On Implementing a Parallel Integer Solver Using Optimization Services

Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

On Implementing a Parallel Integer Solver

Using Optimization Services

Jun Ma

Huanyuan (Wayne) Sheng

Joint work with

Sanjay Mehrotra

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

Outline

• Brief Introduction– Impact Generalized MIP Solver – Optimization Services (OS)

• Distributed Parallel For Integer Programming Using OS

• Conclusion

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

IntroductionImpact GMIP Solver

• IMPACT -- Integrated Mathematical Programming Advanced Computational Tools

• Features– Generalized Mixed Integer Nonlinear Solver (GMIP).– Generalized Hyperplanes based Branch and Bound.– Standalone Solver and Remote Solver Service.– Unified NATIVE Interface with Optimization Services.

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

Impact GMIP Solver Features Algorithms

• Research Focus– Mixed Integer Nonlinear Programming– Parallel computing for MINLP

• Algorithm Studies– Heuristics for generalized branch and bound

methods – Optimization Services based distributed parallel,

e.g. communications, load balance handling.

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

Impact GMIP Solver Features Algorithms

RootNode

Proper BranchingHyperplane

being u

Leftchild

RightChild

Add u

lT xu 1 l

T xu

Growing Left Growing Right

Generate Children Generate Children

• Starting Node

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

Impact GMIP Solver Features Algorithms

• Subsequent Node

ParentNode(Left)

Proper BranchingHyperplane

being u prime

Leftchild

RightChild

Add new u prime

lT xu ''

Growing Left Growing Right

Generate Children Generate Children

SiblingNode

1 lT xu

1'' lT xu

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

Impact GMIP Solver Features Algorithms

• Generate Proper Branching Hyperplanes

– Basis Reduction Based (Mehrotra and Li)• LLL• GBR (Generalized Basis Reduction)

– Heuristics (ongoing)

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

GenerateNodes

Instance

Number OfNodes > 100

N

NodeQueue

Y

DistributedSystem

DistributedSystem

DistributedSystem

End

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

IMPACT GMIP Parallelization over Distributed Optimization Services

ImpactGMIP

OShL

OShL

OShL

OShL

OShL - hookup

CommunicationgetJobID (String OSoL)

solve (String OSiL, String OSoL)

send (String OSiL, String OSoL)

retrieve (String OSoL)

kill (String OSoL)

knock (String OSpL, String OSoL)

OSiL - instance

OSoL - option

Representation

OSrL - result

OSpL - process

Nodes (OSiL Integer)

OSServer

(Linux)

OSServer

(WinXP)

OSServer

(Mac OS)

Lindo

CPLEX

IMPACT

Call back

(OSrL)

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006

Conclusion

• Introduced the Generalized MIP and showed it is friendliness for Parallelization

• Showed Optimization Services has a general and high extendable design fit for many derived researches

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Jun Ma, Sanjay Mehrotra and Huanyuan ShengImpact Solver for Optimization Services, November 8, 2006