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‎paper/paper.bib‎

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title = {Context-Independent Scatter and Tabu Search for Permutation Problems},
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@article{cicirello2016,
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author = {Vincent A. Cicirello},
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title = {The Permutation in a Haystack Problem and the Calculus of Search Landscapes},
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journal = {IEEE Transactions on Evolutionary Computation},
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year = {2016},
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volume = {20},
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number = {3},
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pages = {434--446},
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doi = {10.1109/TEVC.2015.2477284}
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}
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@inproceedings{cicirello2014,
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author = {Vincent A. Cicirello},
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title = {On the Effects of Window-Limits on the Distance Profiles of Permutation Neighborhood Operators},
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booktitle = {Proceedings of the International Conference on Bioinspired Information and Communications Technologies},
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month = {December},
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year = {2014},
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pages = {28--35},
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doi = {10.4108/icst.bict.2014.257872}
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}
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@inproceedings{cicirello2013,
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author = {Vincent A. Cicirello and Robert Cernera},
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title = {Profiling the Distance Characteristics of Mutation Operators for Permutation-Based Genetic Algorithms},
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booktitle = {Proceedings of the 26th International Conference of the Florida Artificial Intelligence Research Society},
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publisher = {AAAI Press},
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month = {May},
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year = {2013},
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pages = {46--51}
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}
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@article{fagin2003,
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author = {Ronald Fagin and Ravi Kumar and D. Sivakumar},
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title = {Comparing Top k Lists},
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year = {2003},
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volume = {17},
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number = {1},
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pages = {134--160}
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}
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@article{hernando2015,
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author={Leticia Hernando and Alexander Mendiburu and Jose A. Lozano},
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journal={IEEE Transactions on Evolutionary Computation},
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title={A Tunable Generator of Instances of Permutation-based Combinatorial Optimization Problems},
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year={2016},
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volume={20},
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number={2},
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pages = {165--179},
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doi = {10.1109/TEVC.2015.2433680}
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}
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@inproceedings{fdc,
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author = {Terry Jones and Stephanie Forrest},
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title = {Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms},
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booktitle = {Proceedings of the 6th International Conference on Genetic Algorithms},
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year = {1995},
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pages = {184--192},
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publisher = {Morgan Kaufmann}
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}
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@article{kendall1938,
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author = {M. G. Kendall},
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title = {A New Measure of Rank Correlation},
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journal = {Biometrika},
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year = {1938},
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month = {June},
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volume = {30},
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number = {1/2},
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pages = {81--93}
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}
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@article{lee58,
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author={C. Lee},
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journal={IRE Transactions on Information Theory},
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title={Some properties of nonbinary error-correcting codes},
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year={1958},
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pages={77--82},
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month={June},
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doi = {10.1109/TIT.1958.1057446}
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}
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@incollection{marti2005,
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author = {Mart\'{i}, Rafael and Laguna, Manuel and Campos, Vicente},
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title = {Scatter Search vs. Genetic Algorithms: An Experimental Evaluation with Permutation Problems},
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booktitle = {Metaheuristic Optimization via Memory and Evolution},
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publisher = {Springer},
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pages = {263--282},
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year = {2005}
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}
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author = {Marina Meil\u{a} and Le Bao},
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}
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@book{mitchell,
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title={An Introduction to Genetic Algorithms},
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author={Melanie Mitchell},
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}
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}
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}
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@article{schiavinotto2007,
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author = {Marc Sevaux and Kenneth S\"{o}rensen},
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}
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@article{sorensen07,
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author = {Kenneth S\"{o}rensen},
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title = {Distance measures based on the edit distance for permutation-type representations},
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}
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author = {Robert A. Wagner and Michael J. Fischer},
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‎paper/paper.md‎

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---
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title: 'JavaPermutationTools: A Java Library of Permutation Distance Metrics'
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tags:
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- Java
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- permutation distance
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- permutation metric
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- fitness landscape analysis
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- evolutionary population management
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authors:
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- name: Vincent A. Cicirello
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orcid: 0000-0003-1072-8559
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affiliation: 1
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affiliations:
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- name: Computer Science, School of Business, Stockton University, Galloway, NJ 08205
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index: 1
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date: 8 August 2018
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bibliography: paper.bib
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---
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# Summary
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Permutations are used to represent a wide variety of ordered data. For example,
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a permutation may represent an individual's preferences (or ranking) of a collection
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of products such as books or music. Or perhaps a permutation may represent a route
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for delivering a set of packages. Permutations can also represent one-to-one mappings
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between sets (e.g., instructors to courses at a fixed time). There are applications
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where measuring the distance between a pair of permutations is necessary. For example,
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a recommender system may want to compare the similarity of two individuals' preferences
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for music, perhaps to make song recommendations. Depending upon the application,
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the permutation features most important to distance calculation may be one or more of
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the absolute positions of the elements (e.g., for one-to-one mappings), the adjacency
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of elements (e.g., the earlier routing example), or the general precedence of pairs of
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elements (e.g., music preference example). Thus, it should be no surprise that there
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exists a large variety of permutation distance metrics in the research literature.
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The motivation and origin of this library of permutation distance metrics is our research
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on evolutionary computation, and other metaheuristic approaches, for solving permutation
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optimization problems. A permutation optimization problem is a problem where solutions
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are represented by permutations of the elements of some set, and where the objective is to
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maximize or minimize some function. For example, a solution to a traveling salesperson
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problem (TSP) is a permutation of the set of cities, and the objective is to find the
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permutation that corresponds to the tour of the cities of minimal cost.
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There are at least two applications of permutation distance that come from evolutionary
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computation. The first application is to maintain population diversity. The various forms
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of evolutionary computation, such as genetic algorithms, genetic programming, etc, solve
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problems through simulated evolutionary processes [@mitchell]. They maintain a population of solutions
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to the problem at hand, and this population evolves over many generations using operators
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such as mutation, crossover, etc. Just as it is in natural evolution, a diverse gene
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pool is important to evolutionary computation. In later generations, if variation among
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the members of the population declines, then the evolutionary search can stagnate. Approaches
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to population management [@sevaux2005], such as in scatter search [@campos2005; @marti2005],
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attempt to maintain diversity among the population of solutions. They require a means of
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measuring distance between population members. And if the problem is one in which solutions are
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represented as permutations, then a permutation distance metric is required.
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The second application of permutation distance for evolutionary computation is that of search
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landscape analysis. A fitness (or search) landscape [@mitchell] is the space of possible
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solutions to an optimization problem spatially organized on a landscape with similar solutions
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as neighbors, and where elevation corresponds to fitness (or solution quality). Peaks (for
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a maximization problem) and valleys (for a minimization problem) correspond to locally optimal
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solutions. The optimization problem is to find an optimal point on that landscape. Search
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landscape analysis is the term covering the theoretical and practical techniques for studying what
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characteristics of a problem make it hard, how different search operators affect fitness landscape
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topology, among others. There is a wide variety of work on fitness landscape analysis, including
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for permutation landscapes [@cicirello2016; @hernando2015; @tayarani2014; @cicirello2014; @cicirello2013; @sorensen07; @schiavinotto2007].
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Some fitness landscape analysis techniques use fitness distance correlation (FDC) [@fdc], the Pearson
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correlation coefficient of the fitness of a solution vs its distance to the nearest optimal solution.
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The search landscape calculus [@cicirello2016] is a fitness landscape analysis technique that examines
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local rates of change of fitness. These as well as others require distance metrics for the type of
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structure you are optimizing.
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During the course of our research on fitness landscape analysis for permutation optimization
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problems [@cicirello2016; @cicirello2014; @cicirello2013], we developed a Java library of permutation
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distance metrics. Most of the distance metrics in the literature are described mathematically with
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no source code available. Thus, our library offers convenient access to efficient implementations of
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a variety of distance metrics that share a common programmatic interface. The following table
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summarizes the distances available in this initial release of the library, along with their runtime,
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whether they satisfy the requirements of a metric, and one or more key citations.
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Distance | Runtime | Metric? | Citations
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-------- | ------- | ------- | ---------
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acyclic edge distance | $O(n)$ | pseudo | [@ronald1997; @ronald1995]
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cyclic edge distance | $O(n)$ | pseudo | [@ronald1997; @ronald1995]
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cyclic r-type distance | $O(n)$ | pseudo | [@cicirello2016]
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deviation distance | $O(n)$ | yes | [@cicirello2016; @campos2005]
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deviation distance normalized | $O(n)$ | yes | [@ronald1998; @sorensen07]
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edit distance | $O(n^2)$ | yes | [@wagner74; @sorensen07]
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exact match distance | $O(n)$ | yes | [@ronald1998]
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interchange distance | $O(n)$ | yes | [@cicirello2013]
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Kendall tau distance | $O(n^2)$ | yes | [@kendall1938; @meila2010; @fagin2003]
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Lee distance | $O(n)$ | yes | [@lee58]
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r-type distance | $O(n)$ | yes | [@campos2005; @marti2005]
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reinsertion distance | $O(n^2)$ | yes | [@cicirello2016; @cicirello2013]
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reversal distance | Init: $O(n!n^3)$ Compute: $O(n^2)$ | yes | [@cicirello2016; @caprara1997]
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squared deviation distance | $O(n)$ | yes | [@sevaux2005]
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The source repository (https://github.com/cicirello/JavaPermutationTools)
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contains source code of the library, programs that provide example
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usage of key functionality, as well as programs that reproduce results from papers that
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have used the library. API documentation is hosted on the web (https://jpt.cicirello.org/).
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# References

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