313 lines
8.6 KiB
Python
313 lines
8.6 KiB
Python
import numpy as np
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from typing import Optional
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from enum import Enum
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# M constant
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M = 1_000_000
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class State(Enum):
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SOLVED = 0
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UNAPPLICABLE = 2
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class Result:
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solved: State
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objective_function_value: Optional[np.int64]
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solution: Optional[np.array]
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def __init__(self,
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solved: State,
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objective_function_value: Optional[np.array] = None,
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solution: np.int64 = None):
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self.solved = solved
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self.objective_function_value = objective_function_value
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self.solution = solution
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def NorthwestCorner(S: np.array,
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C: np.array,
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D: np.array) -> Result:
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num_rows, num_cols = len(S), len(D)
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solution = np.zeros((num_rows, num_cols), dtype=np.int64)
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i, j = 0, 0
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while i < num_rows and j < num_cols:
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quantity = min(S[i], D[j])
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solution[i][j] = quantity
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S[i] -= quantity
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D[j] -= quantity
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if S[i] == 0:
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i += 1
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elif D[j] == 0:
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j += 1
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if sum(S) == 0 and sum(D) == 0:
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objective_function_value = np.sum(solution * C)
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return Result(State.SOLVED, objective_function_value, solution)
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else:
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return Result(State.UNAPPLICABLE)
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def Vogel(
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S: np.array,
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C: np.array,
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D: np.array) -> Result:
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iteration = 0
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while (len(C[0]) > 1 and len(C) > 1):
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iteration += 1
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C_map = dict()
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for y in range(len(C)):
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for x in range(len(C[0])):
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C_map[x, y] = C[y][x]
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C_length = len(C[0])
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C_height = len(C)
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RowD = np.array
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ColD = np.array
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RowD = np.resize(RowD, C_height)
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ColD = np.resize(ColD, C_length)
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# Finding differences
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for y in range(C_height):
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RowD[y] = abs(sorted(C[y])[0] - sorted(C[y])[1])
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for x in range(C_length):
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ColD[x] = abs(sorted(C.T[x])[0] - sorted(C.T[x])[1])
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# Maximum difference
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maxD = max(np.concatenate((ColD, RowD)))
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target_array = None
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target_number = None
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row_index_to_eleminate = None
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column_index_to_eleminate = None
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if maxD in RowD:
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y = np.where(RowD == maxD)[0][0]
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target_array = C[np.where(RowD == maxD)[0]][0]
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target_number = min(target_array)
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x = np.where(target_array == target_number)[0][0]
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if (D[x] >= S[y]):
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row_index_to_eleminate = y
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selected_value = S[y]
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D[x] -= selected_value
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C = np.delete(C, row_index_to_eleminate, 0)
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S = np.delete(S, row_index_to_eleminate, 0)
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else:
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column_index_to_eleminate = x
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selected_value = D[x]
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S[y] -= selected_value
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C = np.delete(C, column_index_to_eleminate, 1)
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D = np.delete(D, column_index_to_eleminate, 0)
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if maxD in ColD:
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x = np.where(ColD == maxD)[0][0]
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target_array = C.T[np.where(ColD == maxD)[0]][0]
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target_number = min(target_array)
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y = np.where(target_array == target_number)[0][0]
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if (D[x] >= S[y]):
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row_index_to_eleminate = y
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selected_value = S[y]
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D[x] -= selected_value
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C = np.delete(C, row_index_to_eleminate, 0)
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S = np.delete(S, row_index_to_eleminate, 0)
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else:
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column_index_to_eleminate = x
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selected_value = D[x]
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S[y] -= selected_value
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C = np.delete(C, column_index_to_eleminate, 1)
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D = np.delete(D, column_index_to_eleminate, 0)
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if target_array is not None:
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objective_function_value = np.sum(np.dot(C, target_array))
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return Result(State.SOLVED, objective_function_value, target_array)
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else:
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return Result(State.UNAPPLICABLE)
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def Russell(
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S: np.array,
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C: np.array,
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D: np.array) -> Result:
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selected = np.zeros(C.shape)
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remaining_rows = np.ones(C.shape[0], dtype=bool)
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remaining_cols = np.ones(C.shape[1], dtype=bool)
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x_0 = np.zeros(C.shape, dtype=np.int64)
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it_count = 0
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while True:
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mask = np.outer(remaining_rows, remaining_cols)
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u = np.max(np.where(mask, C, -M), axis=1)
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v = np.max(np.where(mask, C, -M), axis=0)
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d = np.zeros(C.shape, dtype=np.int64)
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for i in range(C.shape[0]):
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for j in range(C.shape[1]):
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if selected[i][j]:
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d[i][j] = M
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else:
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d[i][j] = C[i][j] - u[i] - v[j]
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i, j = np.unravel_index(np.argmin(d, axis=None), d.shape)
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if (D[j] == 0):
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break
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if (S[i] >= D[j]):
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x_0[i][j] = D[j]
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S[i] -= D[j]
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D[j] = 0
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remaining_cols[j] = 0
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else:
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x_0[i][j] = S[i]
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D[j] -= S[i]
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S[i] = 0
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remaining_rows[i] = 0
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selected[i][j] = 1
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it_count += 1
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if (it_count > 1000):
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return Result(State.UNAPPLICABLE)
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return Result(State.SOLVED, C * x_0, x_0)
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'''
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#SAMPLE INPUT FOR TESTING
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S = np.array([50, 60, 50, 50])
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C = np.array([
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[16, 16, 13, 22, 17],
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[14, 14, 13, 19, 15],
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[19, 19, 20, 23, M ],
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[M, 0, M, 0, 0]])
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D = np.array([30, 20, 70, 30, 60])
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'''
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def print_problem_statement(
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S: np.array,
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C: np.array,
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D: np.array) -> None:
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S = S.astype(object)
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S = np.append(S, "_").reshape(-1, 1)
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matrix = np.append(C, [D], axis=0)
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matrix = np.hstack((matrix, S))
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matrix = matrix.astype(object)
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matrix[matrix == M] = "M"
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print("Initial full matrix:")
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print(matrix)
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#print(print_problem_statement(S,C,D))
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def solve(
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S: np.array,
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C: np.array,
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D: np.array,
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NWExpected: np.array,
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VogelExpected: np.array,
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RussellExpected: np.array,
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) -> int:
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print_problem_statement(S, C, D)
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if (np.sum(S) != np.sum(D)):
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print("The problem is not balanced!")
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return 1
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result1 = NorthwestCorner(S.copy(), C.copy(), D.copy())
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result2 = Vogel(S.copy(), C.copy(), D.copy())
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result3 = Russell(S.copy(), C.copy(), D.copy())
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if (any([result1.solved == State.UNAPPLICABLE,
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result2.solved == State.UNAPPLICABLE,
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result3.solved == State.UNAPPLICABLE])):
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print("The method is not applicable!")
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return 1
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if (not np.all(NWExpected == result1.solution)):
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print("Incorrect initial basic feasible solution for North-West.\n",
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f"Got:\n{result1.solution}.\n Expected:\n{NWExpected}.")
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return 0
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if (not np.all(VogelExpected == result2.solution)):
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print("Incorrect initial basic feasible solution for Vogel's approximation.\n",
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f"Got:\n{result2.solution}.\n Expected:\n{VogelExpected}.")
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return 0
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if (not np.all(RussellExpected == result3.solution)):
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print("Incorrect initial basic feasible solution for Russell's approximation.\n",
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f"Got:\n{result3.solution}.\nExpected:\n{RussellExpected}.")
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return 0
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print("North-West initial basic feasible solution:\n", result1.solution,
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"\nVogel's approximation intial basic feasible solution:\n", result2.solution,
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"\nRussell's approximation initial basic feasible solution:\n", result3.solution)
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return 1
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def TEST_CASE_1():
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print("----------------------RUNNING_TEST_CASE_1----------------------")
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C = np.array([
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[16, 16, 13, 22, 17],
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[14, 14, 13, 19, 15],
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[19, 19, 20, 23, M],
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[M, 0, M, 0, 0]
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], dtype=np.int64)
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S = np.array([
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50, 60, 50, 50
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], dtype=np.int64)
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D = np.array([
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30, 20, 70, 30, 60
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], dtype=np.int64)
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print_problem_statement(S, C, D)
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NWExpected = np.array([
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[30, 20, 0, 0, 0],
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[0, 0, 60, 0, 0],
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[0, 0, 10, 30, 10],
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[0, 0, 0, 0, 50]
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], dtype=np.int64)
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VogelExpected = np.array([
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[0, 0, 50, 0, 0],
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[0, 0, 20, 0, 40],
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[30, 20, 0, 0, 0],
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[0, 0, 0, 30, 20]
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], dtype=np.int64)
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RussellExpected = np.array([
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[0, 0, 40, 0, 10],
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[30, 0, 30, 0, 0],
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[0, 20, 0, 30, 0],
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[0, 0, 0, 0, 50]
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], dtype=np.int64)
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return solve(S, C, D, NWExpected, VogelExpected, RussellExpected)
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if __name__ == "__main__":
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tests = [TEST_CASE_1]
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tests_passed = 0
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for test in tests:
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tests_passed += test()
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print("----------------------RESULTS----------------------")
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print(f"Total number of tests: {len(tests)}")
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print(f"Total number of passed tests: {tests_passed}")
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