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simplex_method_in_fraction.py
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simplex_method_in_fraction.py
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'''
BlandSimplex built to return an optimal basic feasible solution and its value
1. Simplex method - Bland Rule
2. Argument object holds
an array of objective function coefficients
right-hand side entries
a matrix of coefficients for the left-hand-sides of the constraints
3. The processor built to perform mostly on Maximization problem
4. It will add slack variable automaticall
'''
from fractions import Fraction
import pandas as pd
class Arguments:
def __init__(self):
self.equations = ['x_1 + x_2 <= 6', 'x_1 - x_2 <= 0']
self.obj_atrributes = [5, 6] # [5, 2] #an array of objective function coefficients----------5x_1 + 2x_2
self.decision_variable_rhs = [5, 28] # [6, 0] # right-hand side entries
self.decision_variable_lhs = [[1, 1], [4, 7]] # [[1, 1],[1, -1 ]] #coefficients for the left-hand-sides of the constraints
self.no_equations = len(self.decision_variable_lhs)
self.no_variables = len(self.decision_variable_lhs[0])
self.lowbound = "x1, x2 >= 0"
def add_slack_variables(len, arr):
return arr + [ 0 for i in range(len)]
class ConvertIntoStandardForm:
def __init__(self):
self.obj = Arguments()
self.z_cof = 1 #Z coefficient -----------Always 1 initially
self.rhs = [0] + self.obj.decision_variable_rhs #add z = 0 initially in the right hand side
self.basic_variables = ['s_'+str(index+1) for index, i in enumerate(self.rhs[1:])] #Initially s_1, s_2
self.row_0_lhs = add_slack_variables( self.obj.no_equations, [self.z_cof] + [ -1 * r0 for r0 in self.obj.obj_atrributes]) #setting slack values initially to Objective function row
self.rows_lhs = [ [0] + add_slack_variables(self.obj.no_equations, cof) for cof in (self.obj.decision_variable_lhs)] #setting slack values to constraints initially
for idx , cof in enumerate(self.rows_lhs):
cof[ self.obj.no_variables + idx + 1] = 1 # 10
# 01
self.variables = ['z'] + ['x_'+str(i+1) for i in range(self.obj.no_variables)] + self.basic_variables
self.table_columns = self.variables + ['rhs', 'BV']
class MaximizationSimplex:
def __init__(self):
self.obj = Arguments()
self.stdform = ConvertIntoStandardForm()
print('--------------------------------------------------------------------------')
print('L.H.S of Objective Function"s Coefficients ', self.stdform.row_0_lhs)
print('R.H.S :', self.stdform.rhs)
print('Initial Basic Variables ', self.stdform.basic_variables)
print('L.H.S of Constraints" Coefficients : ', self.stdform.rows_lhs)
print('Basic Variables ', self.stdform.basic_variables)
print('Variables are ', self.stdform.variables)
print('table columns :', self.stdform.table_columns )
print('---------------------------------------------------------------------------')
print('Initial Stage ...')
table_rows = [self.stdform.row_0_lhs + [self.stdform.rhs[0]] + ['z']] + [
self.stdform.rows_lhs[i] + [self.stdform.rhs[i + 1]] + [self.stdform.basic_variables[i]]
for i in range(len(self.stdform.rows_lhs))]
df = pd.DataFrame(table_rows,
columns=self.stdform.table_columns)
df.style.set_properties(**{'text-align': 'center'})
print(df)
self._to_positive_objfun()
def substraction_op(self, indx, multiplied_row_0, multiplied_pivot_row):
return multiplied_row_0[indx] + multiplied_pivot_row[indx]
def fetch_pivot_row(self, entering_idx):
MIN = 0
pivot_row = list()
leaving_row_indx = 0
idnx = 0
for r_indx, r_coef in enumerate(self.stdform.rows_lhs):
#print("row ", r_coef, "coef", r_coef[entering_idx], 'row"s index', r_indx, 'rhs value ', self.stdform.rhs[r_indx + 1])
if r_coef[entering_idx] > 0: # coefficient in l.h.s should be greater than 0
ratio = round(self.stdform.rhs[r_indx + 1] / r_coef[entering_idx], 2)
if idnx == 0:
MIN = ratio
pivot_row = r_coef
leaving_row_indx = r_indx
else:
if ratio < MIN:
pivot_row = r_coef
MIN = ratio
leaving_row_indx = r_indx
idnx += 1
#print(MIN, pivot_row , leaving_row_indx, self.stdform.basic_variables[leaving_row_indx])
if pivot_row:
return MIN, pivot_row , leaving_row_indx, self.stdform.basic_variables[leaving_row_indx]
def calculate_ratio_quantities_replacements(self, entering_idx):
fetched_details = self.fetch_pivot_row(entering_idx)
if fetched_details:
MIN, initial_pivot_row, leaving_row_indx, leaving_var = fetched_details
#self.stdform.rhs[leaving_row_indx + 1] = round(self.stdform.rhs[leaving_row_indx + 1] / initial_pivot_row[entering_idx], 2)
self.stdform.rhs[leaving_row_indx + 1] = Fraction(
self.stdform.rhs[leaving_row_indx + 1], initial_pivot_row[entering_idx])
pivot_row = [Fraction(__p, initial_pivot_row[entering_idx]) for __p in initial_pivot_row]
self.stdform.rows_lhs[leaving_row_indx] = pivot_row
pivot = pivot_row[entering_idx]
entering_value = self.stdform.row_0_lhs[entering_idx]
#print('-------------------------------------------------------------------')
#print('Minimum ratio :', MIN, 'Pivot"s row :', pivot_row,'Pivot :',pivot, 'Leaving variable"s index', leaving_row_indx,
#'Leaving variable :',leaving_var, "Entering Varaible's index :" , entering_idx," Entering Variable : " , ( self.stdform.variables[entering_idx] ,entering_value))
#print('--------------------------------------------------------------------')
#########
#self.tabluea_calculations()
multiplied_row_0 = [__i * pivot for __index, __i in enumerate(self.stdform.row_0_lhs)]
multiplied_pivot_row = [__i * entering_value for __index, __i in enumerate(pivot_row)]
rhs_z_multiply = self.stdform.rhs[0] * pivot
rhs_pivot_multply = self.stdform.rhs[leaving_row_indx + 1] * entering_value
if sum([multiplied_pivot_row[entering_idx], multiplied_row_0[entering_idx]]) != 0:
multiplied_pivot_row = [__i * -1 for __index, __i in enumerate(multiplied_pivot_row)]
rhs_pivot_multply = rhs_pivot_multply * -1
self.stdform.row_0_lhs = [self.substraction_op(__i, multiplied_row_0, multiplied_pivot_row) for __i in range(len(self.stdform.row_0_lhs))]
self.stdform.rhs[0] = rhs_z_multiply + rhs_pivot_multply
self.stdform.basic_variables[leaving_row_indx] = self.stdform.variables[entering_idx] # s2 leaves = enters x1
#######
for __rindex, __rs in enumerate(self.stdform.rows_lhs):
if __rindex == leaving_row_indx:
#print('PIVOT"s Row ', pivot_row)
continue
multiplied_neighbour_row = [ __i * pivot for __index, __i in enumerate(__rs)]
multiplied_pivot_row = [__i * __rs[entering_idx] for __index, __i in enumerate(pivot_row)]
rhs_z_multiply = self.stdform.rhs[__rindex + 1] * pivot
rhs_pivot_multply = self.stdform.rhs[leaving_row_indx + 1] * __rs[entering_idx]
#print(rhs_z_multiply, rhs_pivot_multply)
if sum([multiplied_neighbour_row[entering_idx], multiplied_pivot_row[entering_idx]]) != 0:
multiplied_pivot_row = [__i * -1 for __index, __i in enumerate(multiplied_pivot_row)]
rhs_pivot_multply = rhs_pivot_multply * -1
self.stdform.rows_lhs[__rindex] = [self.substraction_op(__i, multiplied_neighbour_row, multiplied_pivot_row) for __i in range(len(__rs))]
self.stdform.rhs[__rindex + 1] = rhs_z_multiply + rhs_pivot_multply
print('------------------------------------------------------------------------------------')
print('-----------------------------------------------------------------------------------')
table_rows = [self.stdform.row_0_lhs + [self.stdform.rhs[0]] + ['z']] + [
self.stdform.rows_lhs[i] + [self.stdform.rhs[i + 1]] + [self.stdform.basic_variables[i]]
for i in range(len(self.stdform.rows_lhs))]
df = pd.DataFrame(table_rows,
columns=self.stdform.table_columns)
df.style.set_properties(**{'text-align': 'center'})
print(df)
print('------------------------------------------------------------------------------------')
return self.stdform.row_0_lhs
def _to_positive_objfun(self):
if [__v for __v in self.stdform.row_0_lhs if __v < 0]:
coef_row0 = min(self.stdform.row_0_lhs)
if coef_row0 < 0:
entering_idx = self.stdform.row_0_lhs.index(coef_row0)
#print(entering_idx, 'entering', self.stdform.rows_lhs)
res = self.calculate_ratio_quantities_replacements(entering_idx)
if res == None:
print('------------------------------------------------------------------------------------')
print('Final Output')
print('------------------------------------------------------------------------------------')
print('UNBOUNDED LP')
table_rows = [self.stdform.row_0_lhs + [self.stdform.rhs[0]] + ['z']] + [ self.stdform.rows_lhs[i] + [self.stdform.rhs[i+1]] + [self.stdform.basic_variables[i]]
for i in range(len(self.stdform.rows_lhs)) ]
df = pd.DataFrame(table_rows,
columns=self.stdform.table_columns)
df.style.set_properties(**{'text-align': 'center'})
print(df)
else:
return self._to_positive_objfun()
else:
print("--------------------------------------------------------------------------------------")
print('Final Output')
print('--------------------------------------------------------------------------------------')
print("")
table_rows = [self.stdform.row_0_lhs + [self.stdform.rhs[0]] + ['z']] + [
self.stdform.rows_lhs[i] + [self.stdform.rhs[i + 1]] + [self.stdform.basic_variables[i]]
for i in range(len(self.stdform.rows_lhs))]
df = pd.DataFrame(table_rows,
columns=self.stdform.table_columns)
df.style.set_properties(**{'text-align': 'center'})
print(df)
MaximizationSimplex()