Using Personal Condor to Solve Quadratic Assignment Problems

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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.

[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

Our Mission
• 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
What’s a QAP?
• Can be thought of as a facility location problem
• The QAP is NP-REALLY-Hard
• TSP: Solve n=13509
• QAP: Solve n=25
Q: Why Is This Important?
• 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?

The Perfect Marriage

+

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

Making the Perfect Marriage
• Something Old
• Something New
• Something Borrowed
• Something Blue
Something Old:
• 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?
Branch
• 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!

Something New:
• A convex quadratic programming relaxation
• Solved with the Frank-Wolfe Algorithm*.
• Each iteration is one linear assignment problem

* Something VERY old

Something Borrowed:
• 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!
Something Blue?
• You could work until you’re blue in the face and not solve QAP instances*

* My sincerest apologies for the terrible pun

The Holy Grail
• 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
Mission Accomplished!

Solution Characteristics

The Ups & Downs
• Master compiled for <= 1000 workers
• Condor schedd bug (Gasp!!!!)
• Master shut down to fix NFS problems
• Condor schedd bug