Rugged and Elementary Landscapes

Klemm, Konstantin; Stadler, Peter F.

doi:10.1007/978-3-642-33206-7_3

Cited by 5 publications

(5 citation statements)

References 63 publications

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“…Besides, one notes that the eigenvalue (λ 2 = 12) for NAES 2 The reader is referred to the Mathematica notebook publicly available online at: https://github.com/marcosdg/ppsn-2018, for the examples details. and WP does not coincide with the eigenvalue (λ 2 = 4) obtained for the mutation Laplacian [8]. Nevertheless, that is expected: two spaces may have identical eigenfunctions but different eigenvalues, possibly affecting the correlation between fitness values (i.e.…”

Section: Discrete Nodal Domains For Uniform Recombination In Boolean ...mentioning

confidence: 88%

“…representing the vertex set of an underlying connected graph, is an eigenfunction of a (generalised) Laplacian matrix L of the graph: L f = λ f ; where λ > 0 is the eigenvalue and the constant f := 1 |X| x∈X f (x) is the average fitness of a configuration in X [8,15]. If a landscape f is not elementary, it can always be decomposed into a linear combination of ELs f k called its Fourier expansion:…”

Section: Elementary Landscapes Theorymentioning

confidence: 99%

“…Non-Fujiyama are those ELs for p > 1 with local optima clustered in more than one region; indeed, many combinatorial problems fall here with p = 2 (e.g. Max Cut) [8]. More formally, by clusters we mean discrete nodal domains [1].…”

Section: Elementary Landscapes Theorymentioning

confidence: 99%

“…Moreover, for Boolean spaces with Hamming distance, it was shown that these elementary landscapes have a unique local optimum, thus coinciding with unimodal landscapes [7,15,18]. -Many combinatorial problems (such as Graph Coloring, Symmetric Travelling Salesman and Graph Bipartitioning) have elementary landscapes with local optima grouped only in a few clusters in the search space, suggesting an approximately globally concave (or convex) structure [8,18]. -Certain recombination spaces (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Bridging Elementary Landscapes and a Geometric Theory of Evolutionary Algorithms: First Steps

García

Moraglio

2018

Parallel Problem Solving From Nature – PPSN XV

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Based on a geometric theory of evolutionary algorithms, it was shown that all evolutionary algorithms equipped with a geometric crossover and no mutation operator do the same kind of convex search across representations, and that they are well-matched with generalised forms of concave fitness landscapes for which they provably find the optimum in polynomial time [13]. Analysing the landscape structure is essential to understand the relationship between problems and evolutionary algorithms. This paper continues such investigations by considering the following challenge: develop an analytical method to recognise that the fitness landscape for a given problem provably belongs to a class of concave fitness landscapes. Elementary landscapes theory provides analytic algebraic means to study the landscape structure [15]. This work begins linking both theories to better understand how such method could be devised using elementary landscapes. Examples on the well known One Max, Leading Ones, Not-All-Equal Satisfiability and Weight Partition problems illustrate the fundamental concepts supporting this approach.

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Section: Discrete Nodal Domains For Uniform Recombination In Boolean ...mentioning

confidence: 88%

Section: Elementary Landscapes Theorymentioning

confidence: 99%

Section: Elementary Landscapes Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bridging Elementary Landscapes and a Geometric Theory of Evolutionary Algorithms: First Steps

García

Moraglio

2018

Parallel Problem Solving From Nature – PPSN XV

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“…Peter Stadler's pioneering the use of graph Laplacians [4] and related tools for analyzing combinatorial optmization fitness landscapes has resulted in significant insights into why some locality structures (and corresponding search operators) perform better than others [5].…”

Section: A Exploiting Problem Domain Structurementioning

confidence: 99%

Principled Evolutionary Algorithm search operator design and the kernel trick

Lane

Azad

Ryan

2016

2016 IEEE Symposium Series on Computational Intelligence (SSCI)

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Configuring an Evolutionary Algorithm (EA) can be a haphazard and inefficient process. An EA practitioner may have to choose between a plethora of search operator types and other parameter settings. In contrast, the goal of EA principled design is a more streamlined and systematic design methodology, which first seeks to better understand the problem domain, and only then uses such acquired insights to guide the choice of parameters and operators. We introduce a new approach to principled design of EAs based on kernel methods. Several popular machine learning and data analysis paradigms, which have been successfully applied to a wide range of difficult real world problems, would fall under this kernel umbrella. We demonstrate how kernel functions, which capture useful problem domain knowledge, can be used to directly construct EA search operators. We test two kernel search operators on a suite of four challenging combinatorial optimization problem domains. These novel kernel search operators exhibit superior performance to some traditional EA search operators.

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Virus Evolution on Fitness Landscapes

Schuster

Stadler

2023

Current Topics in Microbiology and Immunology

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Rugged and Elementary Landscapes

Cited by 5 publications

References 63 publications

Bridging Elementary Landscapes and a Geometric Theory of Evolutionary Algorithms: First Steps

Bridging Elementary Landscapes and a Geometric Theory of Evolutionary Algorithms: First Steps

Principled Evolutionary Algorithm search operator design and the kernel trick

Virus Evolution on Fitness Landscapes

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