Understanding Simple Asynchronous Evolutionary Algorithms Eric O. - - PowerPoint PPT Presentation

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Understanding Simple Asynchronous Evolutionary Algorithms

Eric O. Scott and Kenneth A. De Jong

George Mason University

18 May, 2015

Dagstuhl Seminar 15211

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Domain: Long fitness evaluation times. Parallelization is a must. Evaluation times vary.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

The Generational Master-Slave EA

1: function GenerationalEvolution(n, gens) 2:

P ← ∅

3:

while |P| < n do ⊲ Initialize population.

4:

P ← P ∪ {randomIndividual()}

5:

for i ← 0 to gens do ⊲ Evolutionary loop.

6:

for all ind ∈ P do in parallel

7:

evaluateFitness(ind)

8:

P ← select(P) ⊲ Choose parents.

9:

P ← reproduce(P) ⊲ Mutation and Crossover. return P

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Idle Time in a Generational EA

1 2 3 4 5 6 7 8 9 10 0.00 0.25 0.50 0.75 1.00

Evaluation Time Individual

How Evaluation Time Variance Induces Idle Time

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Asynchronous EA Background

Asynchronous master-slave EAs have been around since the early nineties. Used occasionally by practitioners.

[Rasheed and Davison, 1999, Depolli et al., 2013, Luke, 2014]

Very few papers analyzing their behavior and benefits

[Zeigler and Kim, 1993, Kim, 1994].

Of greater relevance today, as parameter tuning for large simulations is becoming more widespread.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

The Asynchronous Master-Slave EA

Asynchronous: Perform (µ + 1) when an evaluation completes. Asynchronous search behavior: Eliminates idle time. lntroduces reordering => new search trajectory. Wall clock speedup? Convergence time speedup?

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Evaluation Sequence in a Generational EA

25 50 75 100 3 6 9

Time Birth Step

Evaluation Sequence in Wall−Clock Time

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Evaluation Sequence in an Asynchronous EA

300 325 350 375 400 3000 3100 3200 3300

Time Birth Step

Evaluation Sequence in Wall−Clock Time

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Research questions:

1 Eval-Time Selection: Is it biased toward fast-evaluating

genotypes?

2 Evaluation Speedup: How fast is it? 3 True Speedup: Is it smart?

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Evaluation-Time Bias

RQ 1 When individual evaluation times are a heritable trait, does the asynchronous EA given a reproductive advantage to faster-evaluating individuals?

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Evaluation-Time Bias on Flat Landscape

0.00 0.25 0.50 0.75 1.00 25 50 75 100

generation Frequency of Slow−Type Allele

Mean 95% Conf.

• Std. Dev.

Genetic Drift on Flat Landscape

Gene with two alleles: fast and slow. slow takes 10 times longer than fast to evaluate. Flat fitness landscape, no reproductive variation. No observable selection effect favoring fast-evaluating individuals?

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Non-Flat Landscapes: Four Heritability Scenarios

1 Non-Heritable: eval-time is independent of everything. 2 Heritable: eval-time is genetically moderated. 3 Positive fitness-correlation: Faster as we approach the

• ptimum.

4 Negative fitness-correlated scenario: Slower as we approach

the optimum.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

A Function for Demonstrating Evaluation-Time Bias

Fitness function Eval-time Function

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Evaluation-Time Bias on and Fitness

0.00 0.25 0.50 0.75 1.00 A Fast, B Slow Constant Eval−Time Eval−Time = Fitness

Ratio of Runs Converging to Basin A

Convergence to Fast Optimum on Two−Basin Objective

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Premature Convergence on Two-Basin Problem

When basin B is 1.5 times as deep as basin A:

0.0 0.1 0.2 A Fast, B Slow Constant Time A Slow, B Fast

Ratio of Runs Converging to Basin A

Convergence to Fast Optimum on Two−Basin Objective

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Evaluation Speedup Analysis

RQ 2 How great an increase in evaluation throughput does the simple asynchronous EA offer over a parallelized synchronous EA? Evaluation Speedup: How many more individuals the asynchronous EA evaluates per unit time.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Theory for Uniform Distribution

Eval-times distributed on U(a, b) with a population size of n. Expected fraction of idle time: E[ˆ I] ≥ b − a b 1 2 − 1 n + 1

• 1

2 3 4 5 6 7 8 9 10 0.00 0.25 0.50 0.75 1.00

Evaluation Time Individual

How Evaluation Time Variance Induces Idle Time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0.00 0.25 0.50 0.75 1.00

Evaluation Time Individual

How Evaluation Time Variance Induces Idle Time

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion 1.00 1.25 1.50 1.75 2.00 10 20 30

nodes speedup

Eval−time Distribution U(0, 500ms) U(125ms, 500ms)

Speedup in Throughput via Asynchrony

The evaluation speedup is impacted by the variance, the number of processors, and the population size.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion 1.0 1.2 1.4 1.6 10 20 30 40 50

Population Size Speedup

Asynchronous Speedup by Population Size

As the ratio of population-to-processors grows, the variance in eval times is reduced, and less speedup is possible.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Wallclock Time to Convergence: ”True” Speedup

RQ 3 Are the extra evaluations provided by an asynchronous EA constructive? Do they help us converge on the

• ptimum faster?

True Speedup: How much faster the asynchronous EA converges to a good fitness value.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Objective Functions

Performance of the asynchronous EA depends on both Fitness landscape. Relationship between fitness and evaluation time.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Four Heritability Scenarios

1 Non-Heritable: eval-time is independent of everything. 2 Heritable: eval-time is genetically moderated. 3 Positive fitness-correlation: Faster as we approach the

• ptimum.

4 Negative fitness-correlated scenario: Slower as we approach

the optimum.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Speedup on Sphere Function

2 4 6 Non−Heritable Heritable Positive Negative

Speedup

Evaluation Speedup on the Sphere Function

2 4 6 Non−Heritable Heritable Positive Negative

Speedup

True Speedup on the Sphere Function

Performance improvement explained by speedup in fitness evaluations.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Speedup on Rastrigin Function

10 20 30 Non−Heritable Heritable Positive Negative

Speedup

Evaluation Speedup on the Rastrigin Function

10 20 30 Non−Heritable Heritable Positive Negative

Speedup

True Speedup on the Rastrigin Function

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Conclusion

Yes, evaluation-time bias exists, but complicated and esoteric. In practice, the simple asynchronous EA is a reasonably “smart” algorithm – it’s able to capitalize on the extra fitness evaluations it executes. The asynchronous EA can be especially effective when evaluation times are long and eval-time variance, is high. The evaluation speedup is negligible when high-fitness individuals dominate evaluation cost.

Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion

Future Work

Study eval-time variance in real-world problems, and measure the performance of the simple asynchronous EA. A better theoretical grasp on the impact of evaluation time on search trajectories.

References Alexander W Churchill, Phil Husbands, and Andrew Philippides. Tool sequence optimization using synchronous and asynchronous parallel multi-objective evolutionary algorithms with heterogeneous evaluations. In IEEE Congress

• n Evolutionary Computation (CEC) 2013, pages 2924–2931. IEEE, 2013.

Matjaˇ z Depolli, Roman Trobec, and Bogdan Filipiˇ

• c. Asynchronous master-slave parallelization of differential

evolution for multi-objective optimization. Evolutionary computation, 21(2):261–291, 2013. Jinwoo Kim. Hierarchical asynchronous genetic algorithms for parallel/distributed simulation-based optimization. PhD thesis, The University of Arizona, 1994. Sean Luke. The ECJ Owner’s Manual. http://cs.gmu.edu/~eclab/projects/ecj/, 22nd edition, August 2014. Khaled Rasheed and Brian D Davison. Effect of global parallelism on the behavior of a steady state genetic algorithm for design optimization. In Proceedings of the 1999 Congress on Evolutionary Computation, volume 1. IEEE, 1999. Eric O. Scott and Kenneth A. De Jong. Understanding simple asynchronous evolutionary algorithms. In FOGA’15, Proceedings of the 2015 ACM Conference on Foundations of Genetic Algorithms XIII, pages 85–98, New York, NY, 2015. ACM. Mouadh Yagoubi, Ludovic Thobois, and Marc Schoenauer. Asynchronous evolutionary multi-objective algorithms with heterogeneous evaluation costs. In IEEE Congress on Evolutionary Computation (CEC) 2011, pages 21–28. IEEE, 2011. Bernard P Zeigler and Jinwoo Kim. Asynchronous genetic algorithms on parallel computers. In Proceedings of the 5th International Conference on Genetic Algorithms, page 660. Morgan Kaufmann Publishers Inc., 1993.