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Mar 17, 2010 at 18:56 vote accept Milan Babuškov
Mar 16, 2010 at 21:08 history edited Ryan Williams CC BY-SA 2.5
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Mar 16, 2010 at 21:03 comment added Ryan Williams IF X, Y, and Z depend on a,b,c,etc., then they are essentially other variables. It could be that your best bet is to look at "fixed parameter tractable" algorithms for Integer Linear Programming. For example, if there are only k total variables in your problem then the problem can be solved in k^{O(k)} poly(n) time, independently of the domains. See > R. Kannan. Minkowski's convex body theorem and integer programming. Math. Oper. Res., 12(3):415--440, 1987. In my answer above, I will give a simple heuristic example of how to translate an "if...then" into inequalities.
Mar 16, 2010 at 19:06 comment added Milan Babuškov Thanks Ryan. X, Y and Z are really coefficients, but they vary depending on some values of a, b, c, d, ..., h and this needs to be taken into account when searching for minimal w. There is a fixed set of possible values for x, y, z, but more than two. For example, X can have 2, Y can have 5, Z can have only one. It depends on user input. And a, b, c, ... have to be integers. Looking into some answers others have provided, I'm now looking into Integer Programming using branch and bound method. Could you please give an example how to translate the "if-then" I gave in my question?
Mar 16, 2010 at 17:07 history answered Ryan Williams CC BY-SA 2.5