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maximization-simplex-method.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
'''
import pandas as pd
class Arguments:
def __init__(self):
self.equations = ['x_1 + x_2 <= 6', 'x_1 - x_2 <= 0']
self.obj_atrributes = [3, 2, 4] # [5, 2] #an array of objective function coefficients----------5x_1 + 2x_2
self.decision_variable_rhs = [9, 18, -18, -7] # [6, 0] # right-hand side entries
self.decision_variable_lhs = [[1, 1, 1], [3, 1, 4], [-3, -1, -4], [-1, -2, 0]] # [[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 BlandSimplex:
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)
pivot_row = [__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)
BlandSimplex()