What I said is rock solidly true. I hold a Ph.D. in operations research, was Director of Operations research for a major airline, have worked with a good list of some of the best optimization people in the world, and have attacked several challenging combinatorial optimization problems. I've seen people interested and not interested in optimization and concluded with solid evidence that in general, for the problems I mentioned, for optimization, people don't want to be bothered. Here I'm not lacking "imagination" at all. Again, operations research is a dead duck because people don't want to be bothered.

I don't know your field: If you are looking for some 'exact fit' in the sense of, say, the famous NP-complete problem SAT, then the techniques of optimization may be less powerful. But with very different techniques, there has been progress on SAT.

However there is a large body of research with some solid practical power; maybe some of this research would do well for your problems. At least get good with linear programming and, say, C-PLEX. Then look at the old Gilmore-Gomory column generation where the linear program can have many millions of columns, most not even written down yet. Look really hard at nonlinear duality theory -- for a minimization problem, the dual is always maximizing a continuous, concave function! Then look at Lagrangian relaxation. Of course, finish off with branch and bound. Look at the work at Georgia Tech of G. Nemhauser and E. Johnson. Also note: In practice, a large fraction of integer linear programming problems are in fact least cost network flow problems or closely related, and there we can get optimal solutions very quickly and integer optimal solutions for no extra cost. Look at W. Cunningham's work and also D. Bertsekas's. In general, for really large problems, there is a powerful theme: Continuous approximations work well. Your field may not have good knowledge of such work.

Besides, even if what is known is not good for your problems, history shows in solid terms that for progress on your problems, f'get about anything having to do with P versus NP. For getting the solutions you outlined, for years, P versus NP is a fool's errand.

Here I'm giving you good advice in spite of your insult.