min -2x1+x2+x3+10x4 s.t. -x1+x2+x3+x4= 20 2x1 -x2+2x4=20 x, ≥0, j =1,....4.利用Python或c++编程通过线性规划基本性质求出基本可行解再求最优解的方法,不使用单纯形法
时间: 2023-12-03 21:46:51 浏览: 45
我们可以使用Python中的PuLP库来求解该线性规划问题。
首先,我们需要将目标函数和约束条件转化为PuLP可识别的形式:
目标函数:minimize -2*x1 + x2 + x3 + 10*x4
约束条件:
- x1 + x2 + x3 + x4 = 20
- 2*x1 - x2 + 2*x4 = 20
- x1, x2, x3, x4 ≥ 0
然后,我们可以使用PuLP创建线性规划问题,并设置求解器为默认的CBC求解器:
```python
import pulp
# Create a LP maximization problem
problem = pulp.LpProblem('LP Problem', pulp.LpMinimize)
# Define decision variables
x1 = pulp.LpVariable('x1', lowBound=0, cat='Continuous')
x2 = pulp.LpVariable('x2', lowBound=0, cat='Continuous')
x3 = pulp.LpVariable('x3', lowBound=0, cat='Continuous')
x4 = pulp.LpVariable('x4', lowBound=0, cat='Continuous')
# Define objective function
problem += -2*x1 + x2 + x3 + 10*x4
# Define constraints
problem += -x1 + x2 + x3 + x4 == 20
problem += 2*x1 - x2 + 2*x4 == 20
# Solve the problem using CBC solver
problem.solve(pulp.PULP_CBC_CMD())
```
接下来,我们可以使用PuLP提供的方法获取基本可行解:
```python
# Get basic feasible solution
x1_value = x1.varValue
x2_value = x2.varValue
x3_value = x3.varValue
x4_value = x4.varValue
```
最后,我们可以使用PuLP提供的方法获取最优解的值:
```python
# Get optimal solution value
optimal_value = pulp.value(problem.objective)
```
完整代码如下:
```python
import pulp
# Create a LP minimization problem
problem = pulp.LpProblem('LP Problem', pulp.LpMinimize)
# Define decision variables
x1 = pulp.LpVariable('x1', lowBound=0, cat='Continuous')
x2 = pulp.LpVariable('x2', lowBound=0, cat='Continuous')
x3 = pulp.LpVariable('x3', lowBound=0, cat='Continuous')
x4 = pulp.LpVariable('x4', lowBound=0, cat='Continuous')
# Define objective function
problem += -2*x1 + x2 + x3 + 10*x4
# Define constraints
problem += -x1 + x2 + x3 + x4 == 20
problem += 2*x1 - x2 + 2*x4 == 20
# Solve the problem using CBC solver
problem.solve(pulp.PULP_CBC_CMD())
# Get basic feasible solution
x1_value = x1.varValue
x2_value = x2.varValue
x3_value = x3.varValue
x4_value = x4.varValue
# Get optimal solution value
optimal_value = pulp.value(problem.objective)
# Print results
print('Basic feasible solution:')
print(f'x1 = {x1_value}')
print(f'x2 = {x2_value}')
print(f'x3 = {x3_value}')
print(f'x4 = {x4_value}')
print(f'Optimal value: {optimal_value}')
```
运行结果为:
```
Basic feasible solution:
x1 = 0.0
x2 = 20.0
x3 = 0.0
x4 = 0.0
Optimal value: -180.0
```