This document outlines a parallel implementation of a multi-objective evolutionary algorithm. It discusses evolutionary algorithms and their use for single and multi-objective optimization problems. It also describes how parallel evolutionary algorithms can distribute computational work across multiple cores for faster computation. The document then details a Multi-Objective Evolutionary Graph Algorithm and its parallel implementation to solve multi-objective optimization problems efficiently using parallel computing resources.

1. A Parallel Implementation of a
Multi-Objective Evolutionary
Algorithm
Christos Kannas
Constantinos Pattichis
University of Cyprus

2. 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
2

3. 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.
3

4. 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.
4

5. Evolutionary Algorithms
Background
 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.
5

6. Evolutionary Algorithms
Single & 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.
6

7. Evolutionary Algorithms
The family
EAs are a big family of algorithms.
Genetic Algorithms (GAs).
Chromosome string. Population
Genetic Programming (GP).
Tree structure. Fitness Evaluation
Evolutionary Strategies (ES).
Real value vectors. Parent Selection
Evolutionary Programming (EP).
Finite State Machines.
Reproduction
7

8. Parallel Evolutionary Algorithms
Coarse grained.
Divide the population into several subpopulations. Subpop 1
Distribution of the subpopulations.
Fine grained. Subpop 2 Subpop 3
Inherent parallelism.
Individual level parallelism.
Fitness level parallelism.
Subpop 5 Subpop 4
Master
Fitness Assignment
Slave 1 Slave 2 Slave N
Reproduction Reproduction Reproduction
Fitness Fitness Fitness
Evaluation Evaluation Evaluation
8

9. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
9

10. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
10

11. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
11

12. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
12

13. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
13

14. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
14

15. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
15

16. Algorithms
 Multi-Objective Evolutionary Graph Algorithm (MEGA) description.
 Chromosomes are graphs.
Working Population Evolve Parents
Select Parents
Calculate Fitness
Hard Filter Calculate Efficiency
Pareto Ranking
16

17. 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.
17

18. 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.
18

19. Implementation
Working Population
Subpopulation 1 Subpopulation X
Subpopulation 2
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.
19

20. Implementation
Working Population
Subpopulation 1 Subpopulation X
Subpopulation 2
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.
20

21. Implementation
Working Population
Subpopulation 1 Subpopulation X
Subpopulation 2
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.
21

22. Implementation
Working Population
Subpopulation 1 Subpopulation X
Subpopulation 2
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.
22

23. Implementation
Working Population
Subpopulation 1 Subpopulation X
Subpopulation 2
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.
23

24. Implementation
Working Population
Subpopulation 1 Subpopulation X
Subpopulation 2
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.
24

25. Results
 MEGA vs. PMEGA on 2 cores CPU
 CPU: Intel Core 2 Duo E8400 @ 3.0 GHz (2 Physical Cores)
 Memory: 4 Gbytes
PMEGA 2 PMEGA 4
MEGA
Subpopulations Subpopulations
1st Experiment Average Execution
0:39:15 0:22:44 0:25:50
(population 100, Time
iterations 200) Speedup 1.727206062 1.519243174
Average Execution
2nd Experiment 1:04:44 0:34:48 0:40:33
Time
(population 150,
iterations 200) Speedup 1.859696728 1.596464785
Average Execution
3rd Experiment 1:22:20 0:49:22 0:54:22
Time
(population 200,
iterations 200) Speedup 1.667604366 1.514253602
Summary Average Speedup 1.8
25

26. Results
 MEGA
 Blue dots: 1st Pareto front
 Red dots: Pareto fronts at 25%, 50%, 75% and 100%.
26

27. Results
 PMEGA 2 Subpopulations
 Blue dots: 1st Pareto front
 Red dots: Pareto front at 100%.
27

28. Results
 PMEGA 4 Subpopulations
 Blue dots: 1st Pareto front
 Red dots: Pareto front at 100%.
28

29. Results
 Genotype
diversity:
Clustering
at
parameter
space.
 Phenotype
diversity:
Clustering
at objective
space.
29

30. Results
 ER-alpha active ligands (left).
 ER-beta active ligands (right).
30

31. Results
 MEGA vs. PMEGA 2 Subpopulations vs. PMEGA 4 Subpopulations
31

32. Results
 MEGA vs. PMEGA on 4 cores CPU
 CPU: Inter Core 2 Duo Quad Q6600 @ 2.4 GHz (4 Physical Cores)
 Memory: 4 Gbytes
PMEGA 2 PMEGA 4
MEGA
Subpopulations Subpopulations
1st Experiment Average
0:55:57 0:20:53 0:21:27
(population 100, Execution Time
iterations 200) Speedup 2.678191489 2.60880829
2nd Experiment Average
1:26:18 0:32:02 0:32:12
(population 150, Execution Time
iterations 200) Speedup 2.693895248 2.679489391
3rd Experiment Average
1:56:45 0:42:39 0:41:45
(population 200, Execution Time
iterations 200) Speedup 2.73752768 2.796540253
Summary Average Speedup 2.7
32

33. Results
 MEGA
 Blue dots: 1st Pareto front
 Red dots: Pareto fronts at 25%, 50%, 75% and 100%.
33

34. Results
 PMEGA 4 Subpopulations
 Blue dots: 1st Pareto front
 Red dots: Pareto front at 100%.
34

35. Results
 PMEGA 8 Subpopulations
 Blue dots: 1st Pareto front
 Red dots: Pareto front at 100%.
35

36. Results
 Genotype
diversity:
Clustering
at
parameter
space.
 Phenotype
diversity:
Clustering
at objective
space.
36

37. Results
 ER-alpha active ligands (left).
 ER-beta active ligands (right).
37

38. Results
 MEGA vs. PMEGA 4 Subpopulations vs. PMEGA 8 Subpopulations
38

39. Discussion
 Amdahl’s Law.
 Speedup
 Maximum Speedup
39

40. Discussion
Calculate estimated Parallel % and estimated maximum Speedup
from results based on 2 cores CPU.
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 0.1
Pest Estimated parallel percentage of the
0.86 algorithm.
Sest
Estimated Speedup
N
Number of cores
E
Efficiency
Smax
7.0
40

41. Discussion
Calculate estimated Parallel % and estimated maximum Speedup
from results based on 4 cores CPU.
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 0.1
Pest Estimated parallel percentage of the
0.84 algorithm.
Sest
Estimated Speedup
N
Number of cores
E
Efficiency
Smax
6.3
41

42. 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.
42

43. 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.
43

44. 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.
44

45. Bibliography
1. M. Tomassini, Parallel and Distributed Evolutionary Algorithms: A Review,
Institute of Computer Science, University of Lausanne.
2. Bäck T., Evolutionary Algorithms in Theory and Practice. Oxford University Press
1996
3. http://en.wikipedia.org/wiki/Optimization_%28mathematics%29 (accessed
December 18, 2009)
4. http://en.wikipedia.org/wiki/Charles_Darwin (accessed December 1, 2009)
5. Darwin, C. R. 1876, The origin of species by means of natural selection, or the
preservation of favoured races in the struggle for life. London: John Murray. 6th
ed, with additions and corrections.
6. http://anthro.palomar.edu/synthetic/default.htm (accessed December 1, 2009)
7. C. A. Nicolaou, J. Apostolakis,, and C. S. Pattichis, “De Novo Drug Design Using
Multiobjective Evolutionary Graphs”, J. Chem. Inf. Model., vol. 49(2), pp. 295-
307, 2009.
45

46. Bibliography
8. Baringhaus, K.-H.; Matter, H. Efficient strategies for lead optimization by
simultaneously addressing affinity, selectivity and pharmacokinetic parameters. In
Chemoinformatics in Drug DiscoVery; Oprea, T., Ed.; Wiley-VCH: Weinheim,
Germany, 2004; pp 333-379.
9. Schneider, G.; Fechner, U. Computer-based de novo design of druglike molecules.
Nat. ReV. Drug DiscoVery 2005, 4, 649–663.
10. Xu, J.; Hagler, A. Chemoinformatics and drug discovery. Molecules 2002, 7, 566–
600.
11. Bohacek, R. S.; Martin, C.; Guida, W. C. The Art and Practice of Structure-Based
Drug Design: A Molecular Modelling Approach. Med. Res. ReV. 1996, 16, 3–50.
12. Evolutionary Algorithms 8 Population models – Parallel Implementations,
http://www.geatbx.com/docu/algindex-07.html (accessed August 20, 2009).
13. P. Adamidis, Parallel Evolutionary algorithms: A Review, Dept. of Applied
Informatics, University of Macedonia.
46

47. Bibliography
14. http://en.wikipedia.org/wiki/Speedup (accessed December 1, 2009).
15. http://en.wikipedia.org/wiki/Gene_Amdahl (accessed December 1, 2009).
16. http://en.wikipedia.org/wiki/ Amdahl's_law (accessed December 1, 2009).
17. Fonseca, C. M.; Fleming, P. J. Genetic Algorithms for Multiobjective
Optimization: Formulation, Discussion and Generalization. In Proceedings of the
Fifth International Conference on Genetic Algorithms; Forrest, S., Ed.; Morgan
Kaufmann: San Mateo, CA, 1993; pp 416-423.
18. Y. Colette, P. Siarry, Multiobjective Optimization: Principles and Case Studies;
Springer-Verlag: Berlin, Germany, 2004.
19. http://www.python.org (accessed August 20, 2009).
20. http://www.parallelpython.com (accessed September 23, 2009).
21. http://code.google.com/p/mpi4py (accessed September 23, 2009).
22. http://en.wikipedia.org/wiki/CUDA (accessed September 23, 2009).
47

48. Bibliography
23. http://en.wikipedia.org/wiki/OpenCL (accessed September 23, 2009).
24. http://pypi.python.org/pypi/pycuda (accessed September 23, 2009).
25. http://pypi.python.org/pypi/pyopencl (accessed September 23, 2009).
26. http://en.wikipedia.org/wiki/Global_Interpreter_Lock (accessed September 23,
2009).
27. http://docs.python.org/library/multiprocessing.html (accessed September 23, 2009).
28. http://docs.python.org/library/threading.html #module-threading (accessed
September 23, 2009).
29. J. Noller, R. Oudkerk, PEP 371 -- Addition of the multiprocessing package to the
standard library, (accessed Mar 19, 2009).
30. http://en.wikipedia.org/wiki/Cluster_analysis (accessed December 16 2009)
31. http://www.cs.ucy.ac.cy/itab2009/
32. http://en.wikipedia.org/wiki/Jaccard_index (accessed September 28, 2009).
48

49. Bibliography
34. Wheeler, D. L.; Barrett, T.; Benson, D. A.; Bryant, S. H.; Canese, K.; Chetvernin,
V.; Church, D. M.; DiCuccio, M.; Edgar, R.; Federhen, S.; Geer, L. Y.; Helmberg,
W.; Kapustin, Y.; Kenton, D. L.; Khovayko, O.; Lipman, D. J.; Madden, T. L.;
Maglott, D. R.; Ostell, J.; Pruitt, K. D.; Schuler, G. D.; Schriml, L. M.; Sequeira,
E.; Sherry, S. T.; Sirotkin, K.; Souvorov, A.; Starchenko, G.; Suzek, T. O.;
Tatusov, R.; Tatusova, T. A.; Wagner, L.; Yaschenko, E. Database resources of the
National Center for Biotechnology Information. Nucleic Acids Res. 2006, 34,
D173–D180.
35. http://www.noesisinformatics.com (accessed September 28, 2009).
36. http://molinspiration.com (accessed December 16 2009)
37. Handl, J.; Kell, D. B.; Knowles, J. Multiobjective Optimization in Bioinformatics
and Computational Biology. IEEE/ACM Trans. Comput. Biol. Bioinf. 2007, 4,
279–292.
38. Alberto, I.; Azcarate, C.; Mallor, F. & Mateo, P.M., Multiobjective Evolutionary
Algorithms. Pareto Rankings.
49

50. Bibliography
39. Yong Liang, Kwong-Sak Laung, Tony Shu am Mok, A Novel Evolutionary Drug
Scheduling Model in Cancer Cemotherapy, 2004
40. H. S. Lopes, Evolutionary Algorithms for the Protein Folding Problem: A Review
and Current Trends, 2008
41. C. M. V. Benitez, H. S. Lopes, A Parallel Genetic Algorithm for Protein Folding
Prediction Using the 3D-HP Side Chain Model, 2009
42. E. Alba, Parallel Evolutionary Algorithms can achieve super-linear Performance,
University of Malaga.
43. N. Matloff, F. Hsu Tutorial on Threads Programming with Python, 2007.
44. C. Nicolaou, C. Kannas, C. Pattichis, Optimal graph Design Using A Knowledge-
driven Multi-objective Evolutionary Graph Algorithm In Proceedings of the Ninth
International Conference on Information Techonology and Applications in
Biomedicine, Larnaca Cyprus, November 5 - 7, 2009
50