Date post: | 26-Dec-2015 |
Category: |
Documents |
Upload: | victor-shaw |
View: | 215 times |
Download: | 1 times |
Combinatorial Optimization on the Computational Grid
Experiments on Grid5000
Nouredine Melab ([email protected])Member of Grid5000 steering committee
Laboratoire d’InformatiqueFondamentale de Lille
Parallel Cooperative
Optimization Research
Group
INRIA DOLPHIN Project
Combinatorial optimization problems
High-dimensional and complex optimization problems in many areas of industrial concern
Parallel hybrid optimization methods allow to efficiently provide effective solutions, but they remain insufficient for large problems …
… Need of large scale parallelism (Grid computing)
(Multi-Objective))(..., ),(),( )( min
21xxxxf fff
n
Sx
Const.
2n
(Mono-Objective) )(min xf
Sx ( )
A taxonomy of optimization methods
Exact algorithms Heuristics
Branchand X
DynamicProgramming
A*Specific
HeuristicsMeta-heuristics
SingleSolution
Population of solutions
LocalSearch
SimulatedAnnealing
TabuSearch
EvolutionaryAlgorithms
Scatter,Swarm search
Near-optimal solutions for large problem instances
Optimal solutions for small problem
instances
Design and implementation of Grid-based algorithms …
Meta-heuristics (near-optimal)Parallel hybrid design
… solving challenging problems in combinatorial optimization
Exact algorithmsParallel design
Implementation(ParadisEO@Grid)
Cooperation
Implementation(B&B@Grid)
Protein Structure Prediction Flow-Shop scheduling problem
Supported by ANR-GRID DOCK
Supported byACI-GRID DOC-G
Combinatorial Optimization on the Computational GridExperiments on Grid5000
Supported by ANR-GRID CHOC
Meta-heuristics: Parallel models and hybridization mechanisms
Parallel models They allow to improve efficiency and effectiveness Population-based meta-heuristics
Island model, parallel evaluation of the population, parallel evaluation of a single solution
Single solution-based meta-heuristics Multi-start model, parallel exploration of the neighborhood,
parallel evaluation of a single solution
Hybridization mechanisms … … allow to combine different methods for better robustness
and effectiveness, but are CPU-time intensive
N. Melab, E-G. Talbi, S. Cahon, E. Alba and G. Luque. Parallel Meta-heuristics: Algorithms and Frameworks. Chapter 6 in “Parallel Combinatorial Optimization”, Wiley Series on Parallel and Distributed Computing, ISBN: 0-471-72101-8, Nov 2006.
“Gridification” of parallel hybrid meta-heuristics
Major properties of computational grids Multi-administrative domain, heterogeneity, dynamic availability
of resources, large scale
Major adaptations of the different models and mechanisms
Asynchronous design and implementation Granularity management and load balancing Checkpointing-based fault tolerance (a memory for each model) Adaptation of the parameters of each model (e.g. migration
topology for the island model)
N. Melab, S. Cahon and E-G. Talbi. Grid Computing for Parallel Bioinspired Algorithms. Journal of Parallel and Distributed Computing (JPDC), Elsevier Science, Vol.66(8), Pages 1052-1061, 2006.
Our contributions
Multi-Objective EO (MOEO) for the design of multi-objective evolutionary algorithms
Moving Objects (MO) for the design of local search algorithms
ParadisEO for parallel hybrid metaheuristics
PARAllel and DIStributed Evolving Objectshttp://www2.lifl.fr/OPAC/Softwares/ParadisEO/
Message passing (MPI, PVM) Clusters, Networks of Workstations,
Multi-programming (PThreads) Shared Memory Multi-processors
(SMP) Parallel distributed computing
Clusters of SMPs (CLUMPS) Grid computing
Condor-MW and Globus (MPICH-G2)
EO
ParadisEO@Grid
MO MOEO PVM, PThreads MPI (LAM, CH)Condor-MW Globus
S. Cahon, N. Melab and E-G. Talbi. ParadisEO: A Framework for the Reusable Design of Parallel and Distributed Metaheuristics. Journal of Heuristics, Elsevier Science, Vol.10(3), pages 357-380, May 2004.
Evolving Objects framework (EO)
European project(Geneura Team, INRIA, LIACS)
http://eodev.sourceforge.net
Transparent use
ParadisEO-G4: ParadisEO on Globus 4
Design and implementation Gridification of the parallel models and hybridization
mechanisms provided in ParadisEO MPICH-G2 as the communication library
Deployment on the computational Grid (Grid5000) Building of system image for Globus 4 including MPICH-G2 Virtual Globus Grid on Grid5000 for the Grid-based
deployment of the parallel hybrid meta-heuristics provided in ParadisEO
Design and implementation of Grid-based algorithms …
Meta-heuristics (near-optimal)Parallel hybrid design
… solving challenging problems in combinatorial optimization
Exact algorithmsParallel design
Implementation(ParadisEO@Grid)
Cooperation
Implementation(B&B@Grid)
Protein Structure Prediction Flow-Shop scheduling problem
Supported by ANR-GRID DOCK
Supported byACI-GRID DOC-G
Combinatorial Optimization on the Computational GridExperiments on Grid5000
Supported by ANR-GRID CHOC
Protein Structure Prediction on the GridModelling
The problem consists in finding …
… the ground-state (tertiary stable) conformation of a protein from its primary structure composed of a sequence of amino-acids (residues)
Modelled as a bi-objective optimization problem Candidate solutions: Molecular conformations
(geometries) – vectors of torsion angles Molecular conformation with lower free energies (bonded
atoms and non-bonded atoms)
Protein Structure Prediction on the GridComplexity and landscape analysis
For a molecule of 40 residues with 10 conformations per residue, 1040 conformations are obtained in average … 1018 years are required at 1014 conformations explored
per second!
Landscape analysis Multi-modal landscape Need of parallel hybrid (global and local) meta-heuristics and Grid computing
Parallel evaluation of
the population
High-level co-evolutionary hybridizationMulti-start model
High-level co-evolutionary hybridization
Cooperative GAs (Island model)
Parallel asynchronous hierarchical hybrid meta-heuristic
A-A. Tantar, N. Melab, E-G. Talbi, O. Dragos and B. Parain. A Parallel Hybrid Genetic Algorithm for Protein Structure Prediction on the Computational Grid. FGCS, Elsevier Science, Vol.23(3), 398-409, 2007.
... ...
...∂
1∂
2∂
n
...∂'
1∂'
2 ∂'n
Genetic Algorithm Population
Local Search
Optimized Individual
Grid5000: 7 sites, Avg. 800 CPUs – Execution time: 1h – Cumul. time: 1 month
Preliminary experimental results on Grid5000
Implementation with ParadisEO-G4
Protein: Tryptophan-cage from Protein Data Bank (PDB - 1L2Y)
Average Quality Improvement: 62%
Interconnection Grid5000-DAS
Benefits More resources for dealing with very large proteins with
grid-based meta-heuristics New scientific challenge: scalability of ParadisEO-G
Requirements Need of a virtual Globus grid between Grid5000 and DAS
Common certification authority ?
Get longer the default run time of jobs in DAS Deployment time of the virtual Globus grid ~ 10 minutes Only 5 minutes for the combinatorial optimization process on
DAS !!
Design and implementation of Grid-based algorithms …
Meta-heuristics (near-optimal)Parallel hybrid design
… solving challenging problems in combinatorial optimization
Exact algorithmsParallel design
Implementation(ParadisEO@Grid)
Cooperation
Implementation(B&B@Grid)
Protein Structure Prediction Flow-Shop scheduling problem
Supported by ANR-GRID DOCK
Supported byACI-GRID DOC-G
Combinatorial Optimization on the Computational GridExperiments on Grid5000
Supported by ANR-GRID CHOC
Parallel models for exact optimization(B&B inspired)
B&B = Exploration + bounding of tree nodes Parallel models
Parallel multi-parametric model Parallel exploration of the search tree Parallel evaluation of the bounds Parallel evaluation of a single bound/solution
Parallel exploration of the search tree Massive parallelism needing a computational grid Gridification is required
Efficient work distribution during the exploration Need of low cost communications of work units
Efficient checkpointing-based Fault tolerance Search of an exact solution in a volatile
environment Low cost communication and storage of work units
Efficient termination detection May be implicit
The proposed approach: objectives
The approach uses a special coding … Node number Work unit (collection of nodes) = an
interval
Principles of the approach
0
0
0
1 2
2
3 4
4
5
[0,2] [3,5]
[0,5]
The approach is Dispatcher-Worker based on the work stealing paradigm Dispatcher: maintains a pool of work units (intervals) and the global
solution found so far Worker: performs B&B on a given interval and updates the global
solution
Work distribution and check-pointing Communication of intervals (two numbers) Two efficient operators: folding and unfolding of intervals
Design and implementation of Grid-based algorithms …
Meta-heuristics (near-optimal)Parallel hybrid design
… solving challenging problems in combinatorial optimization
Exact algorithmsParallel design
Implementation(ParadisEO@Grid)
Cooperation
Implementation(B&B@Grid)
Protein Structure Prediction Flow-Shop scheduling problem
Supported by ANR-GRID DOCK
Supported byACI-GRID DOC-G
Combinatorial Optimization on the Computational GridExperiments on Grid5000
Supported by ANR-GRID CHOC
N jobs to be scheduled on M machines Each machine can not be simultaneously assigned to two
jobs (colors) Jobs (colors) must be scheduled in the same order on all
machines One objective must be minimized
Cmax: Makespan (Total completion time)
M1
M2
M3
The Flow Shop Scheduling Problem
4 jobs on 3 machines
Network of the campus of Université de Lille1
123
FIL (Lille1)170
IUT A118
1718
A grid of more than 2000 processors
Grid5000 node at Lille
RENATER
NR
...NR
Other sites of GRID’5000
Grid’5000Grid’5000
Front-end
IP forwarding NAT
Dispatcher on a computation node
Experimental results
Standard Taillard’s benchmark: Ta056 - 50 jobs on 20 machines
Best known solution: 3681, Ruiz & Stutzle, 2004 Exact solution: 3679, Mezmaz, Melab & Talbi, 2006
Running wall clock time: 25 days 46 min
CPU time on a single processor: 22 years 185 days 16 hours
Avg. num. of exploited processors: 328
Maximum number of exploited processors: 1 195
Parallel efficiency: 97 % Bordeaux (88), Orsay (360), Sophia (190), Lille (98), Toulouse (112), Rennes (456), Univ. Lille1 (304)
M. Mezmaz, N. Melab, E-G. Talbi. A Grid-enabled Branch and Bound Algorithm for Solving Challenging Combinatorial Optimization Problems. Research Report, INRIA 5945, July 2006 (https://hal.inria.fr/inria-00083814).
Interconnection Grid5000-DAS
Benefits More resources for solving efficiently and optimally larger
problem instances with grid-based combinatorial optimization New scientific challenge: scalability (limits and solutions) The dispatcher has never crashed on Grid5000 (up to 2500
processors)
Requirements Avoiding the special configuration of the front-end to allow
transparent inter-grid communications between the dispatcher and the workers
Viewing DAS as a Grid5000 site and vice versa ?
Best-effort reservation mode in DAS Long-running problems Using the nodes as long as they are not requested for reservation