The atoms of integer programming

Abstract

After thirty years of doing other things, I am once again doing some research on integerprogramming. It has been interesting and exciting for me to see what has changed duringthose thirty years.The practical side of integer programming has developed far more than I would haveever anticipated. Problems of a size and complexity that we would never have thought ofattempting thirty years ago are being done routinely. And this has been accomplished notby some theoretical or conceptual breakthrough (the branch and cut methods generally usedare fundamentally the same as before) but by the intelligent and persistent use of empiricalmethodsandempiricallearning.Addedtothis,ofcourse,is30yearsofprogressinelectronics,which is worth another improvement factor of roughly 1000 in performance.On the theoretical side there is continued interest in special problems: the traveling sales-man problem, for example, is very much alive and well, as are many graph theory problems.There is a large gap between the work on special problems and the work on large practicalproblems. The type of discourse in these two areas is quite different. One area deals in largetest problems and how they run, the other is much more theoretical.