CCGRID07 - A Parallel P2P Branch and Bound Algorithm for Computational Grids

8/6/2019 CCGRID07 - A Parallel P2P Branch and Bound Algorithm for Computational Grids

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A Parallel P2P Branch and Bound

Algorithm for Computational GridsA. Bendjoudi, N. Melab and E-G. Talbi

[email protected], {melab, talbi}@lifl.fr

Laboratoire dInformatique Fondamentale de Lille

Parallel Cooperative

Optimization Research

Group

Universit A/Mira de Bjaacole doctorale dinformatique

R seaux et Sy stmes DistribusReSyD

CEntre de R echerche sur l InformationScientifique et Technique CERIST

Laboratoire des S ystmes Informatiques LSI


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Outline

Motivation and Objectives

Parallel B&B for large scale computing( ParallelBB )Implementation on top of ProActive ( P2PBB )Performance Evaluation

Conclusion et Perspectives


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Branch and Bound Algorithm

BranchingOriginal problem is partitioned into smaller sub problems.

BoundingCompute the estimated optimal solution (lower bound)

of the considered problem and compare to the best

known solution ( upper bound ).Elimination

Identify nodes which dont lead to The best solution and eliminate them

SelectionExploration strategy

(best first search, depth firstsearch, best bound,)

Problem to be solved

Sub-problem

Solutions

P 0

8Optimal solution

B r a n c h i n g

Elimination

Selection


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Motivations

High-dimensional and complex optimization problems in many

areas of industrial concern

B&B most known algorithm for an exact resolution of COPs

Implicit enumeration of the search spaceChoice of a good lower bound improves its performances

These two factors are not sufficient

Parallelization of B&B

Parallel exploration of the B&B search tree allows to provideoptimal solutions

but requires a huge amount of resources for large problems

Need of large scale parallelism (Grid computing)


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Objectives

Parallel B&B Algorithms developed withMaster/Worker paradigm

All communications inter-workers transit via MasterProcessGood strategy (for reduced set of workers)Gap : Creating bottlenecks on Master process

on (large scale deployment)

Use of P2P approachDirect Communications Inter-Workers

Fault toleranceDynamic availability of peers

Master

Wor ker

Wor ker

Wor ker

New solution

Wor ker

Bottleneck

Broadcast of theupper bound


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Outline

MotivationsParallel B&B for large scale computing( ParallelBB )Implementation on top of ProActive ( P2PBB )Performance Evaluation



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ParallelBB,Parallel B&B for large scale computing

Manager/Worker Paradigm with directcommunications inter-workers

Direct communications inter-workersAvoid bottlenecks created on Master Process

The Manager distributes tasks on WorkersSingle work poolWorkers traits their computing parts

in parallel

Master

Wor ker

Wor ker

Wor ker

New solution

Wor ker


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ParallelBB Operations

BranchingManager generates k levels in the tree.

k depends on problem size (PS) and number of workers (#W).PS>> k >> ; #W >> k >>

SelectionManager: Exploration in depth with priority

to most promising node (priority-based queue)Manager: BFS (reversed priority-based stack)

CommunicationsWorker/Worker (upper bound )Worker/Manager (final solution )Manager/Worker (data, task, initial

upper bound, list of workers)

New Solution

K l

e v e

l s

Workers

Manager


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Outline

MotivationsParallel B&B for large scale computing(ParallelBB)Implementation on top of ProActive ( P2PBB )Performance Evaluation



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P2PBB,ParallelBB on top of ProActive (1)

ProActive: Java library which proposes an API, a graphical interface andparallel, distributed and concurrent programming tools.Active Object: remote object having its own thread andreceiving calls on its public methodsObjective: Using Idler CPU cyclesCreating threads with lowest prioritiesResources shared are JVMs, each JVM can receive computationEach JVM participating in the computing launches a daemon( P2P Service )

An overlay network is formedDeployment made using an XML descriptor file.


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,ParallelBB on top of ProActive(2)

P2PBB an active application P2P version of ParallelBB on a P2P platform (ProActive)Developed with two AOs

bbWorker represents a WorkerbbManager represents the Manager

ProActive provides bbWorkers recovered over thewhole network and detected by bbManager byconsulting XML deployment descriptor file.


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,ParallelBB on top of ProActive(3)

Distribution of computation

bbManager sends tasks(passive objects)waits for futures of

objects (result done by a

bbWorker in the future)

Wating for Futures

bbManager

Work pool(passive objects)bbWorkers

Computing


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Sharing the upper bound

A bbWorker broadcasts the upper bound using

Typed Group communications multicast

bbWorkerGroup : represents a set of bbWorkers

recipient of messages


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Fault Tolerance

bbManager uses ProActive listeners and implements

nodeCreated method of ProActive to take into account new

peers connections (new bbWorkers)

With ProActive two types of servers are created

Resource server which returns a free node that can host the

recovered AO

Fault tolerance servers for the check points storage, the

localization of AOs and failure detection.

With P2PBB when a peer (bbWorker) fails, bbManager sends its

part of calculation to others and it recovers only the first solution


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Outline

MotivationsParallel B&B for large scale computing(ParallelBB)Implementation on top of ProActive (P2PBB)Performance Evaluation



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Performance Evaluation

Preliminary experiments on 06, 20, 50 upon cluster at Lille of GRID5000 ( http://www.grid5000.fr )

All processes run with lowest priorityParallel (with/without communications between workers

Taillards benchmarks (Ta 20-05-02, Ta 20-05-03, Ta 20-10-01,Ta 20-10-02)
http://www.grid5000.fr/http://www.grid5000.fr/


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N jobs to be scheduled on M machinesEach machine can not be simultaneously assigned to two

jobs (colors) Jobs (colors) must be scheduled in the same order on all

machinesOne objective must be minimized

Cmax: Makespan (Total completion time)

M1

M2

M3

The Flow-Shop SchedulingProblem

4 jobs on 3 machines


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Two parallel modes are more efficient than the serial one.#computing machines >> performance >>

Best solutions are found using 50 machinesParallel mode with communication are more efficient thanwithout communication oneSolving Ta_3 on 50 machines (more than 18 times moreefficient than using 6 machines)


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Costofslutio

ns(CMax)

Time (/30min)


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Conclusion

Parallel Branch and Bound Algorithm for COPs (ParallelBB)

Master/Worker

Direct Communication between workers

Application to a PFS problemImplementation on top of ProActive (P2PBB)

Asynchronous and single direction calls methods (tasksdistribution)

Typed group communications (knowledge sharing)

ProActive listeners (new connection peers)Future of objects (collection of computation results)

Preliminary experiments in P2P modeEfficiency of collaboration between workers


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Perspectives

Consider other complex problems Q3AP (Quadratic

three-dimensional Assignment Problems)

Improve performances of ParallelBB with:

Injection of initial solution obtained with metaheuristic(hybridization)

Load balancing of the tasks generated by the algorithm

Several forms of tasks granularity

Larger scale experiments on GRID5000

Documents

CCGRID07 - A Parallel P2P Branch and Bound Algorithm for Computational Grids