Are there special properties of w1 and w2, or do they need to be assumed to be entirely arbitrary positive-integer valued functions?
Can any of my followers assist me with a mathematical optimization problem?https://cstheory.stackexchange.com/questions/44411/formalizing-and-optimizing-constraints-involving-booleans-pairs-of-booleans-an …
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The only thing that comes to mind at the moment is that, in this scenario, \forall x,y. w2(x,y) <= min(w1(x),w1(y)). (Perhaps more restrictions will come to mind upon further thought)
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The naive approach to use Z3 to give as many satisfying assignments for all constraints and then rank them by the function evaluations does not really scale for too many satisfying assignments, right?
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I don't know the exact number of satisfying assignments to the Boolean part, but I expect an absurdly huge number of them, too many to even enumerate.
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Have you tried Integer Linear Programming, for instance using Gurobi?
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