get number of solutions with

[Alessandro Danese]

Hello to everyone.

Is it possibile count the number of feasible solutions of a set of constraints with gurobi?

Let's take as example two integers variables {x,y} and two constraints {x<=1; y<=1}.

The number of feasible solutions of the set of constraints is 4, namely {(0,0), (0,1),(1,0),(1,1)}.

Thanks!

Alessandro

[Tim Chippington Derrick]

In principle yes, but the numbers get very big very quickly. 10 binaries would give 1024. 20 variables gives over a million, 30 gives over a billion. 50 variables would lead to potentially 10**15 solutions, so at the rate of solving/rejecting maybe 1 million per second, it would take of the order of 35 years. Combinatorics bites very hard and fast. All the more amazing that these solvers can solve the problems that we throw at them so 'casually', because a 50 variable problem would be considered very tiny.

Tim

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Dr Tim Chippington Derrick

Chippington Derrick Consultants Ltd

Tel: +44 01276 508949

Mob: +44 07971 997948

[Michael Winkler]

You could use the PoolSearchMode together with PoolSolutions parameter to collect all solutions. See


https://www.gurobi.com/documentation/7.0/refman/poolsearchmode.html
https://www.gurobi.com/documentation/7.0/refman/poolsolutions.html#parameter:PoolSolutions

For a more detailed description see also:

https://www.gurobi.com/documentation/7.0/refman/solution_pool.html

Best,
Michael