# Simplex Algorithm

gefragt 2017-08-26 01:29:37 +0100

There's one thing that I could not understand in Simplex is that which element pivots with which element.

I tried all the variables that I could pivot, and I got different answers (yeah, this could be obvious). However, the number of iterations to do the problem increases.

How do I know if have chosen the correct variable to pivot?

y0 := -1 x0 + 2 x1
y1 := -2 x0 + 1 x1
y2 := 1 x0 + 2 x1
-------------------------------------------------------
-oo <= x0 := 0 <= +oo
-oo <= x1 := 0 <= +oo
-oo <= y0 := 0 <= -3
-oo <= y1 := 0 <= 1
4 <= y2 := 0 <= +oo
=======================================================
pivoting x0 with y0 to set y0 := -3
=======================================================
x0 := -1 y0 + 2 x1
y1 := 2 y0 + -3 x1
y2 := -1 y0 + 4 x1
-------------------------------------------------------
-oo <= x0 := 3 <= +oo
-oo <= x1 := 0 <= +oo
-oo <= y0 := -3 <= -3
-oo <= y1 := -6 <= 1
4 <= y2 := 3 <= +oo


In this problem, when I tried to pivot y0 with y1, I got the answer in that iteration. But when I chose to pivot x1 with y1, I had to do one extra step.

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## 1 Antwort

geantwortet 2017-08-26 09:06:38 +0100

What you are asking for is still a topic of research. It is not clear which variable to choose next but of course, we could try all possibilities and would learn this way that some would have been the best choice at a certain stage. Clearly, that is not what we want since it is too expensive, but it shows that there are obviously better and not so good choices. How to distinguish between them is quite unclear and a matter of research. You may consult

http://cs.nyu.edu/courses/fall12/CSCI-GA.2945-002/pastproject2.pdf


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Gefragt: 2017-08-26 01:29:37 +0100

Gesehen: 67 mal

Letztes Update: Aug 26 '17