1 Data Science Institute, Department of Management Science, Lancaster University, UK 2 School of Computer Science and Information Technology, RMIT University, Australia 3 Department of Computer Science, University of Pretoria, South Africa m.epitropakis@lancaster.ac.uk xiaodong.li@rmit.edu.au engel@cs.up.ac.za Results of the 2017 IEEE CEC Competition on Niching Methods for Multimodal Optimization M.G. Epitropakis 1 , X. Li 2 , and A. Engelbrecht 3 IEEE CEC 2017 Competition on Niching Methods
1. Introduction 2. Participants 3. Results 4. Winners 5. Summary 1 Table of contents
Introduction
• Many real-world problems are “multi-modal” by nature, i.e., multiple satisfactory solutions exist stable subpopulations within a single population • Aim: maintain diversity and locate multiple globally optimal solutions. • Challenge: Find an efficient optimization algorithm, which is problems with various characteristics. 2 Introduction • Niching methods: promote and maintain formation of multiple able to locate multiple global optimal solutions for multi-modal
Provide a common platform that encourages fair and easy comparisons across different niching algorithms. • The benchmark suite and the performance measures have been implemented in: C/C++, Java, MATLAB, (Python soon) 3 Competition: CEC 2013/2015/2016/2017 X. Li, A. Engelbrecht, and M.G. Epitropakis, “Benchmark Functions for CEC’2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization”, Technical Report, Evolutionary Computation and Machine Learning Group, RMIT University, Australia, 2013 • 20 benchmark multi-modal functions with different characteristics • 5 accuracy levels: ε ∈ { 10 − 1 , 10 − 2 , 10 − 3 , 10 − 4 , 10 − 5 }
4 F 8 F 9 symmetric Scalable, #optima independent from D, Modified Rastrigin 12 2 unevenly distributed optima 6 Scalable, #optima increase with D, Vincent 36,216 2,3 F 7 unevenly distributed grouped optima 2 Composition Function 1 Shubert Composition Function 3 Scalable, non-separable, non-symmetric Composition Function 4 8 2,3,5,10 F 12 Scalable, non-separable, non-symmetric 6 Scalable, separable, non-symmetric 2,3,5,10 F 11 Scalable, separable, non-symmetric Composition Function 2 8 2 F 10 Scalable, #optima increase with D, 18,81 Simple F 3 # GO Name Characteristics F 1 1 2 Five-Uneven-Peak Trap Simple, deceptive F 2 1 5 Equal Maxima 2,3 1 Id 1 Uneven Decreasing Maxima Simple F 4 2 4 Himmelblau Simple, non-scalable, non-symmetric F 5 2 2 Six-Hump Camel Back Simple, not-scalable, non-symmetric F 6 Dim. Benchmark function set X. Li, A. Engelbrecht, and M.G. Epitropakis, “Benchmark Functions for CEC’2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization”, Technical Report, Evolutionary Computation and Machine Learning Group, RMIT University, Australia, 2013
• The participant with the highest average Peak Ratio global optima found over multiple runs: performance on all benchmarks wins. • In all functions the following holds: the higher the PR value, the better 5 Performance Measures Peak Ratio (PR) measures the average percentage of all known ∑ NR PR = run = 1 # of Global Optima i ( # of known Global Optima ) ∗ ( # of runs ) Who is the winner:
Participants
the Dynamic Modified Restricted Tournament Selection Method and the Dynamic Distance Criterion [1] with a static (dimensionality-dependent) Modified Restricted Tournament Selection Method and the Dynamic Distance Criterion by Camila Silva de Magalhães, Lincon Onório Vidal, Matheus Muller Pereira da Silva, Raquel Gomes Gon calves Farias, Helio José Correa Barbosa, and Laurent Emmanuel Dardenne, from UFRJ and LNCC, Brazil 6 Participants Submissions to the competition: • ( SSGA-DMRTS-DDC : SSGA-1) Steady State Genetic Algorithm with • ( SSGA-DMRTS-DDC-F : SSGA-2) Steady State Genetic Algorithm
Evolution algorithm for Multimodal Optimization [5] neighborhood mutation strategies [4] [2]. In the repository: CMA-ES, IPOP-CMA-ES, DE/nrand/1,2, DECG, DELG, DELS-aj, CrowdingDE, dADE/nrand/1,2, NEA1, NEA2, N-VMO, PNA-NSGAII, A-NSGAII, rlsis, rs-cmsa-es, ascga, nea2+, ... 7 Participants (2) Implemented algorithms for comparisons: • ( CrowdingDE ) Crowding Differential Evolution [3] • ( DE/nrand/1 ) Niching Differential Evolution algorithms with • ( dADE/nrand/1 ) A Dynamic Archive Niching Differential • ( NEA2 ) Niching the CMA-ES via Nearest-Better Clustering [6] • ( NMMSO ) Niching Migratory Multi-Swarm Optimiser of Fieldsend
Results
and CEC2015 repository: https://github.com/mikeagn/CEC2013 8 Results Summary: • 2 new search algorithms • 5 comparators based on the previous competitions @ CEC2013 • 20 multi-modal benchmark functions • 5 accuracy levels ε ∈ { 10 − 1 , 10 − 2 , 10 − 3 , 10 − 4 , 10 − 5 } • Results: per accuracy level & over all accuracy levels • In total (CEC2013, CEC2015, CEC2016) 25 algorithms in the
9 Accuracy level ε = 10 − 1 Accuracy level 1.0e−1 Accuracy level 1.0e−1 1.00 20 1.0 0.8 Peak Ratio in all benchmark functions ● 0.75 15 Algorithms Benchmark function SSGA−1 0.6 SSGA−2 ● CrowdingDE 0.50 ● dADE/nrand/1 10 DE/nrand/1 ● 0.4 NEA2 NMMSO ● 0.25 0.2 5 ● ● 0.0 0.00 1 2 E 1 1 2 O − − D d / d / A S A A E g n n M G G n a a N 1 2 E 1 1 2 O M − − D / / A S S d i r r d d S n n N A A g n n E M S S w / / G G N E E n a a M o D D S S i r r r d n n C A S S w / / N E E d o r D D C A d
10 Accuracy level ε = 10 − 2 Accuracy level 1.0e−2 Accuracy level 1.0e−2 1.00 20 1.0 0.8 Peak Ratio in all benchmark functions 0.75 15 Algorithms Benchmark function SSGA−1 0.6 SSGA−2 CrowdingDE 0.50 dADE/nrand/1 10 DE/nrand/1 0.4 NEA2 NMMSO 0.25 0.2 5 0.0 0.00 ● 1 2 E 1 1 2 O − − D d / d / A S A A E g n n M G G n a a N 1 2 E 1 1 2 O M − − D / / A S S d i r r d d S n n N A A g n n E M S S w / / G G N E E n a a M o D D S S i r r r d n n C A S S w / / N E E d o r D D C A d
11 Accuracy level ε = 10 − 3 Accuracy level 1.0e−3 Accuracy level 1.0e−3 1.00 20 1.0 0.8 Peak Ratio in all benchmark functions 0.75 15 Algorithms Benchmark function SSGA−1 0.6 SSGA−2 CrowdingDE 0.50 dADE/nrand/1 10 DE/nrand/1 0.4 NEA2 NMMSO 0.25 0.2 5 0.0 0.00 ● 1 2 E 1 1 2 O − − D d / d / A S A A E g n n M G G n a a N 1 2 E 1 1 2 O M − − D / / A S S d i r r d d S n n N A A g n n E M S S w / / G G N E E n a a M o D D S S i r r r d n n C A S S w / / N E E d o r D D C A d
12 Accuracy level ε = 10 − 4 Accuracy level 1.0e−4 Accuracy level 1.0e−4 1.00 20 1.0 0.8 Peak Ratio in all benchmark functions 0.75 15 Algorithms Benchmark function SSGA−1 0.6 SSGA−2 CrowdingDE 0.50 dADE/nrand/1 10 DE/nrand/1 0.4 NEA2 NMMSO 0.25 0.2 5 0.0 ● 0.00 ● 1 2 E 1 1 2 O − − D d / d / A S A A E g n n M G G n a a N 1 2 E 1 1 2 O M − − D / / A S S d i r r d d S n n N A A g n n E M S S w / / G G N E E n a a M o D D S S i r r r d n n C A S S w / / N E E d o r D D C A d
13 Accuracy level ε = 10 − 5 Accuracy level 1.0e−5 Accuracy level 1.0e−5 1.00 20 1.0 0.8 Peak Ratio in all benchmark functions 0.75 15 Algorithms Benchmark function SSGA−1 0.6 SSGA−2 CrowdingDE 0.50 dADE/nrand/1 10 DE/nrand/1 0.4 NEA2 NMMSO 0.25 0.2 5 0.0 0.00 ● ● 1 2 E 1 1 2 O − − D d / d / A S A A E g n n M G G n a a N 1 2 E 1 1 2 O M − − D / / A S S d i r r d d S n n N A A g n n E M S S w / / G G N E E n a a M o D D S S i r r r d n n C A S S w / / N E E d o r D D C A d
14 Performance per benchmark across all accuracy levels 1 2 3 4 5 1.00 ● 0.75 ● 0.50 ● 0.25 0.00 6 7 8 9 10 1.00 ● ● ● ● 0.75 ● ● 0.50 ● Peak Ratio 0.25 ● ● ● 0.00 ● ● ● ● 11 12 13 14 15 1.00 ● ● ● ● ● ● ● ● ● ● ● ● 0.75 ● ● ● ● ● ● ● ● ● 0.50 ● ● 0.25 0.00 16 17 18 19 20 1.00 ● ● ● ● ● ● ● ● 0.75 ● ● ● ● 0.50 ● ● ● ● ● 0.25 ● ● 0.00 1 2 E 1 1 2 O 1 2 E 1 1 2 O 1 2 E 1 1 2 O 1 2 E 1 1 2 O 1 2 E 1 1 2 O − − D d / d / A S − − D d / d / A S − − D d / d / A S − − D d / d / A S − − D d / d / A S A A A A A A A A A A g n n E M g n n E M g n n E M g n n E M g n n E M G G n a a N G G n a a N G G n a a N G G n a a N G G n a a N M M M M M S S i r r S S i r r S S i r r S S i r r S S i r r d n n d n n d n n d n n d n n S S w / / N S S w / / N S S w / / N S S w / / N S S w / / N E E E E E E E E E E o o o o o r D D r D D r D D r D D r D D C C C C C A A A A A d d d d d
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