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 ) P ← ∅ 2: while | P | < n do ⊲ Initialize population. 3: P ← P ∪ { randomIndividual () } 4: for i ← 0 to gens do ⊲ Evolutionary loop. 5: for all ind ∈ P do in parallel 6: evaluateFitness ( ind ) 7: P ← select ( P ) ⊲ Choose parents. 8: P ← reproduce ( P ) ⊲ Mutation and Crossover. 9: return P
Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion Idle Time in a Generational EA How Evaluation Time Variance Induces Idle Time 10 9 8 7 Individual 6 5 4 3 2 1 0.00 0.25 0.50 0.75 1.00 Evaluation 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 Evaluation Sequence in Wall−Clock Time 100 75 Birth Step 50 25 0 0 3 6 9 Time
Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion Evaluation Sequence in an Asynchronous EA Evaluation Sequence in Wall−Clock Time 400 375 Birth Step 350 325 300 3000 3100 3200 3300 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 Gene with two alleles: fast and slow . slow takes 10 times Genetic Drift on Flat Landscape 1.00 longer than fast to evaluate. Frequency of Slow−Type Allele 0.75 Flat fitness landscape, no Mean reproductive variation. 0.50 95% Conf. Std. Dev. No observable selection effect 0.25 favoring fast-evaluating individuals? 0.00 0 25 50 75 100 generation
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 optimum. 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 Convergence to Fast Optimum on Two−Basin Objective 1.00 Ratio of Runs Converging to Basin A 0.75 0.50 0.25 0.00 A Fast, B Slow Constant Eval−Time Eval−Time = Fitness
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 : Convergence to Fast Optimum on Two−Basin Objective Ratio of Runs Converging to Basin A 0.2 0.1 0.0 A Fast, B Slow Constant Time A Slow, B Fast
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: � b − a � � 1 � 1 E [ˆ I ] ≥ 2 − b n + 1 How Evaluation Time Variance Induces Idle Time How Evaluation Time Variance Induces Idle Time 50 49 10 48 47 46 45 44 9 43 42 41 40 39 8 38 37 36 35 34 7 33 32 31 Individual Individual 30 29 6 28 27 26 25 24 5 23 22 21 20 19 4 18 17 16 15 14 3 13 12 11 10 9 2 8 7 6 5 4 3 1 2 1 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 Evaluation Time Evaluation Time
Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion Speedup in Throughput via Asynchrony Eval−time Distribution U(0, 500ms) U(125ms, 500ms) 2.00 1.75 speedup 1.50 1.25 1.00 0 10 20 30 nodes 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 Asynchronous Speedup by Population Size 1.6 1.4 Speedup 1.2 1.0 10 20 30 40 50 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 optimum 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 optimum. 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 Evaluation Speedup on the Sphere Function True Speedup on the Sphere Function 6 6 4 4 Speedup Speedup 2 2 0 0 Non−Heritable Heritable Positive Negative Non−Heritable Heritable Positive Negative Performance improvement explained by speedup in fitness evaluations.
Introduction Asynchrony Evaluation-Time Bias Evaluation Speedup True Speedup Conclusion Speedup on Rastrigin Function Evaluation Speedup on the Rastrigin Function True Speedup on the Rastrigin Function 30 30 Speedup Speedup 20 20 10 10 0 0 Non−Heritable Heritable Positive Negative Non−Heritable Heritable Positive Negative
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.
Recommend
More recommend
