Simplex Algorithm

11202023, 07:52 PM
(This post was last modified: 11202023 08:35 PM by ftneek.)
Post: #37




RE: Simplex Algorithm
(11202023 03:34 PM)Albert Chan Wrote: Question about simplex_int(a,bv,v,art,ign,integers) Yes my mistake. Technically 'v' should increase every iteration, not just once. But the user may not care about these extra variable solutions, so for now it's probably not a big deal, but can be fixed. I think I meant to do something like ++v. But I think how the 'v' argument is handled may change in the future, probably when I figure out how to implement "unrestricted" variables (and/or symbolic input). simplex_core works with unrestricted variables, but again for now you have to put it in standard form yourself. Ex: x1 is unrestricted (<=0 or >=0) and integer > x1=x1'x1'' where x1',x1''>=0 and integer From user's perspective, the original system only has v variables. But once in standard form we've added columns for slack and artificial variables (and fixed unrestricted variables), so from simplex_core perspective we should have v=col1. As you say, the only difference v has right now is the number of left most solutions to read. If we had unrestricted variables, the solution user expects != solve original v leftmost variables, we have to recover what the unrestricted variables are from the xi=xi'xi'' relation. I gave an example a few comments ago, integers is a list of variables with integer restriction. For example x1,x2 integer > integers:=[1,2] x2,x3 integer > integers:=[2,3] x1,x3 integer > integers:=[1,3] x3 integer > integers:=[3] Last the point I wanted to make was that for >= constraint we do not actually need to add an artificial variable at all since we use dual simplex, we either multiply constraint by 1 and add slack or add negative slack, which is the same thing because you still have to multiply the row by 1 to make the column 'canonical'. Thus for ">=" constraint giving input of negative slack for initial bv is fine if we pivot on it or multiply the row by 1 as the 'pivot' operation. I will look at the rest of the changes a bit later. My main concern is that it could limit the number of ways the user can input a system and get to the same solution. simplex_core is flexible in how the constraints are ordered.  neek 

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