]]
b = [6, 4]
x0_bounds = (None, None)
x1_bounds = (-3, None)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs', options={'disp': True})
while not res.success:
if not res.fun:
print("Objective function value is 0 at point %s" % res.x)
break
if res.status == 4:
print("The algorithm could not find a feasible solution for the problem")
break
print(res)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='highs', options={'disp': True})
print(res)
```下次再更新一些高难度的常见算法。