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Using Personal Condor to Solve Quadratic Assignment Problems - PowerPoint PPT Presentation

Using Personal Condor to Solve Quadratic Assignment Problems. Jeff Linderoth Axioma, Inc. [email protected] Partners in Crime. Kurt Anstreicher Nate Brixius University of Iowa. Jean-Pierre Goux MCS Division, ANL. LOTS of people in this room! University of Wisconsin.

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Using Personal Condor toSolve Quadratic AssignmentProblems

Jeff Linderoth

Axioma, Inc.

Kurt Anstreicher

Nate Brixius

University of Iowa

Jean-Pierre Goux

MCS Division, ANL

LOTS of people in this room!

University of Wisconsin

• Find the best possible solution to large quadratic assignment problem (QAP) instances

• Prove that the solution is indeed optimal

• Show how to exploit the Computational Grid offered by Personal Condor to make it happen

• Can be thought of as a facility location problem

• The QAP is NP-REALLY-Hard

• TSP: Solve n=13509

• QAP: Solve n=25

• Facility Location

• Hospital Design

• Flight Instrument Layout

• Comparable to other practically important combinatorial optimization problems

• TSP, MIP

The REAL Answer – It’s NOT!

“The Journey Is The Reward”

What can we learn about solving complex

numerical problems on Computational Grids?

+

While my wife likes this slide, really it’s the QAP and Condor that make the perfect marriage!

• Something Old

• Something New

• Something Borrowed

• Something Blue

• Branch-and-Bound

• Bound

• Solve “auxiliary” problem that gives a lower bound on the optimal solution to the problem

• Any assignment of facilities to locations gives an upper bound on the optimal solution

• What if lower bound < upper bound?

• Divide-and-Conquer!

• Recursively make problem smaller by assigning each facility to a fixed location

• Without the bounding, this is complete enumeration. (n!)

This is not “pleasantly parallel” computing!

• A convex quadratic programming relaxation

• Solved with the Frank-Wolfe Algorithm*.

• Each iteration is one linear assignment problem

* Something VERY old

• With Condor it is easy to “borrow” CPU cycles

• Call your friends and colleagues and flock with their Condor pools

• Write an NPACI proposal and Glide-In to supercomputer resources

• If all else fails (Condor/Globus not installed), hobble in!

• You could work until you’re blue in the face and not solve QAP instances*

* My sincerest apologies for the terrible pun

• We want to solve nug30!

• Extrapolating results and using an idea of Knuth*, we conjecture that we will need roughly 10-15 years of CPU time

• How can we be sure to use 10-15 years of CPU time somewhat efficiently?

• We have the additional burden of working in Condor’s extremely dynamic environment!

* Something Old

Making the Marriage Work

• The MW runtime support library helps us cope with the dynamic nature of our platform

• MW – Master Worker paradigm

• Must deal with contention at the master

• Search/ordering strategies at both master and worker are important!

• Parallel Efficiency improves from 50% to 90%

• Lots more details!

• Paper available at www.optimization-online.org

Solution Characteristics

• Master compiled for <= 1000 workers

• Condor schedd bug (Gasp!!!!)

• Master shut down to fix NFS problems

• Condor schedd bug

• Incorrect editing of configuration files resulting in many incorrect submissions

• A good wedding/marriage requires four key ingredients

• There were also four key ingredients to solving nug30

• Powerful mathematics for producing a lower bound

• Innovative branching techniques

• An EXTREMELY powerful computing platform

• “Marrying” the algorithm to the platform in an appropriate manner

• It is possible to do complex numerical calculations on the Computational Grid using Condor!

• It opens the doors to attacking heretofore unsolved problems!

• http://www.mcs.anl.gov/metaneos