Asynchronously Evolving Solutions with Excessively Different - PowerPoint PPT Presentation

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 Takadama 1 1 The University of Electro-Communications, Japan 2 Research Fellow of the Japan Society for the Promotion of Science DC1, Japan

Introduction Synchronous EA and its problem General EA= Synchronous EA evolves individuals depending on evaluations of entire population If evaluation time of individuals di ff ers from each other → sync. EA needs to wait for the slowest one e.g., ( μ + λ )-selection x 1 x 2 Generate μ μ o ff spring x 3 x 4 sorting x 5 x 6 λ Deletion Needs to wait for evaluation of x 6 to select next population Evaluate Select best μ individuals all individuals depending on all evaluations

× × × Asynchronous EA evolves individuals independently ( asynchronously ) e.g., TAGP [Harada2013] x 1 x 2 deletion x 3 x 4 x 5 x 6 x 3 ’ generate o ff spring x 2 ’ x 3 ’’ Advantage : Async. EA needs not to wait for other individuals → can continue an evolution even in di ff erent evaluation time

Di ffi culties of Async. EA 1. How to preserve good individuals? � 2. How to delete bad individuals? good? bad? x 1 ? x 2 ? x 3

Objective To propose EA using Asynchronous Reference-based Evaluation (ARE-EA) ‣ Archive mechanism to preserve good individuals ‣ Reference individual to delete bad individuals To investigate e ff ectiveness of ARE-EA in situation where evaluation times are excessively di ff erent 1. Di ff erent computing speed (e.g., Di ff erence of processing ability) 2. Evaluation failure (e.g., Infinite loop, Communication error)

(Asynchronous) (3) Mutation Proposed method (2) Selection (1) Evaluation & Crossover ARE-EA (5) Fitness (6) Reaper (4) Archiving deletion deletion Archive Population Archive size as ind 1 (Asynchronous) ind 2 ind 1 (1) Evaluation ind 2 Evaluated

(Asynchronous) (3) Mutation Proposed method (2) Selection (1) Evaluation & Crossover ARE-EA (5) Fitness (6) Reaper (4) Archiving deletion deletion Archive Population Archive size ind ref as Reference randomly selected ind ref ind 1 from archive par 1 (Asynchronous) ind 2 ind 1 par 2 (1) Evaluation ind 2 (2) Selection Evaluated Good individuals ( ind ref ) are utilized for selection

(Asynchronous) (3) Mutation Proposed method (2) Selection (1) Evaluation & Crossover ARE-EA (5) Fitness (6) Reaper (4) Archiving deletion deletion Population Archive size ind ref old as Reference (3) Mutation ind ref ind 1 & Crossover par 1 off 1 (Asynchronous) ind 2 ind 1 par 2 off 2 (1) Evaluation ind 2 (2) Selection Evaluated off 1 off 2 new

(Asynchronous) (3) Mutation Proposed method (2) Selection (1) Evaluation & Crossover ARE-EA (5) Fitness (6) Reaper (4) Archiving deletion deletion Archive Population Archive size (4) Archiving ind ref as Asynchronously archiving if ind i >ind ref good individuals Reference (3) Mutation ind ref ind 1 & Crossover par 1 off 1 (Asynchronous) ind 2 ind 1 par 2 off 2 (1) Evaluation ind 2 (2) Selection Evaluated off 1 off 2

(Asynchronous) (3) Mutation Proposed method (2) Selection (1) Evaluation & Crossover ARE-EA (5) Fitness (6) Reaper (4) Archiving deletion deletion Archive (6) Reaper deletion Population Archive size (4) Archiving ind ref as if ind i >ind ref Reference (3) Mutation (5) Fitness ind ref ind 1 & Crossover deletion par 1 off 1 (Asynchronous) if ind i <ind ref ind 2 ind 1 par 2 off 2 (1) Evaluation ind 2 with probability P d (2) Selection Evaluated off 1 Deletion based on comparison with reference off 2 → delete bad individuals

(Asynchronous) (3) Mutation Proposed method (2) Selection (1) Evaluation & Crossover ARE-EA (5) Fitness (6) Reaper (4) Archiving deletion deletion Archive (6) Reaper deletion Population Archive size (4) Archiving ind ref individuals with as long evaluation if ind i >ind ref time is deleted Reference (3) Mutation (5) Fitness ind ref ind 1 & Crossover deletion par 1 off 1 (Asynchronous) if ind i <ind ref ind 2 ind 1 par 2 off 2 (1) Evaluation ind 2 with probability P d (2) Selection Evaluated off 1 off 2

Experiment Comparison ARE-GP vs. ( μ + λ )-GP (asynchronous) (synchronous) in situation where evaluation times are excessively di ff erent Testbed problem Employing Linear GP (LGP) testbeds Instruction set Symbolic regression 1 f ( x ) =x 4 +x 3 +x 2 +x +, -, × , /, sin, cos, exp, ln x 0 …x 7 , constant ={1, 2, …, 9} 2 f ( x ) =x 6 -2x 4 +x 2 3 f ( x ) =sin ( x 2 ) × cos ( x ) - 1 4 f ( x ) =ln ( x+ 1) +ln ( x 2 + 1) [J. McDermott, et al., 2012]

× … … … Settings Di ff erent evaluation time situations (1) Di ff erent computing speed (e.g., Di ff erence of processing ability) Same Di ff erent 100insts./unit time 100insts./unit time 100insts./unit time 80insts./unit time 100insts./unit time 60insts./unit time 100insts./unit time 40insts./unit time 100insts./unit time 20insts./unit time (2) Evaluation failure (e.g., Infinite loop, Communication error) No failure Failure … 5% Failure

Cases Speed Same Di ff erent Failure No failure Case1 Case2 Failure Case3 Case4 *( μ + λ )-GP uses ideal limitation time to cut o ff evaluations in Cases3&4 *ARE-GP : archive size as =5, deletion probability P d =0.5 Evaluation Criterion 20 trials Average fitness according to the same elapsed unit time m fitness = 1 : # of test data m X i ) 2 ( ˆ y i − y ∗ : output : target value y ∗ ˆ m y i i i =1

Speed Same Di ff erent Failure No failure Case1 Case2 Failure Case3 Case4

Speed Result : Case1 Same Di ff erent Failure No failure Case1 Case2 Failure Case3 Case4 (1) f(x)=x 4 +x 3 +x 2 +x (2) f(x)=x 6 -2x 4 +x 2 0.3 0.003 0.25 0.2 0.002 ( μ + λ )-GP fitness fitness 0.15 ARE-GP 0.1 0.001 0.05 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Elapsed unit time (x10^5) Elapsed unit time (x10^5) (3) f ( x ) =sin ( x 2 ) × cos ( x ) - 1 (4) f ( x ) =ln ( x+ 1) +ln ( x 2 + 1) 0.015 0.1 0.08 0.01 0.06 fitness fitness 0.04 0.005 0.02 ARE-GP>( μ + λ )-GP 0 0 0 20 40 60 80 100 0 20 40 60 80 100 → ARE-GP evolves individuals without waisting time Elapsed unit time (10^5) Elapsed unit time (x10^5)

Speed Same Di ff erent Failure No failure Case1 Case2 Failure Case3 Case4

Speed Result : Case4 Same Di ff erent Failure No failure Case1 Case2 (Ideal limitation time is used) Failure Case3 Case4 (1) f(x)=x 4 +x 3 +x 2 +x (2) f(x)=x 6 -2x 4 +x 2 0.6 0.003 0.5 0.4 0.002 ( μ + λ )-GP fitness fitness 0.3 ARE-GP 0.2 0.001 0.1 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Elapsed unit time (x10^5) Elapsed unit time (x10^5) (3) f ( x ) =sin ( x 2 ) × cos ( x ) - 1 (4) f ( x ) =ln ( x+ 1) +ln ( x 2 + 1) 0.015 0.16 ARE-GP evolves individuals without any limitations 0.14 0.12 even though evaluation failure occurs 0.01 0.1 fitness fitness 0.08 0.06 0.005 ARE-GP>( μ + λ )-GP 0.04 0.02 ARE-GP e ffi ciently evolves individuals in situation 0 0 0 20 40 60 80 100 0 20 40 60 80 100 where evaluation times are excessively di ff erent Elapsed unit time (x10^5) Elapsed unit time (x10^5)

Result ARE-GP > ( μ + λ )-GP in all cases and in all testbeds ARE-GP ( μ + λ )-GP only uses a few evaluations can use all evaluations ? f 1 ? f 2 f 3 ? f 4 f 4 f 5 ? f 6 f 6

Comparison of Case1&Case4 Ratio of fitness between Case1 and Case4 (1) f(x)=x 4 +x 3 +x 2 +x 0.3 0.6 0.25 0.5 0.2 0.4 Case1 Case4 fitness fitness 0.15 0.3 0.1 0.2 0.05 0.1 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Elapsed unit time (x10^5) Elapsed unit time (x10^5) ( μ + λ )-GP . f case4 (t) 10 ( μ + λ )-GP . f case1 (t) Case4 decreases Case4<Case1 f_Case4/f_Case1 performance than Case1 1 Case4 increases Case4>Case1 performance than Case1 ARE-GP . f case4 (t) 0.1 0 20 40 60 80 100 ARE-GP . f case1 (t) Elapsed unit time (x10^5)

Comparison of Case1&Case4 (1) f(x)=x 4 +x 3 +x 2 +x (2) f(x)=x 6 -2x 4 +x 2 10 10 Case4<Case1 f_Case4/f_Case1 Case4<Case1 f_Case4/f_Case1 1 1 Case4>Case1 Case4>Case1 0.1 0.1 0 20 40 60 80 100 0 20 40 60 80 100 Elapsed unit time (x10^5) Elapsed unit time (x10^5) (3) f ( x ) =sin ( x 2 ) × cos ( x ) - 1 (4) f ( x ) =ln ( x+ 1) +ln ( x 2 + 1) 10 10 Case4<Case1 f_Case4/f_Case1 Case4<Case1 f_Case4/f_Case1 1 1 Case4>Case1 Case4>Case1 0.1 0.1 0 20 40 60 80 100 0 20 40 60 80 100 ARE-GP has possibility to improve search performance Elapsed unit time (x10^5) Elapsed unit time (x10^5) in di ff erent evaluation time

Conclusion Objective ‣ Proposing EA using Asynchronous Reference-based Evaluation (ARE-EA) ‣ Investigating e ff ectiveness of ARE-EA in excessively di ff erent evaluation times - di ff erent computing speed - evaluation failure Implications ‣ ARE-GP>( μ + λ )-GP - in excessively di ff erent evaluation time ‣ ARE-GP improves performance in di ff erent evaluation time Future works ‣ Validation in parallel computing environment ‣ Adaptation of parameters P d and as