Cell Mapping Techniques for Exploratory Landscape Analysis

Kerschke, Pascal; Preuß, Mike; Hernández, Carlos; Schütze, Oliver; Sun, Jian‐Qiao; Grimme, Christian; Rudolph, Günter; Bischl, Bernd; Trautmann, Heike

doi:10.1007/978-3-319-07494-8_9

Cited by 32 publications

(28 citation statements)

References 18 publications

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“…The feature sets were then computed using the R-package flacco (Kerschke, 2017b) for all four problem dimensions, 24 BBOB problems and five problem instances that were used by the performance data (see Section 4.1). For each of these 480 problems, we calculated the six 'classical' ELA feature sets from Mersmann et al (2011) (convexity, curvature, levelset, local search, metamodel and y-distribution), as well as the basic, (cell mapping) angle 9 (Kerschke et al, 2014), dispersion (Lunacek and Whitley, 2006), information content (Muñoz Acosta et al, 2015a), nearest better clustering and principal component features, resulting in a total of 102 features per problem instance.…”

Section: Instance Feature Datamentioning

confidence: 99%

“…Therefore, the selector is able to pick an optimizer from the portfolio, which solves the respective problem on average twice as fast. Eight features resulted from the feature selection approach and were included in Model 1: three features from the y-distribution feature set (the skewness, kurtosis and number of peaks of a kernel-density estimation of the problems' objective values; see Mersmann et al, 2011), one levelset feature (the ratio of mean misclassification errors when using a linear (LDA) and mixed discriminant analysis (MDA); Mersmann et al, Acosta et al, 2015a), one cell mapping feature (the standard deviation of the distances between each cell's center and worst observation; see Kerschke et al, 2014) and one of the basic features (the best fitness value within the sample).…”

Section: Analyzing the Best Algorithm Selectormentioning

confidence: 99%

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Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning

Kerschke

Trautmann

2019

Evolutionary Computation

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139

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In this paper, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection models in continuous black-box optimization problems. Focussing on algorithm performance results of the COCO platform of several years, we construct a representative set of high-performing complementary solvers and present an algorithm selection model that -compared to the portfolio's single best solver -on average requires less than half of the resources for solving a given problem. Therefore, there is a huge gain in efficiency compared to classical ensemble methods combined with an increased insight into problem characteristics and algorithm properties by using informative features. Acting on the assumption that the function set of the Black-Box Optimization Benchmark is representative enough for practical applications the model allows for selecting the best suited optimization algorithm within the considered set for unseen problems prior to the optimization itself based on a small sample of function evaluations. Note that such a sample can even be reused for the initial population of an evolutionary (optimization) algorithm so that even the feature costs become negligible.

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Section: Instance Feature Datamentioning

confidence: 99%

Section: Analyzing the Best Algorithm Selectormentioning

confidence: 99%

Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning

Kerschke

Trautmann

2019

Evolutionary Computation

Self Cite

139

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“…Within flacco, basically all feature computations and visualizations are based on a so-called feature object, which stores all the relevant information of the problem instance. It contains the initial design, i.e., a data frame of all the (exemplary) observations from the decision space along with their corresponding objective values and -if provided -the number of blocks per input dimension (e.g., required for the cell mapping approach, Kerschke et al (2014)), as well as the exact (mathematical) function definition, which is needed for those feature sets, which perform additional function evaluations, e.g., the local search features (which were already mentioned in Figure 2). Such a feature object can be created in different ways as shown in Figure 3.…”

Section: Integrated Ela Featuresmentioning

confidence: 99%

“…The fact that feature-based landscape analysis also exists in other domains -e.g., in discrete optimization (Daolio, Liefooghe, Verel, Aguirre, and Tanaka 2016;Jones 1995;Ochoa, Verel, Daolio, and Tomassini 2014) including its subdomain, the Traveling Salesperson Problem (Mersmann et al 2013;Hutter, Xu, Hoos, and Leyton-Brown 2014;Pihera and Musliu 2014) -also lead to attempts to discretize the continuous problems and afterwards use a so-called cell mapping approach (Kerschke et al 2014), or compute barrier trees on the discretized landscapes (Flamm, Hofacker, Stadler, and Wolfinger 2002).…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems Using the R-Package Flacco

Kerschke

Trautmann

2019

Studies in Classification, Data Analysis, and Knowledge Organization

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This paper provides an introduction into the R-package flacco. A slightly modified version of this document has recently been submitted to the Journal of Statistical Software and is currently under review.Choosing the best-performing optimizer(s) out of a portfolio of optimization algorithms is usually a difficult and complex task. It gets even worse, if the underlying functions are unknown, i.e., so-called Black-Box problems, and function evaluations are considered to be expensive. In the case of continuous single-objective optimization problems, Exploratory Landscape Analysis (ELA) -a sophisticated and effective approach for characterizing the landscapes of such problems by means of numerical values before actually performing the optimization task itself -is advantageous. Unfortunately, until now it has been quite complicated to compute multiple ELA features simultaneously, as the corresponding code has been -if at all -spread across multiple platforms or at least across several packages within these platforms.This article presents a broad summary of existing ELA approaches and introduces flacco, an R-package for f eature-based landscape analysis of continuous and constrained optimization problems. Although its functions neither solve the optimization problem itself nor the related Algorithm Selection Problem (ASP), it offers easy access to an essential ingredient of the ASP by providing a wide collection of ELA features on a single platform -even within a single package. In addition, flacco provides multiple visualization techniques, which enhance the understanding of some of these numerical features, and thereby make certain landscape properties more comprehensible. On top of that, we will introduce the package's build-in, as well as web-hosted and hence platform-independent, graphical user interface (GUI), which facilitates the usage of the package -especially for people who are not familiar with R -making it a very convenient toolbox when working towards algorithm selection of continuous single-objective optimization problems.

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“…The resulting sample resembles a D-dimensional grid in S. For unbounded problems, suitable bounds must be introduced. A variant of systematic sampling has been recently used to sample and analyse the 2-D BBOB problem set; search spaces are discretised into 10 × 10 "cells", with 1000 solutions randomly distributed over the cells [87]. While systematic sampling is useful in low dimensions, the sample size required increases exponentially with D. Furthermore, because solutions are sampled at precise increments, important structures within highly regular problems may be concealed between sample points.…”

Section: Methods and Techniquesmentioning

confidence: 99%

Analysing and comparing problem landscapes for black-box optimization via length scale

Morgan¹

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Optimization problems are of fundamental practical importance and can be found in almost every aspect of human endeavour. Yet remarkably, we have a very limited understanding of the nature of optimization problems and subsequently of how, why and when different algorithms perform well or poorly. The notion of a problem landscape captures the relationship between the objective function and the problem variables. It is clear that the structure of this landscape is vital in understanding optimization problems, however analysis of this structure presents major challenges. Apart from the often high-dimensionality of problem landscapes, information available in the black-box setting is limited to the solutions in the ii

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Cell Mapping Techniques for Exploratory Landscape Analysis

Cited by 32 publications

References 18 publications

Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning

Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning

Comprehensive Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems Using the R-Package Flacco

Analysing and comparing problem landscapes for black-box optimization via length scale

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