Using personal condor to solve quadratic assignment problems
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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 to solve quadratic assignment problems

Using Personal Condor toSolve Quadratic AssignmentProblems

Jeff Linderoth

Axioma, Inc.

[email protected]


Partners in crime
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
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
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
Q: Why Is This Important?

  • Answer #1: Practical applications

    • Facility Location

    • Hospital Design

    • Flight Instrument Layout

  • Answer #2: Similarity

    • Comparable to other practically important combinatorial optimization problems

    • TSP, MIP


The real answer it s not
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
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
Making the Perfect Marriage

  • Something Old

  • Something New

  • Something Borrowed

  • Something Blue


Something old
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
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
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
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
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
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 m arriage w ork
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
Mission Accomplished!

Solution Characteristics



The ups downs
The Ups & Downs

  • Human (read Jeff) error

    • Master compiled for <= 1000 workers

  • Condor schedd bug (Gasp!!!!)

  • Master shut down to fix NFS problems

  • Condor schedd bug

  • Human (read Jeff) error

    • Incorrect editing of configuration files resulting in many incorrect submissions






The moral of the story
The Moral of the Story

  • 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


The true moral
The TRUE Moral

  • 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


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