def __init__(self, type=OptimizationType.maximization, **kwargs):
self.variable_names = [] # 所有变量，包括松弛变量
self.original_variables = [] # 优化目标中包含的变量
self.left_side = [] # 存储扩展后方程组左侧的系数
self.right_side = [] # 存储扩展后方程组右侧的常数
self.ratio = [] # 存储各方程组的离速
self.basic_variables = [] # 基变量列表
self.slack_variables = [] # 松弛变量列表
self.artificial_variables = [] # 人工变量列表
self.surplus_variables = [] # 剩余变量
if type == OptimizationType.maximization:
eq0 = [FractionWithM(1)]
for v in kwargs:
self.variable_names.append(v)
self.original_variables.append(len(self.variable_names) - 1)
eq0.append(FractionWithM(-kwargs[v]))
else:
eq0 = [FractionWithM(-1)]
for v in kwargs:
self.variable_names.append(v)
self.original_variables.append(len(self.variable_names) - 1)
eq0.append(FractionWithM(kwargs[v]))
self.left_side.append(eq0)
self.right_side.append(FractionWithM(0))
self.ratio.append('')
self.basic_variables.append(None)
def add_greater_constraint(self, constraint, **kwargs):
eq0 = self.left_side[0]
eq0.append(FractionWithM(0))
eq0.append(FractionWithM(M=1, value=0))
for i in range(1, len(self.left_side)):
eq = self.left_side[i]
eq.append(FractionWithM(0))
eq.append(FractionWithM(0))
eq = [FractionWithM(0)]
for var in self.variable_names:
if var in kwargs:
eq.append(FractionWithM(kwargs[var]))
else:
eq.append(FractionWithM(0))
eq.append(FractionWithM(-1))
eq.append(FractionWithM(1))
self.left_side.append(eq)
self.right_side.append(FractionWithM(constraint))
self.ratio.append('')
self.variable_names.append('_ss' +
str(len(self.surplus_variables) + 1))
self.surplus_variables.append(len(self.variable_names) - 1)
self.variable_names.append('_a' +
str(len(self.artificial_variables) + 1))
self.artificial_variables.append(len(self.variable_names) - 1)
self.basic_variables.append(len(self.variable_names) - 1)
def __init__(self, **kwargs):
"""
创建优化模型，并建立（最大化）优化目标函数
:param kwargs: 目标函数中各变量的系数
"""
self.variable_names = [] # 所有变量的变量名，包括松弛变量
self.original_variables = [] # 优化目标中包含的变量
self.left_side = [] # 存储扩展后方程组左侧的系数矩阵（用二维列表表示）
self.right_side = [] # 存储扩展后方程组右侧的常数
self.ratio = [] # 存储各方程组的离速
self.basic_variables = [] # 基变量列表
self.slack_variables = [] #松弛变量列表
self.artificial_variables = [] #人工变量列表
eq0 = [FractionWithM(1)]
for v in kwargs:
self.variable_names.append(v)
self.original_variables.append(len(self.variable_names) - 1)
eq0.append(FractionWithM(-kwargs[v]))
self.left_side.append(eq0)
self.right_side.append(FractionWithM(0))
self.ratio.append('')
self.basic_variables.append(None)
def add_equal_constraint(self, constraint, **kwargs):
"""
添加约束（等于）
:param constaint: 右侧的约束值，必须大于0
:param kwargs: 左侧各变量的系数
:return: 无
"""
eq0 = self.left_side[0]
eq0.append(FractionWithM(M=1, value=0))
for i in range(1, len(self.left_side)):
eq = self.left_side[i]
eq.append(FractionWithM(0))
eq = [FractionWithM(0)]
for var in self.variable_names:
if var in kwargs:
eq.append(FractionWithM(kwargs[var]))
else:
eq.append(FractionWithM(0))
eq.append(FractionWithM(1))
self.left_side.append(eq)
self.right_side.append(FractionWithM(constraint))
self.ratio.append('')
self.variable_names.append('_a' + str(len(self.left_side) - 1))
self.artificial_variables.append(len(self.variable_names) - 1)
self.basic_variables.append(len(self.variable_names) - 1)
def add_less_constraint(self, constraint, **kwargs):
for eq in self.left_side:
eq.append(FractionWithM(0))
eq = [FractionWithM(0)]
for var in self.variable_names:
if var in kwargs:
eq.append(FractionWithM(kwargs[var]))
else:
eq.append(FractionWithM(0))
eq.append(FractionWithM(1))
self.left_side.append(eq)
self.right_side.append(FractionWithM(constraint))
self.ratio.append('')
self.variable_names.append('_s' + str(len(self.slack_variables) + 1))
self.slack_variables.append(len(self.variable_names) - 1)
self.basic_variables.append(len(self.variable_names) - 1)
def add_less_constraint(self, constraint, **kwargs):
"""
添加约束（小于等于）
:param constaint: 右侧的约束值，必须大于0
:param kwargs: 左侧各变量的系数
:return: 无
"""
for eq in self.left_side:
eq.append(FractionWithM(0))
eq = [FractionWithM(0)]
for var in self.variable_names:
if var in kwargs:
eq.append(FractionWithM(kwargs[var]))
else:
eq.append(FractionWithM(0))
eq.append(FractionWithM(1))
self.left_side.append(eq)
self.right_side.append(FractionWithM(constraint))
self.ratio.append('')
self.variable_names.append('_s' + str(len(self.left_side) - 1))
self.slack_variables.append(len(self.variable_names) - 1)
self.basic_variables.append(len(self.variable_names) - 1)
def solve(self):
print("Intial form:")
print('---------------------------------')
self._display(highlight=False)
print()
print("Converting Equaiton(0) to proper form:")
print('---------------------------------')
self._eliminate_artificials()
self._display(highlight=False)
iteration = 0
while True:
iteration += 1
print(f'iteration {iteration}:')
print('---------------------------------')
# Optimality Test
# find the variable with the minimum negative coeffecient
eq0 = self.left_side[0]
min_v = FractionWithM(0)
min_i = -1
for i in range(1, len(eq0)):
if eq0[i] < min_v:
min_v = eq0[i]
min_i = i
if min_v == 0:
print("The solution is optimal")
break
enter_basic = min_i
# Minumum Ratio Test
min_ratio = None
min_i = -1
for i in range(1, len(self.left_side)):
eq = self.left_side[i]
if eq[enter_basic] == 0:
self.ratio[i] = ''
else:
denominator = eq[enter_basic]
if denominator <= 0:
self.ratio[i] == ''
else:
self.ratio[i] = self.right_side[i] / denominator
if min_ratio is None or self.ratio[i] < min_ratio:
min_ratio = self.ratio[i]
min_i = i
if min_i == -1:
print("can't find the minimum ratio!")
return
leaving_basic_eq_index = min_i
leaving_basic = self.basic_variables[min_i]
self._display(enter_basic - 1, leaving_basic_eq_index)
print("Entering basic :", self.variable_names[enter_basic - 1])
print("leaving basic:", self.variable_names[leaving_basic])
# Gaussian Elimination
leaving_basic_eq = self.left_side[min_i]
denominator = leaving_basic_eq[enter_basic]
for i in range(len(leaving_basic_eq)):
leaving_basic_eq[i] /= denominator
self.right_side[min_i] /= denominator
self.basic_variables[min_i] = enter_basic - 1
for i in range(len(self.left_side)):
if i == min_i:
continue
eq = self.left_side[i]
multiple = eq[enter_basic]
for j in range(len(eq)):
eq[j] -= multiple * leaving_basic_eq[j]
self.right_side[i] -= multiple * self.right_side[min_i]
self._display(highlight=False)
self._display_solution()