2009 MSc Presentation for Parallel-MEGA

A Parallel Implementation of a Multi-Objective Evolutionary

AlgorithmChristos Kannas

Constantinos Pattichis

University of Cyprus

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Outline Introduction Goals Evolutionary Algorithms

Background Single & Multi Objective Optimization The family

Parallel Evolutionary Algorithms Algorithms

Multi-Objective Evolutionary Graph Algorithm Parallel Multi-Objective Evolutionary Graph Algorithm

Implementation Results Discussion Conclusion and Future Work Bibliography

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Introduction The majority of software programs are written for serial computation, which does not

take advantage of the multi-/many-core technology available in current CPUs. Parallel computing can use multi-/many-cores CPUs and/or General Programming

enabled GPUs. In general, parallel programs are very dependent on the specific hardware architecture

for which they were developed. General parallel programming turns out to be extremely difficult to implement due to the existence of different hardware architectures and to the limitations of current programming paradigms and languages.

Evolutionary Algorithms are stochastic search and optimization techniques which were inspired by natural evolution and population genetics. EAs are an interdisciplinary research field with relationships to biology, artificial intelligence, numerical optimization and applications for decision support in almost any engineering discipline.

Parallel Evolutionary Algorithms (PEAs) emerged for two main reasons: one is the need to achieve time-savings by distributing the computational effort and the second is to benefit from a parallel environment from an algorithmic point of view.

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Goals

The goals of this thesis are to: Explore the possibility of using a Parallel Evolutionary Algorithm on a

multi-/many-core CPU environment. Implement a Parallel Evolutionary Algorithm that exploits multi-/many-core

architectures, so as to produce solutions of the same quality as an ordinary Evolutionary Algorithm in much less time.

Learn more about parallel programming in multi-/many-core environment with the use of high level programming languages, such as Python.

Gain experiences in Parallel Evolutionary Algorithms, their strengths, weakness and potential applications.

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Evolutionary AlgorithmsBackground

Evolutionary Algorithms are based on a model of natural, biological evolution, which was formulated for the first time by Charles Darwin [4]. Darwin’s “Theory of Evolution” explains the adaptive change of species by the principle of natural selection, which favours those species for survival and further evolution that are best adapted to their environmental conditions. In addition to selection, Darwin recognized the occurrence of small, apparently random and undirected variations between the phenotypes (any observable characteristic or trait of an organism).

Modern biochemistry and genetics has extended the Darwinian Theory by microscopic findings concerning the mechanisms of heredity, the resulting theory is called the “Synthetic Theory of Evolution” [6]. This theory is based on genes as transfer units of heredity. Genes are occasionally changed by mutations. Selection acts on the individual, which expresses in its phenotype the complex interactions within its genotype, its total genetic information, as well as the interaction of the genotype with the environment in determining the phenotype. The evolving unit is the population which consists of a common gene pool included in the genotypes of the individuals.

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Evolutionary AlgorithmsSingle & Multi Objective Optimization

EAs are search algorithms aiming to find an optimal solution to the problem.Optimization can be classified in two major families.

Single Objective OPtimization (SOOP).For problems that have to satisfy one objective function.A single optimal solution is found.

Multi Objective OPtimization (MOOP).For problems that have to satisfy many objective functions.A list of equally optimal solutions are found, called Pareto front.

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Evolutionary AlgorithmsThe family

EAs are a big family of algorithms.Genetic Algorithms (GAs).

Chromosome string.Genetic Programming (GP).

Tree structure.Evolutionary Strategies (ES).

Real value vectors.Evolutionary Programming (EP).

Finite State Machines.

Population

Fitness Evaluation

Parent Selection

Reproduction

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Parallel Evolutionary Algorithms

Coarse grained.Divide the population into several subpopulations.Distribution of the subpopulations.

Fine grained.Inherent parallelism.

Individual level parallelism.Fitness level parallelism.

Subpop 1

Subpop 2 Subpop 3

Subpop 4Subpop 5

MasterFitness Assignment

Slave 1Reproduction

Fitness Evaluation

Slave 2Reproduction

Fitness Evaluation

Slave NReproduction

Fitness Evaluation

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Algorithms

Multi-Objective Evolutionary Graph Algorithm (MEGA) description. Chromosomes are graphs.

Working Population

Calculate Fitness

Hard Filter

Pareto Ranking

Calculate Efficiency

Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms


Working Population

Calculate Fitness

Hard Filter

Pareto Ranking


Select Parents

Evolve Parents

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Algorithms

Parallel Multi-Objective Evolutionary Graph Algorithm (PMEGA) description. Divide population into several subpopulations.

Number of subpopulations sets the number of tasks. Evolve subpopulations independently and isolated.

Isolation time. Merge results.

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Implementation

Programming language Python. Use of processes. No threads due to Global Interpreter Lock(GIL). Task scheduling with the use of a Pool of Processes.

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ImplementationWorking Population

Subpopulation 1

Subpopulation 2

Subpopulation X

Pool of processes, N processes for an N core CPU.

Each process is assigned a task to evolve a subpopulation, using MEGA algorithm.

Process 1

Process 2

Process N

Processes return their results.

Merge the results.

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Subpopulation 1

Subpopulation 2

Subpopulation X



Process 1

Process 2

Process N


Merge the results.

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Subpopulation 1

Subpopulation 2

Subpopulation X



Process 1

Process 2

Process N


Merge the results.

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Subpopulation 1

Subpopulation 2

Subpopulation X



Process 1

Process 2

Process N


Merge the results.

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Subpopulation 1

Subpopulation 2

Subpopulation X



Process 1

Process 2

Process N


Merge the results.

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Subpopulation 1

Subpopulation 2

Subpopulation X



Process 1

Process 2

Process N


Merge the results.

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Results

MEGA vs. PMEGA on 2 cores CPU CPU: Intel Core 2 Duo E8400 @ 3.0 GHz (2 Physical Cores) Memory: 4 Gbytes

MEGAPMEGA 2

SubpopulationsPMEGA 4

Subpopulations

1st Experiment (population 100, iterations 200)

Average Execution Time

0:39:15 0:22:44 0:25:50

Speedup 1.727206062 1.519243174

2nd Experiment (population 150, iterations 200)


1:04:44 0:34:48 0:40:33

Speedup 1.859696728 1.596464785

3rd Experiment (population 200, iterations 200)


1:22:20 0:49:22 0:54:22

Speedup 1.667604366 1.514253602

Summary Average Speedup 1.8

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Results

MEGA Blue dots: 1st Pareto front Red dots: Pareto fronts at 25%, 50%, 75% and 100%.

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Results

PMEGA 2 Subpopulations Blue dots: 1st Pareto front Red dots: Pareto front at 100%.

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Results


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Results Genotype

diversity: Clustering at parameter space.

Phenotype diversity: Clustering at objective space.

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Results

ER-alpha active ligands (left). ER-beta active ligands (right).

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Results MEGA vs. PMEGA 2 Subpopulations vs. PMEGA 4 Subpopulations

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Results

MEGA vs. PMEGA on 4 cores CPU CPU: Inter Core 2 Duo Quad Q6600 @ 2.4 GHz (4 Physical Cores) Memory: 4 Gbytes

MEGAPMEGA 2

SubpopulationsPMEGA 4

Subpopulations

1st Experiment (population 100, iterations 200)


0:55:57 0:20:53 0:21:27

Speedup 2.678191489 2.60880829

2nd Experiment (population 150, iterations 200)


1:26:18 0:32:02 0:32:12

Speedup 2.693895248 2.679489391

3rd Experiment (population 200, iterations 200)


1:56:45 0:42:39 0:41:45

Speedup 2.73752768 2.796540253

Summary Average Speedup 2.7

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Results

MEGA Blue dots: 1st Pareto front Red dots: Pareto fronts at 25%, 50%, 75% and 100%.

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Results


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Results


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Results Genotype

diversity: Clustering at parameter space.

Phenotype diversity: Clustering at objective space.

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Results

ER-alpha active ligands (left). ER-beta active ligands (right).

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Results MEGA vs. PMEGA 4 Subpopulations vs. PMEGA 8 Subpopulations

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Discussion

Amdahl’s Law.

Speedup

Maximum Speedup

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Discussion

N Sest E

2 1.8 0.9

4 2.8 0.7

8 4.0 0.5

16 5.1 0.3

32 5.9 0.2

64 6.4 0.1Pest

0.86Estimated parallel percentage of the

algorithm.Sest

Estimated SpeedupN

Number of coresE

EfficiencySmax

7.0

Calculate estimated Parallel % and estimated maximum Speedup from results based on 2 cores CPU.

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Discussion

N Sest E

4 2.7 0.7

8 3.8 0.5

16 4.7 0.3

32 5.4 0.2

64 6.4 0.1Pest

0.84Estimated parallel percentage of the

algorithm.Sest

Estimated SpeedupN

Number of coresE

EfficiencySmax

6.3

Calculate estimated Parallel % and estimated maximum Speedup from results based on 4 cores CPU.

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Discussion

The estimated parallelized part of the algorithm is 85% so by applying Amdahl’s Law and setting the number of CPUs to infinite, then the maximum estimated speedup is 6.6.

When comparing PMEGA with itself, using different number of subpopulations at the same problem, a minor reduction to the speedup gained is observed.

PMEGA can provide similar solutions with MEGA. PMEGA’s subpopulations can provide solutions that are different

among subpopulations. Despite the fact that subpopulations were selected at random without the use of any knowledge.

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Conclusions

MEGA and PMEGA behave comparably. The differences observed between the final Pareto-front approximations produced, are partly due to the way PMEGA splits the working population into subpopulations.

PMEGA can achieve a maximum speedup of 6.6. On the other hand is stated clearly that when using a two cores CPU, PMEGA completes in the half time that MEGA needs and when using a four cores CPU, PMEGA completes almost in one third of the time that MEGA needs.

Number of subpopulations has an effect on the quality of the results obtained. With more subpopulations the more uniform the resulting solutions are, at least in objective space.

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Future Work

Algorithmic improvements in the way subpopulations are selected with the aid of knowledge-driven approaches in order to improve the quality of the optimization search and reduce the number of iterations needed for convergence.

Also an investigation if further parallelization is possible in order to achieve a better maximum speedup.

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Documents

2009 MSc Presentation for Parallel-MEGA