SimplexMethod

README.md

@@ -1,2 +1,13 @@
 # SimplexMethod
+Команда: Заргаров Марат, Сергунов Максим
+
+Найти оптимальное решение симплекс методом:
+f(x) = 2x1 + 3x2 -> max
+
+Ограничения: 
+x1 + 3x2 <= 18
+2x1 + x2 <= 16
+x2 <= 5
+3x1 <= 21
+x1,x2 >= 0
 

SimplexMethod.py

@@ -0,0 +1,86 @@
+import numpy as np
+import math
+
+class Simplex:
+    def __init__(self, source):
+        self.m, self.n = source.shape
+        self.table = np.zeros((self.m, self.n + self.m - 1))
+        self.basis = []
+
+        for i in range(self.m):
+            for j in range(self.n):
+                self.table[i, j] = source[i, j]
+
+            if (self.n + i) < self.table.shape[1]:
+                self.table[i, self.n + i] = 1
+                self.basis.append(self.n + i)
+
+        self.n = self.table.shape[1]
+
+    def calculate(self, result):
+        while not self.is_it_end():
+            main_col = self.find_main_col()
+            main_row = self.find_main_row(main_col)
+            self.basis[main_row] = main_col
+
+            new_table = np.zeros((self.m, self.n))
+
+            for j in range(self.n):
+                new_table[main_row, j] = self.table[main_row, j] / self.table[main_row, main_col]
+
+            for i in range(self.m):
+                if i == main_row:
+                    continue
+
+                for j in range(self.n):
+                    new_table[i, j] = self.table[i, j] - self.table[i, main_col] * new_table[main_row, j]
+
+            self.table = new_table
+
+        for i in range(len(result)):
+            k = self.basis.index(i + 1) if i + 1 in self.basis else None
+            if k != None:
+                result[i] = self.table[k, 0]
+            else:
+                result[i] = 0
+
+        return self.table
+
+    def is_it_end(self):
+        return all(self.table[self.m - 1, 1:] >= 0)
+
+    def find_main_col(self):
+        return np.argmin(self.table[self.m - 1, 1:]) + 1
+
+    def find_main_row(self, main_col):
+        main_row = 0
+        for i in range(self.m - 1):
+            if self.table[i, main_col] > 0:
+                main_row = i
+                break
+        for i in range(main_row + 1, self.m - 1):
+            if (self.table[i, main_col] > 0) and ((self.table[i, 0] / self.table[i, main_col]) < (self.table[main_row, 0] / self.table[main_row, main_col])):
+                main_row = i
+
+        return main_row
+
+if __name__ == "__main__":
+    table = np.array([[18, 1, 3],
+                      [16, 2, 1],
+                      [5, 0, 0],
+                      [21, 3, 0],
+                      [0, -2, -3]])
+
+    result = np.zeros(2)
+    table_result = Simplex(table).calculate(result)
+
+    print("Оптимальная таблица:")
+    for i in range(table_result.shape[0]):
+        for j in range(table_result.shape[1]):
+            print("%5.2f " % table_result[i][j], end='')
+        print()
+
+    print("\nРешение:")
+    print(f"x1 = {result[0]}")
+    print(f"x2 = {math.ceil(result[1])}")
+    print(f"max = {-table[-1][-2] * result[0] + -table[-1][-1] * math.ceil(result[1])}")