Extending Exploratory Landscape Analysis for Multi-Objective and - - PowerPoint PPT Presentation
Extending Exploratory Landscape Analysis for Multi-Objective and Multimodal Problems Pascal Kerschke & Mike Preu Information Systems and Statistics Group, University of M unster, Germany Thursday, October 13th, 2016 October 13th, 2016
Pascal Kerschke & Mike Preuß
Information Systems and Statistics Group, University of M¨ unster, Germany
Thursday, October 13th, 2016
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introducing Exploratory Landscape Analysis
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existing ELA features
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ELA for multimodal problems
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ELA for multi-objective problems
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flacco library
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algorithm selection problem1
find the individually best suited algorithm for an unseen
1Rice, J. (1976). The Algorithm Selection Problem. In Advances in Computers (pp. 65-118).
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algorithm selection problem1
find the individually best suited algorithm for an unseen
1Rice, J. (1976). The Algorithm Selection Problem. In Advances in Computers (pp. 65-118).
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Exploratory Landscape Analysis (ELA): we aim at finding the right algorithm but also at improving problem or algorithm/problem dependency understanding basic idea (exploratory!): we start with very simple features without clear purpose match existing high-level features (expert knowledge) with our ELA features currently: mostly continuous (black-box) (global) optimization, but also in other domains (e.g. TSP)
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Convexity y-Distribution Levelset Multimodality Global structure Plateaus Search space homogeneity Meta Model Local Search Global to local
Variable scaling Separability Basin size homogeneity Curvature Mersmann, O., Preuss, M. & Trautmann, H. (2010). Benchmarking Evolutionary Algorithms: Towards Exploratory Landscape Analysis. In Proceedings of PPSN XI (pp. 71 - 80).
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we do not know functional relationships when designing features but we can match them to high-level characteristics (multimodality, funnel structure, etc.) of optimization problems this enables recognizing important problem properties quickly based on initial design of samples xi1, . . . , xiD and their corresponding fitness value yi, i = 1, . . . , n given an evaluated initial design (initial population?), most ELA features are for free there are already several different feature sets
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General Cell Mapping Features
Kerschke, P., Preuss, M., Hern´ andez, C., Sch¨ utze, O., Sun, J.-Q., Grimme, C., Rudolph, G., Bischl, B. & Trautmann, H. (2014). Cell Mapping Techniques for Exploratory Landscape
Barrier Tree Features
Hern´ andez, C., Sch¨ utze, O., Emmerich, M. T. M., & Xiong, F. R. (2014). Barrier Tree for Continuous Landscapes by Means of Generalized Cell Mapping. In Proceedings of EVOLVE 2014.
6 . 2 e − 2 1 . 9 e − 1 3 . 1 e − 1 4 . 4 e − 1 5 . 6 e − 1 6 . 9 e − 1 8 . 1 e − 1 9 . 4 e − 1 Cell Coordinate (1st Dimension) 1 . e − 1 3 . e − 1 5 . e − 1 7 . e − 1 9 . e − 1 Cell Coordinate (2nd Dimension) Cell ID (1st Dimension) 1 2 3 4 5 6 7 8 Cell ID (2nd Dimension) 1 2 3 4 5
38 (root) x y f ( x , y )
38 (root)
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Cell Mapping Features
Kerschke, P., Preuss, M., Hern´ andez, C., Sch¨ utze, O., Sun, J.-Q., Grimme, C., Rudolph, G., Bischl, B. & Trautmann, H. (2014). Cell Mapping Techniques for Exploratory Landscape
Information Content Features
Mu˜ noz, M. A., Kirley, M., Halgamuge, S. K. (2015). Exploratory Landscape Analysis of Continuous Space Optimization Problems using Information Content. In IEEE Transactions on Evolutionary Computation (pp. 74 - 87).
−4 −2 2 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
log10(ε) H(ε) & M(ε)
M(ε) Hmax εs M0 εratio
Information Content Plot October 13th, 2016 10 / 37
Dispersion Features
Lunacek, M. & Whitley, D. (2006). The Dispersion Metric and the CMA Evolution Strategy. In Proceedings of GECCO 2006 (pp. 477 - 484).
Nearest Better Clustering Features
Kerschke, P., Preuss, M., Wessing, S. & Trautmann H. (2015). Detecting Funnel Structures by Means of Exploratory Landscape Analysis. In Proceedings of GECCO 2015 (pp. 265 - 272).
Length Scale Features
Morgan, R. & Gallagher M. (2015). Analyzing and Characterising Optimization Problems Using Length Scale. In Soft Computing (pp. 1 - 18).
Ruggedness Features
Malan, K. M. & Engelbrecht, A. P. (2013). Ruggedness, Funnels and Gradients in Fitness Landscapes and the Effect on PSO Performance. In Proceedings of CEC 2013 (pp. 963 - 970).
Hill Climbing Features
Abell, T., Malitsky, Y. & Tierney, K. (2013). Features for Exploiting Black-Box Optimization Problem Structure. In Proceedings of LION 2013 (pp. 30 - 36).
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different aims possible currently most important (competitions): multiglobal
two main algorithmic approaches:
parallel, large populations sequential, coordinated restarts
several components that may be used: archives, clustering methods, methods for obtaining well distributed samples ELA could be helpful for selecting components/methods
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Example: (recent research) → Funnel Detection
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funnel: local optima are located near to each other and pile up to an “upside-down mountain” knowledge about underlying global structure, i.e. funnels, helps selecting the right algorithm (a) funnel (b) non-funnel (“random”)
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different algorithm candidates for either category but there is a wide variety within classes funnel and non-funnel (a) funnel (b) non-funnel (“random”)
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detailed results in our GECCO paper2 used MPM23 to generate a set of 4,000 training instances initial designs of size 50 × D observations (small!) trained four classifiers (random forest, rpart, kknn and ksvm) experimentally driven reduction of the full feature set (300+ features) to 8 features validated results on BBOB and subset of problems from CEC-2013 niching competition
2Kerschke, P., Preuss, M., Wessing, S. & Trautmann H. (2016). Low-Budget Exploratory Landscape Analysis on Multiple Peaks Models. In Proceedings of GECCO 2016 (pp. 229-236) 3multiple peaks model 2 generator, available in python (optproblems0.9, Wessing, S.) and R (smoof, Bossek, J.)
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CV−Iteration 1 2 3 4 5 6 7 8 9 10 e l a _ m e t a . l i n _ s i m p l e . a d j _ r 2 e l a _ m e t a . l i n _ s i m p l e . i n t e r c e p t n b c . n b _ f i t n e s s . c
d i m e l a _ m e t a . q u a d _ w _ i n t e r a c t . a d j _ r 2 e l a _ m e t a . l i n _ w _ i n t e r a c t . a d j _ r 2 e l a _ m e t a . q u a d _ s i m p l e . a d j _ r 2 n b c . n n _ n b . s d _ r a t i
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source: lmarti.github.io October 13th, 2016 21 / 37
in single-objective optimization, ELA has shown to be useful for describing the problem landscape based on a small initial design currently, there exist almost no landscape features for continuous multi-objective optimization problems let’s convert the single-objective high-level properties to the multi-objective case
4Kerschke, P., Wang, H., Preuss, M., Grimme, C., Deutz, A., Trautmann, H., & Emmerich, M. (2016). Towards Analyzing Multimodality of Multiobjective Landscapes. In Proceedings of PPSN 2016 (pp. 962-972)
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X1 X2 X1 X2
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X1 X2 X1 X2
X1 X2
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X1 X2
Y1 Y2
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considered features characteristics:
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percentage of counts of global to local Pareto fronts
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percentage of lengths of global to local Pareto fronts
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...
Y1 Y2
1 + 1 + 1 = 1 3 ≈ 0.33
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considered features characteristics:
1
percentage of counts of global to local Pareto fronts
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percentage of lengths of global to local Pareto fronts
3
...
Y1 Y2
1.07 0.19
1.19 1.19 + 1.07 + 0.19 = 1.19 2.45 ≈ 0.49
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Quite simple for small problems. But what happens if the problems become (just a little bit) more multimodal?
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X1 X2 Decision Space
Y2 Objective Space
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0.25 0.50 0.75 1.00 count_ratio.global count_ratio.conn_ps count_ratio.conn_pf length_ratio.global_ps length_ratio.global_pf length_ratio.conn_ps length_ratio.conn_pf Ratio Problem Complexity
complex
Landscape Characteristics
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Wanted: Various experimental landscape features (= based on samples) for multi-objective – although not necessarily multimodal – landscapes!
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flacco: Feature-Based Landscape Analysis of Continuous and Constraint Optimization Problems unified interface for multiple (single-objective) sets of configurable features stable release on CRAN / developers version on GitHub multiple vizualisation techniques (partially shown on these slides) tracks # of function evaluations and run time - per feature set FLACCO is described in more detail in our CEC paper5
5Kerschke, P. & Trautmann, H. (2016). The R-Package FLACCO for Exploratory Landscape Analysis with Applications to Multi-Objective Optimization Problems. In Proceedings of CEC 2016.
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6
6Tutorial: http://kerschke.github.io/flacco-tutorial/site/
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how can we characterize multi-objective landscapes?
how can we characterize multimodal landscapes?
enhance flacco with more ELA features how can we find the smallest most informative feature set?
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by how much can we still reduce the size of the initial designs without losing (too much) information?! where can we find representative real-world problems / appropriate benchmarks? can we transfer landscape features from / to different domains? use ELA features for improved algorithm selection on different benchmarks (e.g. BBOB)
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