Michael's Home Page: Integer Programming Research

My interest in integer programming is fairly new. Teaching decomposition-coordination methods in higher courses over the years however made me (along with other researchers/teachers in my groups over the years) realize early on how often the wheel is reinvented in this field; that, for example, the use of Lagrangian relaxation in integer programming is so much more classic than is made clear in papers written these days - it is also interesting that much of the early development was made by a Swede! :-) [For those who do not know, I refer to Peter Jennergren.]

Together with my former supervisor Torbjörn Larsson, I have previously worked on improvements on Benders decomposition techniques as well as accelerations of Dantzig-Wolfe decomposition, but most of that research has had the most natural use in continuous optimization. [Continuing the historical notes, it is fun to see that discussions on the slow convergence of Dantzig-Wolfe near an optimal solution are far from new but is referred to already - if not even earlier! - by Nemhauser and Widhelm in an OR paper from 1971.] Together with Ann-Brith Strömberg, we have also taken a look at solving convexified versions of integer programs by Lagrangian relaxation, but all the above have yet to be finished. The first paper in the list summarizes work on optimality conditions for integer programs (as well as more general ones) and their application to Lagrangian heuristics.

Also in recent years I have become involved in research in maintenance optimization, particularly concerning aircraft engines but more recently also in energy production.

Reports on Optimality Conditions and Lagrangian Heuristics:

Reports on Maintenance Optimization:

Michael Patriksson
Department of Mathematics,
Chalmers University of Technology,
Gothenburg (Göteborg)
mipat@math.chalmers.se

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