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Distance measures based on the edit distance for permutation-type representations

Kenneth Sörensen
2006 Journal of Heuristics  
The distance measures are based on the edit distance. We introduce several extensions to the simple edit distance for more complex problem representations and show how each of these can be calculated.  ...  In this paper, we develop and discuss several distance measures for permutation type representations of solutions of combinatorial optimisation problems.  ...  CONCLUSIONS In this paper, we develop several extensions of the edit distance measure, that can be used to measure the similarity or difference between solutions of combinatorial problems, that can be  ... 
doi:10.1007/s10732-006-9001-3 fatcat:lpsi5gnewnaknlxkkr64osi34q

Topological crossover for the permutation representation

Alberto Moraglio, Riccardo Poli
2005 Proceedings of the 2005 workshops on Genetic and evolutionary computation - GECCO '05  
In this paper we explore how the topological framework applies to the permutation representation and in particular analyse the consequences of having more than one notion of distance available.  ...  Also, we study the interactions among distances and build a rational picture in which pre-existing recombination/crossover operators for permutation fit naturally.  ...  We classify distances for permutations based on their origin into: • Notions of distance arising from the interpretation of permutations: these measure the distance between the objects represented by two  ... 
doi:10.1145/1102256.1102330 dblp:conf/gecco/MoraglioP05 fatcat:rass45w3ejfy5bxjk5i66dcosa

Classification of Permutation Distance Metrics for Fitness Landscape Analysis [chapter]

Vincent A. Cicirello
2019 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
The classification can assist in identifying appropriate metrics based on optimization problem feature for use in fitness landscape analysis.  ...  The result is aligned with existing classifications of permutation problem types produced through less formal means, including the A-permutation, Rpermutation, and P-permutation types, and has also identified  ...  For this landscape, we find that the two forms of R-type distance offer the highest FDC (see Table 11 ) and that FDC is otherwise low for the other permutation distance measures.  ... 
doi:10.1007/978-3-030-24202-2_7 fatcat:bluv3wftjnexviwfk5qkk245qy

On the Effects of Window-Limits on the Distance Profiles of Permutation Neighborhood Operators

Vincent Cicirello
2015 Proceedings of the 8th International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)  
We provide profiles of the distance characteristics of window-limited variations of several of the more common permutation neighborhood operators.  ...  In this paper, we profile window-limited variations of several commonly employed neighborhood operators for problems in which candidate solutions are represented as permutations.  ...  Interchange Distance is an edit distance measure.  ... 
doi:10.4108/icst.bict.2014.257872 dblp:conf/bionetics/Cicirello14 fatcat:5irollm2qzesjei7reob3igcpq

A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space [article]

Yourim Yoon, Yong-Hyuk Kim, Alberto Moraglio, Byung-Ro Moon
2009 arXiv   pre-print
Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space.  ...  It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations.  ...  X G : based on sorting by reversals for permutations • Crossover of phenotypes X P : based on sorting by reversals for circular permutations implemented using simple permutations: circular shift to match  ... 
arXiv:0907.3200v1 fatcat:nhvubd5hxfhftj7anjlkgjmw5q

Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning [article]

Robin Winter, Frank Noé, Djork-Arné Clevert
2021 arXiv   pre-print
We demonstrate the effectiveness of our proposed model on various graph reconstruction and generation tasks and evaluate the expressive power of extracted representations for downstream graph-level classification  ...  In this work we address this issue by proposing a permutation-invariant variational autoencoder for graph structured data.  ...  Graph Editing Distance A classical way of measuring graph similarity is the so called graph editing distance (GED) [51] .  ... 
arXiv:2104.09856v2 fatcat:dcmxbft6hrbxpmjpkn4fdovzfu

An Ecological Approach to Measuring Locality in Linear Genotype to Phenotype Maps [chapter]

Tom Seaton, Julian F. Miller, Tim Clarke
2012 Lecture Notes in Computer Science  
Weak locality is identified in a case study on Cartesian Genetic Programming (CGP), a directed acyclic graph representation.  ...  Recent research has considered the role of locality in GP representations.  ...  Dan Franks and other members of the York Centre for Complex Systems Analysis for advice concerning the Mantel statistic.  ... 
doi:10.1007/978-3-642-29139-5_15 fatcat:jbvbznlrqzev5a2xhoo6lmioem

Evolutionary Puzzles: An Introduction to Genome Rearrangement [chapter]

Mathieu Blanchette
2001 Lecture Notes in Computer Science  
In the context of gene order data, a useful measure of evolutionary distance is the minimum number of basic operations needed to transform the gene order of one species into that of another.  ...  The first one, called distance matrix method, relies on the estimation of the evolutionary distance between each pair of species considered.  ...  The most popular distance measure between two gene orders is the edit-distance, defined as the smallest number of rearrangements needed to transform one gene order into the other.  ... 
doi:10.1007/3-540-45718-6_106 fatcat:4gmsmubsmfbitfryfdmrhmw42y

Kendall tau sequence distance: Extending Kendall tau from ranks to sequences

Vincent Cicirello
2018 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems  
For example, there are several edit distance measures for permutations, including Wagner and Fischer's string edit distance since a permutation is a special case of a string.  ...  In this paper, we begin with a metric on permutations, and adapt it to measure the distance between  ...  Note that as an adjacent swap edit distance, it specifically concerns the p representation of the permutation and not the σ notation.  ... 
doi:10.4108/eai.13-7-2018.163925 fatcat:pl5bokktzjh7ljjlzyqv5ylzxi

Geometry of evolutionary algorithms

Alberto Moraglio
2011 Proceedings of the 13th annual conference companion on Genetic and evolutionary computation - GECCO '11  
Crossover Design: TSP Example Edit distance duality for permutations: • producing offspring in the segment between parents on a space generated by moves of type x (e.g., swaps) • producing offspring permutations  ...  : • measure of distance in the search space • measure of similarity on the underlying representation • this can be used to help identifying an operational definition of crossover representation (implementation  ... 
doi:10.1145/2001858.2002144 dblp:conf/gecco/Moraglio11 fatcat:gnuqgi6yqrh43pykngodjt7ali

Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces

Yong-Hyuk Kim, Alberto Moraglio, Ahmed Kattan, Yourim Yoon
2014 Mathematical Problems in Engineering  
We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs.  ...  This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation.  ...  For example, hamming distance is an edit distance between binary strings based on the unit edit of a bit flip.  ... 
doi:10.1155/2014/184540 fatcat:rwoakrxlhrbmjmrtl75amfnw5u

Kendall Tau Sequence Distance: Extending Kendall Tau from Ranks to Sequences [article]

Vincent A. Cicirello
2019 arXiv   pre-print
An edit distance is a measure of the minimum cost sequence of edit operations to transform one structure into another.  ...  For example, there are several edit distance measures for permutations, including Wagner and Fischer's string edit distance since a permutation is a special case of a string.  ...  There is at least one instance where a metric on strings is suggested for permutations. Specifically, Sörensen [2007] suggested using string edit distance to measure distance between permutations.  ... 
arXiv:1905.02752v3 fatcat:i5hxwgcuszhyrbhcy66erntd2i

A Brief Index for Proximity Searching [chapter]

Eric Sadit Téllez, Edgar Chávez, Antonio Camarena-Ibarrola
2009 Lecture Notes in Computer Science  
In this paper we show how to represent the permutation as a binary vector, using just one bit for each permutant (instead of log κ in the plain representation).  ...  When a query arrives the relative displacements in the permutants between the query and a particular object is measured.  ...  Fig. 3 . 3 Results for brief index against full permutations for and english dictionary, using edit distance.  ... 
doi:10.1007/978-3-642-10268-4_62 fatcat:ap7chd7jfvfjdlljbhygn6nxo4

Finding Non-Arbitrary Form-Meaning Systematicity Using String-Metric Learning for Kernel Regression

E.Dario Gutierrez, Roger Levy, Benjamin Bergen
2016 Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)  
Furthermore, we introduce a novel metric learning algorithm that can learn weighted edit distances that minimize kernel regression error.  ...  Arbitrariness of the sign-the notion that the forms of words are unrelated to their meanings-is an underlying assumption of many linguistic theories.  ...  Acknowledgments This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.  ... 
doi:10.18653/v1/p16-1225 dblp:conf/acl/GutierrezLB16 fatcat:yffdi2unmzhuxd6tt3kqq5jtgy

Rapid Similarity Retrieval from Image and Video [chapter]

Svetha Venkatesh, Horst Bunke, Kim Shearer
2000 Multimedia Image and Video Processing  
an edit distance measure.  ...  However, the edit distance measure is not suitable for similarity retrieval for image and video databases.  ... 
doi:10.1201/9781420037562.ch15 fatcat:x2lovfu55fajphgcuve3kjyahu
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