Using Personal Condor to Solve Quadratic Assignment Problems

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Using Personal Condor to Solve Quadratic Assignment Problems

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Using Personal Condor to Solve Quadratic Assignment Problems

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Using Personal Condor toSolve Quadratic AssignmentProblems

Jeff Linderoth

Axioma, Inc.

jlinderoth@axiomainc.com

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

- 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 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

- 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

Number of Workers

- 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

Number of Workers on June 12

Number of Workers at Three Biggest Contributors

Number of Workers at Three Next Largest Contributors

KLAPS

- 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