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July 12-16, 2014 Genetic and Evolutionary Computation Conference (GECCO 2014)@Vancouver, BC, Canada Asynchronously Evolving Solutions with Excessively Different Evaluation Time by Reference-based Evaluation 2014/07/15 Tomohiro Harada 1,2 , Keiki

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SLIDE 1

Asynchronously Evolving Solutions with Excessively Different Evaluation Time by Reference-based Evaluation

2014/07/15 Tomohiro Harada1,2, Keiki Takadama1

1The University of Electro-Communications, Japan 2Research Fellow of the Japan Society for the Promotion of Science DC1, Japan Genetic and Evolutionary Computation Conference (GECCO 2014)@Vancouver, BC, Canada July 12-16, 2014

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SLIDE 2

Introduction

Synchronous EA and its problem

μ λ μ

Select best μ individuals depending on all evaluations Deletion

sorting

Evaluate all individuals

Generate

  • ffspring

x1 x2 x3 x4 x5 x6

Needs to wait for evaluation of x6 to select next population

General EA=Synchronous EA

evolves individuals depending on evaluations of entire population

If evaluation time of individuals differs from each other →sync. EA needs to wait for the slowest one

e.g., (μ+λ)-selection

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SLIDE 3

Asynchronous EA

evolves individuals independently (asynchronously) e.g., TAGP [Harada2013] Advantage : Async. EA needs not to wait for other individuals →can continue an evolution even in different evaluation time

generate offspring deletion

× × ×

x1 x2 x3 x4 x5 x6 x3’ x2’ x3’’

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SLIDE 4

Difficulties of Async. EA

  • 1. How to preserve good individuals?
  • 2. How to delete bad individuals?

? ?

x1 x2 x3 good? bad?

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SLIDE 5

Objective

To propose EA using Asynchronous Reference-based Evaluation (ARE-EA) To investigate effectiveness of ARE-EA in situation where evaluation times are excessively different

  • 1. Different computing speed
  • 2. Evaluation failure

(e.g., Difference of processing ability) (e.g., Infinite loop, Communication error)

  • Archive mechanism to preserve good individuals
  • Reference individual to delete bad individuals
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SLIDE 6

Proposed method

ARE-EA

Population ind1 ind2 ind1 ind2 Archive Archive size as (1) Evaluation

(Asynchronous)

Evaluated

(3) Mutation & Crossover (6) Reaper deletion (5) Fitness deletion (4) Archiving (1) Evaluation

(Asynchronous)

(2) Selection

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SLIDE 7

Proposed method

ARE-EA

indref Population ind1 ind2 ind1 ind2 Archive Archive size as indref

Evaluated

par1 par2 (2) Selection (1) Evaluation

(Asynchronous)

Reference

randomly selected from archive

Good individuals (indref) are utilized for selection

(3) Mutation & Crossover (6) Reaper deletion (5) Fitness deletion (4) Archiving (1) Evaluation

(Asynchronous)

(2) Selection

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SLIDE 8

Proposed method

ARE-EA

indref Population ind1 ind2 ind1 ind2 Archive size as indref

  • ff2
  • ff1

Evaluated

par1 par2

  • ff1
  • ff2

Reference (2) Selection (3) Mutation & Crossover (1) Evaluation

(Asynchronous)

  • ld

new

(3) Mutation & Crossover (6) Reaper deletion (5) Fitness deletion (4) Archiving (1) Evaluation

(Asynchronous)

(2) Selection

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SLIDE 9

Proposed method

ARE-EA

indref Population ind1 ind2 ind1 ind2 Archive Archive size as indref

  • ff2
  • ff1

Evaluated

par1 par2

  • ff1
  • ff2

if indi>indref Reference (2) Selection (3) Mutation & Crossover (4) Archiving (1) Evaluation

(Asynchronous)

Asynchronously archiving good individuals

(3) Mutation & Crossover (6) Reaper deletion (5) Fitness deletion (4) Archiving (1) Evaluation

(Asynchronous)

(2) Selection

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SLIDE 10

Proposed method

ARE-EA

indref Population ind1 ind2 ind1 ind2 Archive Archive size as indref

  • ff2
  • ff1

Evaluated

par1 par2

  • ff1
  • ff2

with probability Pd if indi>indref Reference (2) Selection (3) Mutation & Crossover (4) Archiving (5) Fitness deletion if indi<indref (1) Evaluation

(Asynchronous)

Deletion based on comparison with reference →delete bad individuals (6) Reaper deletion

(3) Mutation & Crossover (6) Reaper deletion (5) Fitness deletion (4) Archiving (1) Evaluation

(Asynchronous)

(2) Selection

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SLIDE 11

Proposed method

ARE-EA

indref Population ind1 ind2 ind1 ind2 Archive Archive size as indref

  • ff2
  • ff1

Evaluated

par1 par2

  • ff1
  • ff2

with probability Pd if indi>indref Reference (2) Selection (3) Mutation & Crossover (4) Archiving (6) Reaper deletion if indi<indref individuals with long evaluation time is deleted (1) Evaluation

(Asynchronous)

(5) Fitness deletion

(3) Mutation & Crossover (6) Reaper deletion (5) Fitness deletion (4) Archiving (1) Evaluation

(Asynchronous)

(2) Selection

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SLIDE 12

Experiment

Employing Linear GP (LGP) testbeds

Instruction set +, -, ×, /, sin, cos, exp, ln x0…x7, constant={1, 2, …, 9} Symbolic regression 1 f(x)=x4+x3+x2+x 2 f(x)=x6-2x4+x2 3 f(x)=sin(x2)×cos(x)-1 4 f(x)=ln(x+1)+ln(x2+1)

Testbed problem vs.

(asynchronous) (synchronous)

ARE-GP (μ+λ)-GP

in situation where evaluation times are excessively different

Comparison

[J. McDermott, et al., 2012]

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SLIDE 13

Settings

(2) Evaluation failure (e.g., Infinite loop, Communication error) Different evaluation time situations

Same Different

(1) Different computing speed (e.g., Difference of processing ability)

No failure Failure

… 80insts./unit time 100insts./unit time 20insts./unit time 60insts./unit time 40insts./unit time … 100insts./unit time 100insts./unit time 100insts./unit time 100insts./unit time 100insts./unit time … … 5% Failure

×

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SLIDE 14

Cases

Same Different No failure Case1 Case2 Failure Case3 Case4 Failure Speed

Evaluation Criterion Average fitness according to the same elapsed unit time

20 trials *(μ+λ)-GP uses ideal limitation time to cut off evaluations in Cases3&4 *ARE-GP : archive size as=5, deletion probability Pd=0.5

: target value y∗

i

: output ˆ yi fitness = 1 m

m

X

i=1

( ˆ yi − y∗

i )2

: # of test data m

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SLIDE 15

Same Different No failure Case1 Case2 Failure Case3 Case4 Failure Speed

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SLIDE 16

(4)f(x)=ln(x+1)+ln(x2+1)

Result : Case1

Same Different No failure Case1 Case2 Failure Case3 Case4 Failure Speed

fitness 0.05 0.1 0.15 0.2 0.25 0.3 Elapsed unit time (x10^5) 20 40 60 80 100 fitness 0.001 0.002 0.003 Elapsed unit time (x10^5) 20 40 60 80 100 fitness 0.005 0.01 0.015 Elapsed unit time (10^5) 20 40 60 80 100 fitness 0.02 0.04 0.06 0.08 0.1 Elapsed unit time (x10^5) 20 40 60 80 100

(1)f(x)=x4+x3+x2+x (2)f(x)=x6-2x4+x2 (3)f(x)=sin(x2)×cos(x)-1

(μ+λ)-GP ARE-GP ARE-GP>(μ+λ)-GP →ARE-GP evolves individuals without waisting time

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SLIDE 17

Same Different No failure Case1 Case2 Failure Case3 Case4 Failure Speed

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SLIDE 18

Result : Case4

Same Different No failure Case1 Case2 Failure Case3 Case4 Failure Speed

fitness 0.1 0.2 0.3 0.4 0.5 0.6 Elapsed unit time (x10^5) 20 40 60 80 100 fitness 0.001 0.002 0.003 Elapsed unit time (x10^5) 20 40 60 80 100 fitness 0.005 0.01 0.015 Elapsed unit time (x10^5) 20 40 60 80 100 fitness 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Elapsed unit time (x10^5) 20 40 60 80 100

(1)f(x)=x4+x3+x2+x (2)f(x)=x6-2x4+x2 (3)f(x)=sin(x2)×cos(x)-1 (4)f(x)=ln(x+1)+ln(x2+1)

(μ+λ)-GP ARE-GP

(Ideal limitation time is used)

ARE-GP evolves individuals without any limitations even though evaluation failure occurs ARE-GP>(μ+λ)-GP ARE-GP efficiently evolves individuals in situation where evaluation times are excessively different

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SLIDE 19

Result

  • nly uses a few evaluations

can use all evaluations ARE-GP (μ+λ)-GP

ARE-GP > (μ+λ)-GP in all cases and in all testbeds

? ? ? f4 ? f6 f6 f5 f4 f3 f2 f1

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SLIDE 20

f_Case4/f_Case1 0.1 1 10 Elapsed unit time (x10^5) 20 40 60 80 100

Comparison of Case1&Case4

Ratio of fitness between Case1 and Case4

(1)f(x)=x4+x3+x2+x

fitness

0.05 0.1 0.15 0.2 0.25 0.3

Elapsed unit time (x10^5)

20 40 60 80 100

fitness

0.1 0.2 0.3 0.4 0.5 0.6

Elapsed unit time (x10^5)

20 40 60 80 100

Case4<Case1 Case4>Case1

Case4 decreases performance than Case1 Case4 increases performance than Case1

Case1 Case4

(μ+λ)-GP .fcase4(t) (μ+λ)-GP .fcase1(t) ARE-GP .fcase4(t) ARE-GP .fcase1(t)

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SLIDE 21

f_Case4/f_Case1 0.1 1 10 Elapsed unit time (x10^5) 20 40 60 80 100 f_Case4/f_Case1 0.1 1 10 Elapsed unit time (x10^5) 20 40 60 80 100 f_Case4/f_Case1 0.1 1 10 Elapsed unit time (x10^5) 20 40 60 80 100 f_Case4/f_Case1 0.1 1 10 Elapsed unit time (x10^5) 20 40 60 80 100

Comparison of Case1&Case4

Case4>Case1 Case4<Case1 Case4>Case1 Case4<Case1 Case4>Case1 Case4<Case1 Case4>Case1 Case4<Case1

(1)f(x)=x4+x3+x2+x (2)f(x)=x6-2x4+x2 (3)f(x)=sin(x2)×cos(x)-1 (4)f(x)=ln(x+1)+ln(x2+1)

ARE-GP has possibility to improve search performance in different evaluation time

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SLIDE 22

Conclusion

Objective

  • Proposing EA using Asynchronous Reference-based

Evaluation (ARE-EA)

  • Investigating effectiveness of ARE-EA in excessively

different evaluation times

  • different computing speed
  • evaluation failure

Implications

  • ARE-GP>(μ+λ)-GP
  • in excessively different evaluation time
  • ARE-GP improves performance in different evaluation time

Future works

  • Validation in parallel computing environment
  • Adaptation of parameters Pd and as