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Using Personal Condor to Solve Quadratic Assignment Problems

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Presentation Transcript

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?

- 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 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

- 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

- 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

- 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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