object SimplexBGTest extends App
The SimplexBGTest object is used to test the SimplexBG class.
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Test the BG Simplex Algorithm for solving Linear Programming problems.
Test the BG Simplex Algorithm for solving Linear Programming problems.
- a
the constraint matrix
- b
the limit/RHS vector
- c
the cost vector
- x_B
the indices of the initial basis
- def test1(): Unit
Test case 1: Initialize matrix 'a', vectors 'b' and 'c', and optionally the basis 'x_B'.
Test case 1: Initialize matrix 'a', vectors 'b' and 'c', and optionally the basis 'x_B'. For BG Simplex, matrix 'a' must be augmented with an identity matrix and vector 'c' augmented with zeros. ------------------------------------------------------------------------- Minimize z = -1x_0 - 2x_1 + 1x_2 - 1x_3 - 4x_4 + 2x_5 Subject to 1x_0 + 1x_1 + 1x_2 + 1y_3 + 1y_4 + 1x_5 <= 6 2x_0 - 1x_1 - 2x_2 + 1y_3 + 0y_4 + 0x_5 <= 4 0x_0 + 0x_1 + 1x_2 + 1y_3 + 2y_4 + 1x_5 <= 4 where z is the objective variable and x is the decision vector. ------------------------------------------------------------------------- Solution: primal x_1 = 4, x_7 = 8, x_4 = 2 dual y_1 = -2, y_2 = 0, y_3 = -1 objF f = -16 i.e., x = (4, 8, 2), x_B = (1, 7, 4), y = (-2, 0, -1), f = -16
- See also
Linear Programming and Network Flows, Example 5.1
- def test2(): Unit
Test case 2: Solution: x = (2/3, 10/3, 0), x_B = (0, 1, 5), f = -22/3
Test case 2: Solution: x = (2/3, 10/3, 0), x_B = (0, 1, 5), f = -22/3
- See also
Linear Programming and Network Flows, Example 5.2
- def test3(): Unit
Test case 3: Solution: x = (1/3, 0, 13/3), x_B = (0, 2, 4), f = -17
Test case 3: Solution: x = (1/3, 0, 13/3), x_B = (0, 2, 4), f = -17
- See also
Linear Programming and Network Flows, Example 3.9
- def test4(): Unit
Test case 4: randomly generated LP problem.
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