Friday, January 4, 2019

Implied Multiple Objectives

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In [1] a simple problem was posed: Given data: try to load the trucks such that they have as few different items as possible. It is no...
Sunday, December 23, 2018

Linearizing multiple XOR operations

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I have never encountered this in a model. but nevertheless this is an interesting question. How can we handle \[y = x_1 \oplus x_2 \oplu...
2 comments:
Friday, December 21, 2018

An interesting linearization involving xor

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XOR gate sold by Amazon [1] In [2] a question was asked: How can we solve \[x^TAy = b\] for \(x_i, y_i \in \{-1,+1\}\)? In this ...
Monday, December 10, 2018

More queens problems (2)

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In [1], I discussed the  Minimum Dominating Set of Queens Problem . Here is a variant: Given an \(n \times n\) chess board, place \(n\) ...
Saturday, December 8, 2018

More queens problems

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In [1] the famous \(n\)-queens problem was discussed: how many queens can we place on a chess-board such that non of them are attacked by o...
1 comment:
Tuesday, November 27, 2018

Chess and solution pool

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The \(n\)-queens problem is a popular example of a "chessboard non-attacking problem" [1,2]: On an \(n \times n\) chessboard p...
Monday, November 19, 2018

Solving many scenarios

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In [1] a problem is described: Select 2 teams of 6 players from a population of 24 players such that the average ELO rating of each tea...
Sunday, November 11, 2018

Selecting Chess Players

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In [1] a simple problem was posted: We have a population of \(N=24\) players, each with an ELO rating \(r_i\) We need to select \(2...
Saturday, November 10, 2018

Quadratic Programming with Binary Variables

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Quadratic Programming models where the quadratic terms involve only binary variables are interesting from a modeling point view: we can ap...