Simplex Algorithm
11-14-2023, 10:39 AM
Post: #18
 ftneek Member Posts: 83 Joined: Oct 2022
RE: Simplex Algorithm
(11-14-2023 09:23 AM)Albert Chan Wrote:  simplex_le can do dual problem, with identity matrix squeeze inside.
Video 1st dual probelm (time = 6 .. 17 minutes)

> simplex_le([[2,4,40],[1,1,12],[5,1,40],[20,30,0]],+∞)

That is impressive, much less typing, and matches the standard form output of simplex2. Can simplex_le() already solve dual problem with "=" constraints? I think the only thing it really needs is a way to set up artificial variables.

Odd, for whatever reason the video explained it the opposite way from my understanding. According to our source, primal is given by b column while dual is found in c row. Anyhow, the final tableau matches simplex2 exactly!

If you would like to make another optimization, there is potentially one regarding duality. Sometimes the dual or the primal is easier to solve (it might have positive variables or only needs slack variables, or a certain quality that makes it "easier"). Choosing the "easier" problem to solve may require less computation, and the solution to the harder problem is provided by duality.

Finally, I had a little time to start making some "tests". But for some reason test 3 returns 0, even after directly copying the result from the command history... Would you happen to know why? I'm not sure if this is the best way to maintain tests, and it would be nice if they don't all show up in the catalog, only a single wrapper that runs them. Since we only are checking the equivalency of 2 items, does it really need to be a cas program? I would appreciate tips on how to organize it, I think it's important to ensure refactoring simplex2 does not cause correct solutions to change.

Code:
#cas test_simplex():= BEGIN RETURN {test_case_1(),test_case_2(),test_case_3(),test_case_4()}; END; // Example 3.7.2 test_case_1():= BEGIN RETURN simplex2([[1,2,0,1,1,0,0,20],[2,1,1,0,0,1,0,10],[-1,4,-2,3,0,0,1,40],[1,4,3,2,0,0,0,0],[0,0,0,0,1,1,1,0]],{5,6,7},7,3,0)==[35,[5,0,0,15,0,0,0],[[1,1/2,1/2,0,3/4,0,-1/4,5],[0,0,0,0,-3/2,1,1/2,0],[0,3/2,-1/2,1,1/4,0,1/4,15],[0,1/2,7/2,0,-5/4,0,-1/4,-35]]]; END; test_case_2():= BEGIN RETURN simplex2([[2,4,-1,0,0,1,0,0,22],[3,2,0,-1,0,0,1,0,20],[4,5,0,0,-1,0,0,1,40],[6,5,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,0]],{6,7,8},8,3,0)==[320/7,[20/7,40/7,46/7,0,0,0,0,0],[[0,1,0,4/7,-3/7,0,-4/7,3/7,40/7],[1,0,0,-5/7,2/7,0,5/7,-2/7,20/7],[0,0,1,6/7,-8/7,-1,-6/7,8/7,46/7],[0,0,0,10/7,3/7,0,-10/7,-3/7,-320/7]]]; END; test_case_3():= BEGIN RETURN simplex2([[-2,-4,1,0,0,-22],[-3,-2,0,1,0,-20],[-4,-5,0,0,1,-40],[6,5,0,0,0,0]],{3,4,5},5,0,0)==[320/7,[20/7,40/7,46/7,0,0],[[0,0,1,6/7,-8/7,46/7],[1,0,0,-5/7,2/7,20/7],[0,1,0,4/7,-3/7,40/7],[0,0,0,10/7,3/7,-320/7]]]; END; test_case_4():= BEGIN RETURN 4; END; #end

- neek
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 Messages In This Thread Simplex Algorithm - ftneek - 11-11-2023, 11:21 PM RE: Simplex Algorithm - Albert Chan - 11-11-2023, 11:51 PM RE: Simplex Algorithm - Albert Chan - 11-12-2023, 12:38 AM RE: Simplex Algorithm - Albert Chan - 11-12-2023, 05:11 PM RE: Simplex Algorithm - ftneek - 11-12-2023, 05:40 PM RE: Simplex Algorithm - Albert Chan - 11-13-2023, 02:48 PM RE: Simplex Algorithm - ftneek - 11-12-2023, 12:00 AM RE: Simplex Algorithm - ftneek - 11-12-2023, 01:44 AM RE: Simplex Algorithm - Albert Chan - 11-12-2023, 11:04 PM RE: Simplex Algorithm - ftneek - 11-13-2023, 01:51 AM RE: Simplex Algorithm - Albert Chan - 11-12-2023, 08:46 PM RE: Simplex Algorithm - ftneek - 11-12-2023, 10:09 PM RE: Simplex Algorithm - ftneek - 11-13-2023, 05:34 PM RE: Simplex Algorithm - Albert Chan - 11-13-2023, 10:46 PM RE: Simplex Algorithm - Albert Chan - 11-14-2023, 02:25 AM RE: Simplex Algorithm - ftneek - 11-14-2023, 06:24 AM RE: Simplex Algorithm - Albert Chan - 11-14-2023, 09:23 AM RE: Simplex Algorithm - ftneek - 11-14-2023 10:39 AM RE: Simplex Algorithm - Albert Chan - 11-15-2023, 04:36 PM RE: Simplex Algorithm - ftneek - 11-15-2023, 05:58 PM RE: Simplex Algorithm - Albert Chan - 11-16-2023, 11:42 AM RE: Simplex Algorithm - Albert Chan - 11-16-2023, 07:15 PM RE: Simplex Algorithm - ftneek - 11-17-2023, 07:47 AM RE: Simplex Algorithm - Albert Chan - 11-17-2023, 11:04 AM RE: Simplex Algorithm - ftneek - 11-18-2023, 01:27 AM RE: Simplex Algorithm - ftneek - 11-18-2023, 10:31 PM RE: Simplex Algorithm - Albert Chan - 11-19-2023, 12:57 AM RE: Simplex Algorithm - ftneek - 11-19-2023, 07:05 AM RE: Simplex Algorithm - Albert Chan - 11-19-2023, 04:58 PM RE: Simplex Algorithm - Albert Chan - 11-20-2023, 06:12 PM RE: Simplex Algorithm - ftneek - 11-21-2023, 08:36 AM RE: Simplex Algorithm - Albert Chan - 11-21-2023, 02:05 PM RE: Simplex Algorithm - ftneek - 11-19-2023, 08:02 PM RE: Simplex Algorithm - ftneek - 11-20-2023, 12:18 AM RE: Simplex Algorithm - Albert Chan - 11-20-2023, 02:14 AM RE: Simplex Algorithm - ftneek - 11-20-2023, 09:02 AM RE: Simplex Algorithm - Albert Chan - 11-20-2023, 11:42 AM RE: Simplex Algorithm - Albert Chan - 11-20-2023, 03:34 PM RE: Simplex Algorithm - ftneek - 11-20-2023, 07:52 PM RE: Simplex Algorithm - Albert Chan - 11-21-2023, 05:58 PM RE: Simplex Algorithm - Albert Chan - 11-21-2023, 11:20 PM RE: Simplex Algorithm - Albert Chan - 11-22-2023, 06:44 PM RE: Simplex Algorithm - Albert Chan - 11-22-2023, 10:10 PM RE: Simplex Algorithm - Albert Chan - 12-24-2023, 03:46 PM RE: Simplex Algorithm - ftneek - 12-24-2023, 07:32 PM RE: Simplex Algorithm - Albert Chan - 12-24-2023, 08:05 PM RE: Simplex Algorithm - ftneek - 11-23-2023, 01:23 AM RE: Simplex Algorithm - Albert Chan - 11-23-2023, 06:35 AM RE: Simplex Algorithm - ftneek - 12-22-2023, 07:38 AM RE: Simplex Algorithm - Albert Chan - 12-22-2023, 04:07 PM RE: Simplex Algorithm - ftneek - 12-22-2023, 07:28 PM RE: Simplex Algorithm - Albert Chan - 12-23-2023, 04:44 AM RE: Simplex Algorithm - ftneek - 12-23-2023, 07:46 AM RE: Simplex Algorithm - Albert Chan - 12-23-2023, 10:23 AM RE: Simplex Algorithm - ftneek - 12-23-2023, 09:30 PM RE: Simplex Algorithm - ftneek - 01-07-2024, 02:40 AM

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