単純形法——Python実現(一)

1紹介
本明細書で提供される単純形Pythonは、sympyおよびnumpyライブラリに基づいて実装される.使用する場合は、まず関連ライブラリをインストールしてください.
  の利点:ターゲット関数と不等式制約の元の形式で直接入力できます.  短所(BUG):

すべての変数は>=0

でなければなりません.

未解決拘束条件が全て等式の場合

注記:x 1+x 2=5 x_のような等式制約1 + x_2=5 x 1+x 2=5コード入力形式c0 = (x1+x2, 5)2関連ライブラリのインストール

	pip install numpy 
	pip install sympy

3単純形法Python実現
Simplex.pyコード内容は私のアップロード(ここをクリック)を参照して、コードテストの後にアップロードして、間違いがありません~
4計算例

from sympy import *
from simplex import *


def example_0():

    x1, x2, x3 = symbols('x1, x2, x3')
    obj = -3 * x1 + x2 + x3
    variables = [x1, x2, x3]

    c0 = -4 * x1 + x2 + 2 * x3 >= 3
    c1 = x1 - 2 * x2 + x3 <= 11
    c2 = (-2 * x1 + x3, 1)    #     
    constrs = [c0, c1, c2]
    constrs_com = [GEQ, LEQ, EQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', simplex.optimal_y)


def example_1():

    x1, x2 = symbols('x1, x2')
    obj = -(2*x1 + 3*x2)
    variables = [x1, x2]

    c0 = x1 + 2*x2 <= 8
    c1 = 4*x1 <= 16
    c2 = 4*x2 <= 12
    constrs = [c0, c1, c2]
    constrs_com = [LEQ, LEQ, LEQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', -simplex.optimal_y)


def example_2():

    # X=[21/5, 6/5], min_f=-18
    x1, x2 = symbols('x1, x2')
    obj = -4*x1 - x2
    variables = [x1, x2]

    c0 = -x1 + 2*x2 <= 4
    c1 = 2*x1 + 3*x2 <= 12
    c2 = x1 - x2 <= 3
    constrs = [c0, c1, c2]
    constrs_com = [LEQ, LEQ, LEQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', simplex.optimal_y)


def example_3():

    x1, x2, x3, x4, x5 = symbols('x1, x2, x3, x4, x5')
    obj = 2*x1 + 3*x2 + 5*x3 + 2*x4 + 3*x5
    variables = [x1, x2, x3, x4, x5]

    c0 = x1 + x2 + 2*x3 + x4 + 3*x5 >= 4
    c1 = 2*x1 - x2 + 3*x3 + x4 + x5 >= 3
    constrs = [c0, c1]
    constrs_com = [GEQ, GEQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', simplex.optimal_y)


def example_4():

    # X=[3, 0], max_f=6
    x1, x2 = symbols('x1, x2')
    obj = -(2*x1 - x2)
    variables = [x1, x2]

    c0 = x1 + x2 >= 2
    c1 = x1 - x2 >= 1
    c2 = x1 <= 3
    constrs = [c0, c1, c2]
    constrs_com = [GEQ, GEQ, LEQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', -simplex.optimal_y)


def example_5():

    # X=[0, 12, 5, 8], min_f=-19
    x1, x2, x3, x4 = symbols('x1, x2, x3, x4')
    obj = x1 - 2*x2 + x3
    variables = [x1, x2, x3, x4]

    c0 = 2*x1 - x2 + 4*x3 <= 8
    c1 = -x1 + 2*x2 - 4*x3 <= 4
    c2 = (x1 + x2 - 2*x3 + x4, 10)
    constrs = [c0, c1, c2]
    constrs_com = [LEQ, LEQ, EQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', simplex.optimal_y)


def example_6():

    # X=[0,1, 0], min_f=-1
    x1, x2, x3 = symbols('x1, x2, x3')
    obj = x1 - x2
    variables = [x1, x2, x3]

    c0 = -x1 + 2*x2 + x3 <= 2
    c1 = (-4*x1+4*x2-x3, 4)
    c2 = (x1-x3, 0)
    constrs = [c0, c1, c2]
    constrs_com = [LEQ, EQ, EQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', simplex.optimal_y)


def example_7():

    x1, x2, x3 = symbols('x1, x2, x3')
    obj = 3*x1 - 2*x2 + x3
    variables = [x1, x2, x3]

    c0 = 2*x1 + 3*x2 >= 8
    c1 = (2*x1 - 3*x2 + x3, 1)
    constrs = [c0, c1]
    constrs_com = [GEQ, EQ]

    simplex = Simplex(obj, variables, constrs, constrs_com)
    simplex.start()
    print('==> X=', simplex.optimal_X)
    print('==> y=', simplex.optimal_y)


def main():

    print('-'*25, '  ', '-'*25)
    print('-   0 -     ">=", "<=" “=”,      >=0,  min')
    print('-   1 -     "<=",      >=0,  max')
    print('-   2 -     "<=",      >=0,  mix')
    print('-   3 -     ">=",      >=0,  min')
    print('-   4 -     ">=" "<=",      >=0,  max')
    print('-   5 -     "<=" “=”,      >=0,  min')
    print('-   6 -     "<=" “=”,      >=0,  min')
    print('-   7 -     ">=" “=”,      >=0,  min')
    print('-' * 56)

    ex = input('      (0~7):')
    if int(ex) == 0:
        example_0()
    elif int(ex) == 1:
        example_1()
    elif int(ex) == 2:
        example_2()
    elif int(ex) == 3:
        example_3()
    elif int(ex) == 4:
        example_4()
    elif int(ex) == 5:
        example_5()
    elif int(ex) == 6:
        example_6()
    elif int(ex) == 7:
        example_7()


if __name__ == "__main__":
    main()