When I was noodling with the Traveling Salesman problem, I was sure that what I really needed was to spend X% of available resources on the Big Gamble (a low probability algorithm with fast results), Y% on a common heuristic and the rest on the honest work of plowing through the linear equations progressively culling the remaining scenarios that need to be tested. I had limited success with this though. I just haven’t done enough LP to make anything noteworthy, and it was a tool sharpening exercise, which made me a little more effective at more mundane batch processing tasks, not a great mind of NP-completeness.