> To address Andrew's earlier comment, "Nevertheless, imagine that you > have obtained all the feasible or optimal > solutions. In which way would you use them?", I want to cite an > anecdote.
Thank you for the story. > It would be interesting to generate all solutions. If that is > expensive, generating a lot of reasonable solutions would be great. > This is an example of a case where you want to see all (or many) > feasible solutions. I suspect that it should be the case when a > problem involves the human factor. > I think that the main problem which the modeler encounters in many practical cases is that it is often impossible to formalize some requirements to the solution, which is called "optimal". Imagine, for example, that given a cantus firmus one needs to find (compose) a "best" counterpoint to it. Though in this case it is easy to describe the solution space with binary variables, and even there exists some formal theory, nor constraints neither objective can be formalized to the end. So the only way is to find a set of solutions and try to choose a "best" one by listening to them :) Formalization is the problem, not a human factor. Mentioning a Turing machine I didn't mean modeling it literally. I only meant that that was said by Manfred Padberg: "The functioning of the whole world can--with a sufficient degree of approximation--be modeled as a huge mixed-integer linear program." If we can formalize something, we can describe it algorithmically, and therefore we can model it as mip. Here is another example. If a class of matrices is described with binary variables (as in Klas' example), and there is some requirement, say, that all eigenvalues must have postive real parts, this requirement can be formalized and therefore can be described as mip constraints. This doesn't mean, of course, that one needs to model computing eigenvalues with a Turing machine or similar device, just because the class of matrices is parametrized by binary variables, i.e. we don't need to consider a general case which assumes arbitrary matrices. Obviously, positiveness of real parts of eignevalues or some other property of any matrix from the class is a binary function of binary variables, and the problem is only how to find that function and describe it efficiently. This is my opinion. _______________________________________________ Help-glpk mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-glpk
