I'm using the Java API to CP Optimizer. If I want to use an integer variable as an index to a 1-D variable array (IloIntVar[]), IloCP.element() works fine. My question is whether there is an "elegant" method to use two IloIntVar instances to index a 2-D variable array (IloIntVar[][]). Trying to do this with two applications of element() does not work. I was hoping that calling element() with an IloIntVar[][] argument would return one row of the matrix (IloIntVar[]), but it throws an error.

The inelegant solution is to flatten the 2-D matrix to a 1-D matrix by doing arithmetic on the indices (converting (i, j) to a single index k), but that makes the code both a bit hard to read and a bit prone to programmer error. Is there a better approach?

Thanks,
Paul

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Paul Rubin
Professor Emeritus
Michigan State University
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There is no direct way to model an element over a 2-D array of variables (or values), you have to flatten the array and index it with n*x + y.

In the case you have a 2-D array of values the domain reduction of n*x + y is an approximation on bounds (as for most linear constraints in CP Optimizer). It can be beneficial to add a strong constraint over the indexes

strong([x, y])

At presolve, this will enumerate all combinations of values for x and y and create an allowedAssignments constraint over x, y, and any variable that is fixed by fixing x and y. On flattened n-dimensional element constraints over values this provides a perfect domain reduction in most cases.

Using a strong for 2-D array of variables can give more domain reductions as well if there are implied fixed variables when x and y are fixed. It depends on the model. 

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Philippe Refalo
IBM ILOG CP Optimizer
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Thanks Philippe. I was not aware of the strong constraint.

Paul

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Paul Rubin
Professor Emeritus
Michigan State University
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Original Message:
Sent: Thu April 27, 2023 06:18 AM
From: Philippe Refalo
Subject: CP Optimizer multidimensional element operation

There is no direct way to model an element over a 2-D array of variables (or values), you have to flatten the array and index it with n*x + y.

In the case you have a 2-D array of values the domain reduction of n*x + y is an approximation on bounds (as for most linear constraints in CP Optimizer). It can be beneficial to add a strong constraint over the indexes

strong([x, y])

At presolve, this will enumerate all combinations of values for x and y and create an allowedAssignments constraint over x, y, and any variable that is fixed by fixing x and y. On flattened n-dimensional element constraints over values this provides a perfect domain reduction in most cases.

Using a strong for 2-D array of variables can give more domain reductions as well if there are implied fixed variables when x and y are fixed. It depends on the model. 

Philippe

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Philippe Refalo
IBM ILOG CP Optimizer
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