Introduction CEC 2019 Competitions CEC-C02 Competition on - PowerPoint PPT Presentation

M odified L -SHADE for S ingle O bjective R eal- P arameter O ptimization Contributed by Jia-Fong Yeh, Ting-Yu Chen, and Tsung-Che Chiang Department of Computer Science and Information Engineering, National T aiwan Normal University, T aiwan Personal contact 60647005S@ntnu.edu.tw, mazer0701@gmail.com, tcchiang@ieee.org 2019 IEEE CONGRESS ON EVOLUTIONARY COMPUTATION, WELLINGTON, NEW ZEALAND, 10-13 JUNE 2019

Contents 1 I ntroduction The Problem introduction 2 S HADE Adaptive Parameter Linear population size reduction Algorithms overview 3 P roposed algorithm — mL-SHADE Proposed mL-SHADE mechanism 4 E xperiments and Results Minor change Performance compression 5 C onclusion Contents Conclusion L-SHADE mL-SHADE Experiments and Results Introduction

Introduction CEC 2019 Competitions CEC-C02 Competition on "Evolutionary Multi-task Optimization" CEC-C03 Competition on "Online Data-Driven Multi-Objective Optimization Competition" CEC-C04 Competition on "Smart Grid and Sustainable Energy Systems" CEC-C05 Competition on "Evolutionary Computation in Uncertain Environments: A Smart Grid Application" CEC EC-C06 Competition on "100-Digit Challenge on Single Objective Numerical Optimization" CEC-C07 FML-based Machine Learning Competition for Human and Smart Machine Co-Learning on Game of Go CEC-C08 General Video Game AI Single-Player Learning Competition CEC-C09 Strategy Card Game AI Competition CEC-C10 Nonlinear Equation Systems Competition Contents Conclusion Introduction L-SHADE mL-SHADE Experiments and Results

Introduction The 100-digit challenge Modification Additional mutation In 2019 CEC Special Session Single-Object Real-Parameter Optimization Add + Solve mL-SHADE Memory perturbation Modified L-SHADE L-SHADE T erminal value - Remove [L- SHADE] R. T anabe, and A. S. Fukunaga, “Improving the Search Performance of SHADE Using Linear Population Size Reduction, ” in IEEE CEC, pp. 1658 – 1665, 2014. Contents Conclusion Introduction L-SHADE mL-SHADE Experiments and Results

L-SHADE Algorithms overview L-SHADE / mL-SHADE ( Uniform random initialization ) Initialization ( Current-to-pbest/1 strategy + Gene repair ) Mutation ( Binomial crossover ) Crossover Generation < Max No ( Fitness comparison ) Selection Yes Final Population Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Adaptive F and CR CR Parameter L-SHADE Population Size Reduction Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Adaptive Parameter L-SHADE Hist stor ory y memory y syst stem em Crate History memory system M F,H Initialization M F M F,1 M F,2 M F,H-1 …… …… M CR,H-1 M CR,H M CR M CR,1 M CR,2 Select F and CR CR i i Mutation M is mean value of the successful F and CR CR • which can generate the better solution in Crossover No each iteration Generation < Max Each mean value will be utilized to generate Selection • Update history memory system F and CR CR next iteration Yes Final Population Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Adaptive Parameter 𝐼 Initial ializ izat ation ion 0.5 0.5 0.5 0.5 M F …… Mutation 0.5 0.5 0.5 0.5 M CR …… Crossover In the initialization stage, all element of history table will be set to be 0.5, and each of them will be updated when the set of better Selection solution is found Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Adaptive Parameter 𝐼 M F,H-1 Initialization M F M F,H M F,2 M F,1 …… M CR,2 M CR M CR,H-1 M CR,H M CR,1 …… Mutati ation on For each target vector 𝑦 𝑗 will generated 𝐺 𝑗 and 𝐷𝑆 𝑗 as follow. Crossover over 𝑗 index is selected randomly from [1,H] 𝑠 Selection 𝑠𝑏𝑜𝑒𝑑 𝑗 ( ) is a Cauchy distribution 𝐺 𝑗 = randc 𝑗 𝑁 𝐺,𝑠 𝑗 , 0.1 𝑗𝑔 𝑁 𝐷𝑆,𝑠 𝑗 ≠ 0( ⊥ ) 𝑠𝑏𝑜𝑒𝑜 𝑗 ( ) is a normal distribution 𝐷𝑆 𝑗 = ቊrandn 𝑗 𝑁 𝐷𝑆,𝑠 𝑗 , 0.1 0 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 ** 0 ( ⊥ terminal value) Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Adaptive Parameter At the selection, if the trial vector’s ( 𝑣 ) fitness is better than or equal to target vector’s ( Ԧ 𝑦 ), their fitness value, 𝐺 𝑗 , and 𝐷𝑆 𝑗 will be stored in S table. Initialization F Mutation ∆𝑔 𝑙 𝑇 2 𝑥 𝑙 = 𝑛𝑓𝑏𝑜 𝑥𝑀 (𝐺) = σ 𝑙=1 𝑥 𝑙 ∙ 𝐺 𝑙 ∆𝑔 𝑙 = 𝑔 𝑣 𝑗,𝐻 − 𝑔 𝑦 𝑗,𝐻 𝑇 ∆𝑔 Crossover σ 𝑚=1 𝑚 𝑇 σ 𝑙=1 𝑥 𝑙 ∙ 𝐺 𝑙 Improvement-based weight Fitness improvement Selec ection ion 1 2 3 weighted Lehmer mean 𝑇 2 𝑛𝑓𝑏𝑜 𝑥𝑀 (CR) = σ 𝑙=1 𝑥 𝑙 ∙ 𝐷𝑆 𝑙 𝑇 σ 𝑙=1 𝑥 𝑙 ∙ 𝐷𝑆 𝑙 CR CR Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Adaptive Parameter 𝐼 M F,H-1 Initialization M F M F,H M F,2 M F,1 …… M CR M CR,H-1 M CR,H M CR,1 ⊥ …… Mutation First End Crossover Selec ection ion 1. If S table is not empty, mean value of 𝑁 𝐺,𝑙 and 𝑁 𝐷𝑆,𝑙 will be updated by new mean F and CR CR 2. If mean value of CR CR is 0, then 𝑁 𝐷𝑆,𝑙 will be set as the terminal value ⊥ (0) and that element will never be changed to be the other number again. Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

L-SHADE Linear population size reduction 𝑂𝑄 𝐻+1 = 𝑠𝑝𝑣𝑜𝑒(( 𝑂 𝑛𝑗𝑜 − 𝑂 𝑗𝑜𝑗𝑢 𝑁𝐵𝑌_𝑂𝐺𝐹 ) × 𝑂𝐺𝐹 + 𝑂 𝑗𝑜𝑗𝑢 ) Initialization 𝑂 𝑗𝑜𝑗𝑢 = 18 × 𝐸 , 𝑂 𝑛𝑗𝑜 = 4 Mutation 𝑂 𝑗𝑜𝑗𝑢 NFE is the current number of fitness evaluations NF Crossover MAX_N X_NFE FE is the maximum number of fitness evaluations Selec ection ion 𝑂 𝑛𝑗𝑜 MAX_ X_NFE Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

mL-SHADE L-SHADE mL-SHADE - T erminal value Memory perturbation Additional mutation operator Contents mL-SHADE Conclusion Introduction L-SHADE Experiments and Results

mL-SHADE Remove Terminal value As L-SHADE will update the 𝑁 𝐷𝑆,𝑙 element inside history memory table to be ⊥ every time, when it found the mean of CR CR equal 0 and never change to be the Initial ializ izat ation ion other value again. It also forces the target vector to CR CR as 0, it select the ⊥ from history table. Mutation This can end the exploration and start to exploitation. Crossover Binomial crossover we found that in some cases, all 𝑁 𝐷𝑆 element are set to terminal value when the Selec ection ion evolution phase is very early. **This may affect the performance of the algorithm, so we re remove the terminal value in mL-SHADE algorithm. Contents mL-SHADE Conclusion Introduction L-SHADE Experiments and Results

mL-SHADE Memory perturbation We found that the memory may not be updated for a long time, which means that the fitness value has not improved. One of the reasons why fitness value stops improving is that the control parameters are not suitable for the current population. Fitness value 𝑁 𝐷𝑆,𝑙 = 1.0 − 𝑁 𝐷𝑆,𝑙 Stuck > N stuck 𝑁 𝐺,𝑙 = 1.0 − 𝑁 𝐺,𝑙 Generation number Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

mL-SHADE (polynomial mutation) Additional mutation operation After the trial vector is generated, po polyno lynomi mial muta utati tion on (PM) (PM) is applied to mL-SHADE generate a mutated trial vector, and choose the better one to be the final trial vector. Initialization Best Selection Mutation Crossover polyn lynomial mial No muta tatio ion Polyno lynomial mial mutat ation on Generation < Max Selection Yes Final Population 𝑦 𝑗 𝑣 𝑗 𝑣 𝑗 trial vector target vector trial vector mutated trial vector mutated trial vector 1.000002663 1.000002663 1.022785566 1.000522663 1.000522663 Contents Conclusion Introduction mL-SHADE L-SHADE Experiments and Results

Experiment and Result Discussion • 100-Digit Challenge on Single Objective Numerical Optimization (CEC C06) was utilized to test the performance of our algorithm • We compared mL-SHADE with the other seven algorithms including L-SHADE • The source code of those algorithms can be downloaded from organizer’s website. Contents Conclusion Introduction L-SHADE mL-SHADE Experiments and Results

Experiment and Result Discussion Parameter setting Para rame meter ter Meani eaning ng mL mL-SHA SHADE L-SHA SHADE N init size of the initial population 18  D 18  D N min minimal population size 4 4 H size of the history memory 6 6 r arc archive size | A | = round( r arc  N init ) 1.0 2.6 p required in the cur-to- p best/1 mutation 0.11 0.11 m r probability of polynomial mutation 0.05 N/A p m,  parameters of polynomial mutation 1/ D , 10 N/A MaxNFE maximum number of fitness evaluations 2  10 6 10000  D No. N stuck No. N stuck uck uck 6 400 1 400 2 400 7 400 3 6 (same as H ) 8 400 4 400 9 6 (same as H ) 5 400 10 400 Contents Conclusion Introduction L-SHADE mL-SHADE Experiments and Results