可以打印单纯形表的LP求解器！
Project description
FDSMLP 线性规划求解器！
时间有限，制作了用两阶段法完成线性规划的方法。
求解器可以输出具体的单纯形表解题步骤，做作业利器！
使用
0 库的安装
直接pip
pip install FDSMLP -i https://pypi.org/project
1 库的导入
from FDSMLP.Simplex import Two_step_simplex
2 使用
A = [
[1, 1, 2],
[-1 2, 1],
[1, 0, -2]
]# 约束条件方程
b = [1, 3, -1]# 目标函数系数，数量可以比A的列数少，会自动补全为0
constrain = [4, 4, 5]# 约束条件右侧的常量
constraints =["<=","=",">="]# 约束条件方程的符号，支持不等号，会自动初始化为标准型
# 两阶段法求解器的初始化
simplex=Two_step_simplex(b,A,constrain,constraints)
3 设置单纯形表的打印风格，可以设置每一格的输出宽度
例：
simplex.set_cell_width(11)
print(simplex)
单纯形表打印结果：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X4 | 4.000 | 1.000 | 1.000 | 2.000 | 1.000 | 0.000 | 0.000 | 0.000 |
0 | X6 | 4.000 | -1.000 | 2.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.000 |
0 | X7 | 5.000 | 1.000 | 0.000 | -2.000 | 0.000 | -1.000 | 0.000 | 1.000 |
-------------------------------------------------------------------------------------------------------------------------
| | | 1.000 | 3.000 | 1.000 | 1.000 | -1.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
simplex.set_cell_width(6)
print(simplex)
单纯形表打印结果：
| | |1.000 |3.000 |-1.000|0.000 |0.000 |0.000 |0.000 |
-----------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-----------------------------------------------------------------------
0 | X4 |4.000 |1.000 |1.000 |2.000 |1.000 |0.000 |0.000 |0.000 |
0 | X6 |4.000 |-1.000|2.000 |1.000 |0.000 |0.000 |1.000 |0.000 |
0 | X7 |5.000 |1.000 |0.000 |-2.000|0.000 |-1.000|0.000 |1.000 |
-----------------------------------------------------------------------
| | |1.000 |3.000 |1.000 |1.000 |-1.000|0.000 |0.000 |
-----------------------------------------------------------------------
4 求解
from FDSMLP.Simplex import Two_step_simplex
A = [
[0, 1, 2, 1, 0],
[-1, 2, 1, 1, 1],
[3, 0, 3, 1, 0],
]
b = [1, 3, -1]
constrain = [4, 4, 4]
constraints =["=","=","="]
simplex=Two_step_simplex(b,A,constrain,constraints)
simplex.solve()
输出结果:
开始执行两步法进行线性规划求解：
原始目标函数为：
max y = 1 * X1 + 3 * X2 - 1 * X3 - 0 * X4 - 0 * X5
原始约束条件为：
0 * X1 + 1 * X2 + 2 * X3 + 1 * X4 + 0 * X5 = 4
- 1 * X1 + 2 * X2 + 1 * X3 + 1 * X4 + 1 * X5 = 4
3 * X1 + 0 * X2 + 3 * X3 + 1 * X4 + 0 * X5 = 4
进行标准化后的目标函数为：
max y = 1 * X1 + 3 * X2 - 1 * X3 - 0 * X4 - 0 * X5
标准化后得约束条件为：
0 * X1 + 1 * X2 + 2 * X3 + 1 * X4 + 0 * X5 = 4
- 1 * X1 + 2 * X2 + 1 * X3 + 1 * X4 + 1 * X5 = 4
3 * X1 + 0 * X2 + 3 * X3 + 1 * X4 + 0 * X5 = 4
使用两步法修改目标函数为：
max y = 2 * X1 + 3 * X2 + 6 * X3 + 3 * X4 + 1 * X5 - 0 * X6 - 0 * X7
使用两步法修改约束条件为：
0 * X1 + 1 * X2 + 2 * X3 + 1 * X4 + 0 * X5 + 1 * X6 + 0 * X7 = 4
- 1 * X1 + 2 * X2 + 1 * X3 + 1 * X4 + 1 * X5 + 0 * X6 + 0 * X7 = 4
3 * X1 + 0 * X2 + 3 * X3 + 1 * X4 + 0 * X5 + 0 * X6 + 1 * X7 = 4
初始化单纯形表后结果如下：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X6 | 4.000 | 0.000 | 1.000 | 2.000 | 1.000 | 0.000 | 1.000 | 0.000 |
0 | X5 | 4.000 | -1.000 | 2.000 | 1.000 | 1.000 | 1.000 | 0.000 | 0.000 |
0 | X7 | 4.000 | 3.000 | 0.000 | 3.000 | 1.000 | 0.000 | 0.000 | 1.000 |
-------------------------------------------------------------------------------------------------------------------------
| | | 2.000 | 3.000 | 6.000 | 3.000 | 1.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
开始进行第一阶段运算：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X6 | 4.000 | 0.000 | 1.000 | 2.000 | 1.000 | 0.000 | 1.000 | 0.000 |
0 | X5 | 4.000 | -1.000 | 2.000 | 1.000 | 1.000 | 1.000 | 0.000 | 0.000 |
0 | X7 | 4.000 | 3.000 | 0.000 | 3.000 | 1.000 | 0.000 | 0.000 | 1.000 |
-------------------------------------------------------------------------------------------------------------------------
| | | 2.000 | 3.000 | 6.000 | 3.000 | 1.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
以X3为入基变量，X7为出基变量进行转轴计算，得：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X6 | 1.333 | -2.000 | 1.000 | 0.000 | 0.333 | 0.000 | 1.000 | -0.667 |
0 | X5 | 2.667 | -2.000 | 2.000 | 0.000 | 0.667 | 1.000 | 0.000 | -0.333 |
-1 | X3 | 1.333 | 1.000 | 0.000 | 1.000 | 0.333 | 0.000 | 0.000 | 0.333 |
-------------------------------------------------------------------------------------------------------------------------
| | | -4.000 | 3.000 | 0.000 | 1.000 | 1.000 | 0.000 | -2.000 |
-------------------------------------------------------------------------------------------------------------------------
以X2为入基变量，X5为出基变量进行转轴计算，得：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X6 | 0.000 | -1.000 | 0.000 | 0.000 | 0.000 | -0.500 | 1.000 | -0.500 |
3 | X2 | 1.333 | -1.000 | 1.000 | 0.000 | 0.333 | 0.500 | 0.000 | -0.167 |
-1 | X3 | 1.333 | 1.000 | 0.000 | 1.000 | 0.333 | 0.000 | 0.000 | 0.333 |
-------------------------------------------------------------------------------------------------------------------------
| | | -1.000 | 0.000 | 0.000 | 0.000 | -0.500 | 0.000 | -1.500 |
-------------------------------------------------------------------------------------------------------------------------
第一阶段算法执行完毕，得到如上结果，此时的检验数结果为：[5.0, 0.0, 0.0, -0.6666666666666667, -1.5, 0.0, 0.8333333333333333]
人工变量X6在基变量中，进行判断
人工变量对应行的原始决策变量约束存在不为0的值，直接删除所有人工变量和基变量人工变量对应的行
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X6 | 0.000 | -1.000 | 0.000 | 0.000 | 0.000 | -0.500 | 1.000 | -0.500 |
3 | X2 | 1.333 | -1.000 | 1.000 | 0.000 | 0.333 | 0.500 | 0.000 | -0.167 |
-1 | X3 | 1.333 | 1.000 | 0.000 | 1.000 | 0.333 | 0.000 | 0.000 | 0.333 |
-------------------------------------------------------------------------------------------------------------------------
| | | 5.000 | 0.000 | 0.000 | -0.667 | -1.500 | 0.000 | 0.833 |
-------------------------------------------------------------------------------------------------------------------------
以X1为入基变量，X6为出基变量进行转轴计算，得：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
1 | X1 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | 0.500 | -1.000 | 0.500 |
3 | X2 | 1.333 | 0.000 | 1.000 | 0.000 | 0.333 | 1.000 | -1.000 | 0.333 |
-1 | X3 | 1.333 | 0.000 | 0.000 | 1.000 | 0.333 | -0.500 | 1.000 | -0.167 |
-------------------------------------------------------------------------------------------------------------------------
| | | 0.000 | 0.000 | 0.000 | -0.667 | -4.000 | 5.000 | -1.667 |
-------------------------------------------------------------------------------------------------------------------------
以X5为入基变量，X1为出基变量进行转轴计算，得：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
-------------------------------------------------------------------------------------------------------------------------
0 | X5 | -0.000 | 2.000 | -0.000 | -0.000 | -0.000 | 1.000 | -2.000 | 1.000 |
3 | X2 | 1.333 | -2.000 | 1.000 | 0.000 | 0.333 | 0.000 | 1.000 | -0.667 |
-1 | X3 | 1.333 | 1.000 | 0.000 | 1.000 | 0.333 | 0.000 | 0.000 | 0.333 |
-------------------------------------------------------------------------------------------------------------------------
| | | 8.000 | 0.000 | 0.000 | -0.667 | 0.000 | -3.000 | 2.333 |
-------------------------------------------------------------------------------------------------------------------------
最终单纯形表为：
| | | 1.000 | 3.000 | -1.000 | 0.000 | 0.000 |
-------------------------------------------------------------------------------------------------
CB | XB | b | X1 | X2 | X3 | X4 | X5 |
-------------------------------------------------------------------------------------------------
0 | X5 | -0.000 | 2.000 | -0.000 | -0.000 | -0.000 | 1.000 |
3 | X2 | 1.333 | -2.000 | 1.000 | 0.000 | 0.333 | 0.000 |
-1 | X3 | 1.333 | 1.000 | 0.000 | 1.000 | 0.333 | 0.000 |
-------------------------------------------------------------------------------------------------
| | | 8.000 | 0.000 | 0.000 | -0.667 | 0.000 |
-------------------------------------------------------------------------------------------------
[0, 1.3333333333333335, 1.3333333333333333, 0, -0.0]
线性规划解得最优解为：[0, 1.3333333333333335, 1.3333333333333333, 0, -0.0],此时目标函数极大值为：2.666666666666667
在实际终端中运行，每次转轴的变量都会标红显示
5 内置的parse_input函数使用
from FDSMLP.core.utils.input_parser import parse_input
from FDSMLP.Simplex import Two_step_simplex
constrain,A,b,constraints=parse_input()
simplex=Two_step_simplex(b,A,constrain,constraints)
simplex.solve()
输出结果如下：
请输入目标函数的系数，用空格分隔: 1 3 -1
请输入约束条件（例如 '1 2 <= 3'），输入 'end' 或直接回车结束输入: 1 1 2 <= 4
请输入约束条件（例如 '1 2 <= 3'），输入 'end' 或直接回车结束输入: -1 2 1 <= 4
请输入约束条件（例如 '1 2 <= 3'），输入 'end' 或直接回车结束输入:
开始执行两步法进行线性规划求解：
原始目标函数为：
max y = 1.0 * X1 + 3.0 * X2 - 1.0 * X3
原始约束条件为：
1.0 * X1 + 1.0 * X2 + 2.0 * X3 <= 4.0
- 1.0 * X1 + 2.0 * X2 + 1.0 * X3 <= 4.0
...
说明
该项目目前不依赖第三方库，只依赖于python内置模块 其实做的时候就后悔了，但是写都写了，懒得改了，反正大家也就拿来图一乐
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
FDSMLP-1.0.3.tar.gz
(10.6 kB
view details)
Built Distribution
Filter files by name, interpreter, ABI, and platform.
If you're not sure about the file name format, learn more about wheel file names.
Copy a direct link to the current filters
FDSMLP-1.0.3-py3-none-any.whl
(12.6 kB
view details)
File details
Details for the file FDSMLP-1.0.3.tar.gz.
File metadata
- Download URL: FDSMLP-1.0.3.tar.gz
- Upload date:
- Size: 10.6 kB
- Tags: Source
- Uploaded using Trusted Publishing? No
- Uploaded via: twine/4.0.2 CPython/3.9.12
File hashes
| Algorithm | Hash digest | |
|---|---|---|
| SHA256 |
8cd835dc1bc872ed8e803ee2f9d7dd78e6429af7af7fa33bafc878939fcb1665
|
|
| MD5 |
4e107a38d9a9f79cdf47f3a5e2929b85
|
|
| BLAKE2b-256 |
85ffe82eb32b600ad13e9509a850c778f5a65e3cb331204bd52fdf083d2161ed
|
File details
Details for the file FDSMLP-1.0.3-py3-none-any.whl.
File metadata
- Download URL: FDSMLP-1.0.3-py3-none-any.whl
- Upload date:
- Size: 12.6 kB
- Tags: Python 3
- Uploaded using Trusted Publishing? No
- Uploaded via: twine/4.0.2 CPython/3.9.12
File hashes
| Algorithm | Hash digest | |
|---|---|---|
| SHA256 |
b4b24291718ea2546d3c8c2792b2703b2af3015bf08cd471645c63855b527d92
|
|
| MD5 |
5aea9fc818d9f3507121e6b0af90b666
|
|
| BLAKE2b-256 |
463957003a3973227bcb2517990c0a6b42f9420273d40d45491364637dad8b6c
|
