Provably Optimal Self-adjusting Step Sizes for Multi-valued Decision Variables View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2016

AUTHORS

Benjamin Doerr , Carola Doerr , Timo Kötzing

ABSTRACT

We regard the problem of maximizing a OneMax-like function defined over an alphabet of size r. In previous work [GECCO 2016] we have investigated how three different mutation operators influence the performance of Randomized Local Search (RLS) and the (1+1) Evolutionary Algorithm. This work revealed that among these natural mutation operators none is superior to the other two for any choice of r. We have also given in [GECCO 2016] some indication that the best achievable run time for large r is \(\varTheta (n \log r (\log n + \log r))\), regardless of how the mutation operator is chosen, as long as it is a static choice (i.e., the distribution used for variation of the current individual does not change over time). Here in this work we show that we can achieve a better performance if we allow for adaptive mutation operators. More precisely, we analyze the performance of RLS using a self-adjusting mutation strength. In this algorithm the size of the steps taken in each iteration depends on the success of previous iterations. That is, the mutation strength is increased after a successful iteration and it is decreased otherwise. We show that this idea yields an expected optimization time of \(\varTheta (n (\log n + \log r))\), which is optimal among all comparison-based search heuristics. This is the first time that self-adjusting parameter choices are shown to outperform static choices on a discrete multi-valued optimization problem. More... »

PAGES

782-791

References to SciGraph publications

Book

TITLE

Parallel Problem Solving from Nature – PPSN XIV

ISBN

978-3-319-45822-9
978-3-319-45823-6

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-45823-6_73

DOI

http://dx.doi.org/10.1007/978-3-319-45823-6_73

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033020271


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "\u00c9cole Polytechnique", 
          "id": "https://www.grid.ac/institutes/grid.10877.39", 
          "name": [
            "\u00c9cole Polytechnique"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Doerr", 
        "givenName": "Benjamin", 
        "id": "sg:person.01327223002.89", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01327223002.89"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "CNRS and Sorbonne Universit\u00e9s, UPMC Univ Paris 06, LIP6"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Doerr", 
        "givenName": "Carola", 
        "id": "sg:person.010360414373.45", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010360414373.45"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Hasso-Plattner-Institut"
          ], 
          "type": "Organization"
        }, 
        "familyName": "K\u00f6tzing", 
        "givenName": "Timo", 
        "id": "sg:person.014204051473.89", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014204051473.89"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-3-642-15844-5_1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000452291", 
          "https://doi.org/10.1007/978-3-642-15844-5_1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/1967654.1967671", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004292096"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00453-015-0048-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004365082", 
          "https://doi.org/10.1007/s00453-015-0048-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.tcs.2014.11.028", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008296423"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2739480.2754684", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012276676"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-58484-6_258", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013453413", 
          "https://doi.org/10.1007/3-540-58484-6_258"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/11513575_14", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014437848", 
          "https://doi.org/10.1007/11513575_14"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0963548309990599", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017811806"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00453-012-9622-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017937785", 
          "https://doi.org/10.1007/s00453-012-9622-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2908812.2908950", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017940419"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-87744-8_46", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038138435", 
          "https://doi.org/10.1007/978-3-540-87744-8_46"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-87744-8_46", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038138435", 
          "https://doi.org/10.1007/978-3-540-87744-8_46"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00453-011-9585-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040023322", 
          "https://doi.org/10.1007/s00453-011-9585-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/2908812.2908891", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040036399"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00224-004-1177-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040195428", 
          "https://doi.org/10.1007/s00224-004-1177-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1043679011", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-05094-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043679011", 
          "https://doi.org/10.1007/978-3-662-05094-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-05094-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043679011", 
          "https://doi.org/10.1007/978-3-662-05094-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/4235.771166", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061172023"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tevc.2014.2308294", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061605203"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/icec.1995.489123", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1095760180"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2016", 
    "datePublishedReg": "2016-01-01", 
    "description": "We regard the problem of maximizing a OneMax-like function defined over an alphabet of size r. In previous work [GECCO 2016] we have investigated how three different mutation operators influence the performance of Randomized Local Search (RLS) and the (1+1) Evolutionary Algorithm. This work revealed that among these natural mutation operators none is superior to the other two for any choice of\u00a0r. We have also given in [GECCO 2016] some indication that the best achievable run time for large r is \\(\\varTheta (n \\log r (\\log n + \\log r))\\), regardless of how the mutation operator is chosen, as long as it is a static choice (i.e., the distribution used for variation of the current individual does not change over time). Here in this work we show that we can achieve a better performance if we allow for adaptive mutation operators. More precisely, we analyze the performance of RLS using a self-adjusting mutation strength. In this algorithm the size of the steps taken in each iteration depends on the success of previous iterations. That is, the mutation strength is increased after a successful iteration and it is decreased otherwise. We show that this idea yields an expected optimization time of \\(\\varTheta (n (\\log n + \\log r))\\), which is optimal among all comparison-based search heuristics. This is the first time that self-adjusting parameter choices are shown to outperform static choices on a discrete multi-valued optimization problem.", 
    "editor": [
      {
        "familyName": "Handl", 
        "givenName": "Julia", 
        "type": "Person"
      }, 
      {
        "familyName": "Hart", 
        "givenName": "Emma", 
        "type": "Person"
      }, 
      {
        "familyName": "Lewis", 
        "givenName": "Peter R.", 
        "type": "Person"
      }, 
      {
        "familyName": "L\u00f3pez-Ib\u00e1\u00f1ez", 
        "givenName": "Manuel", 
        "type": "Person"
      }, 
      {
        "familyName": "Ochoa", 
        "givenName": "Gabriela", 
        "type": "Person"
      }, 
      {
        "familyName": "Paechter", 
        "givenName": "Ben", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-45823-6_73", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-319-45822-9", 
        "978-3-319-45823-6"
      ], 
      "name": "Parallel Problem Solving from Nature \u2013 PPSN XIV", 
      "type": "Book"
    }, 
    "name": "Provably Optimal Self-adjusting Step Sizes for Multi-valued Decision Variables", 
    "pagination": "782-791", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-45823-6_73"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9d4dafd647aabdf4bb39fb90b46720dda8223ff95c5baf6d3d408799c1f575d7"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1033020271"
        ]
      }
    ], 
    "publisher": {
      "location": "Cham", 
      "name": "Springer International Publishing", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-45823-6_73", 
      "https://app.dimensions.ai/details/publication/pub.1033020271"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T15:22", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8672_00000263.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-3-319-45823-6_73"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-45823-6_73'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-45823-6_73'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-45823-6_73'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-45823-6_73'


 

This table displays all metadata directly associated to this object as RDF triples.

173 TRIPLES      23 PREDICATES      46 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-45823-6_73 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author N9574b2388f9a47b499556117b5da2b42
4 schema:citation sg:pub.10.1007/11513575_14
5 sg:pub.10.1007/3-540-58484-6_258
6 sg:pub.10.1007/978-3-540-87744-8_46
7 sg:pub.10.1007/978-3-642-15844-5_1
8 sg:pub.10.1007/978-3-662-05094-1
9 sg:pub.10.1007/s00224-004-1177-z
10 sg:pub.10.1007/s00453-011-9585-3
11 sg:pub.10.1007/s00453-012-9622-x
12 sg:pub.10.1007/s00453-015-0048-0
13 https://app.dimensions.ai/details/publication/pub.1043679011
14 https://doi.org/10.1016/j.tcs.2014.11.028
15 https://doi.org/10.1017/s0963548309990599
16 https://doi.org/10.1109/4235.771166
17 https://doi.org/10.1109/icec.1995.489123
18 https://doi.org/10.1109/tevc.2014.2308294
19 https://doi.org/10.1145/1967654.1967671
20 https://doi.org/10.1145/2739480.2754684
21 https://doi.org/10.1145/2908812.2908891
22 https://doi.org/10.1145/2908812.2908950
23 schema:datePublished 2016
24 schema:datePublishedReg 2016-01-01
25 schema:description We regard the problem of maximizing a OneMax-like function defined over an alphabet of size r. In previous work [GECCO 2016] we have investigated how three different mutation operators influence the performance of Randomized Local Search (RLS) and the (1+1) Evolutionary Algorithm. This work revealed that among these natural mutation operators none is superior to the other two for any choice of r. We have also given in [GECCO 2016] some indication that the best achievable run time for large r is \(\varTheta (n \log r (\log n + \log r))\), regardless of how the mutation operator is chosen, as long as it is a static choice (i.e., the distribution used for variation of the current individual does not change over time). Here in this work we show that we can achieve a better performance if we allow for adaptive mutation operators. More precisely, we analyze the performance of RLS using a self-adjusting mutation strength. In this algorithm the size of the steps taken in each iteration depends on the success of previous iterations. That is, the mutation strength is increased after a successful iteration and it is decreased otherwise. We show that this idea yields an expected optimization time of \(\varTheta (n (\log n + \log r))\), which is optimal among all comparison-based search heuristics. This is the first time that self-adjusting parameter choices are shown to outperform static choices on a discrete multi-valued optimization problem.
26 schema:editor N01ab0ca4c04d47a2a3a68ad3592d30ea
27 schema:genre chapter
28 schema:inLanguage en
29 schema:isAccessibleForFree false
30 schema:isPartOf N65802eba4c9940218a6ef39d34ecc8dd
31 schema:name Provably Optimal Self-adjusting Step Sizes for Multi-valued Decision Variables
32 schema:pagination 782-791
33 schema:productId N56f3df48fe1f4579b7bc745cb9988fdc
34 N7b5b84580a6b483697332c4959dee54a
35 Nb60eeb9be9d945d18c3ed49e559aa946
36 schema:publisher N22a20c67ce154c0db3c011c973d4cefc
37 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033020271
38 https://doi.org/10.1007/978-3-319-45823-6_73
39 schema:sdDatePublished 2019-04-15T15:22
40 schema:sdLicense https://scigraph.springernature.com/explorer/license/
41 schema:sdPublisher N9ba16c5fa30446e3ab64255de61562fa
42 schema:url http://link.springer.com/10.1007/978-3-319-45823-6_73
43 sgo:license sg:explorer/license/
44 sgo:sdDataset chapters
45 rdf:type schema:Chapter
46 N01ab0ca4c04d47a2a3a68ad3592d30ea rdf:first N90262f3064ed44edbba80beefd7a36a0
47 rdf:rest Nc0cb47efeeff4619b6f61dd95058ea44
48 N06f8107749fb402dbab5548b8ab58170 rdf:first N0fd5b045779d4f5eb835fe4ed26ede8d
49 rdf:rest N705a680444bf4b50b993bf8b251d9e6c
50 N0fd5b045779d4f5eb835fe4ed26ede8d schema:familyName Ochoa
51 schema:givenName Gabriela
52 rdf:type schema:Person
53 N1ee7b171786942349e03ee7c542c47be rdf:first Ncd7bb07e5cee4745adfc66f4f1333d08
54 rdf:rest Nfc6bea706739481b8c3dbbfa2454b687
55 N22a20c67ce154c0db3c011c973d4cefc schema:location Cham
56 schema:name Springer International Publishing
57 rdf:type schema:Organisation
58 N2b694623df0b488998d88b41a8cac9c6 schema:familyName López-Ibáñez
59 schema:givenName Manuel
60 rdf:type schema:Person
61 N35f5a32680cf43f2822384493724a592 schema:name CNRS and Sorbonne Universités, UPMC Univ Paris 06, LIP6
62 rdf:type schema:Organization
63 N4548f175b11c47748a4ef4cc487eab85 schema:familyName Paechter
64 schema:givenName Ben
65 rdf:type schema:Person
66 N56f3df48fe1f4579b7bc745cb9988fdc schema:name readcube_id
67 schema:value 9d4dafd647aabdf4bb39fb90b46720dda8223ff95c5baf6d3d408799c1f575d7
68 rdf:type schema:PropertyValue
69 N65802eba4c9940218a6ef39d34ecc8dd schema:isbn 978-3-319-45822-9
70 978-3-319-45823-6
71 schema:name Parallel Problem Solving from Nature – PPSN XIV
72 rdf:type schema:Book
73 N705a680444bf4b50b993bf8b251d9e6c rdf:first N4548f175b11c47748a4ef4cc487eab85
74 rdf:rest rdf:nil
75 N73666179fb424e18bb641872e439f1e0 rdf:first sg:person.014204051473.89
76 rdf:rest rdf:nil
77 N7b5b84580a6b483697332c4959dee54a schema:name dimensions_id
78 schema:value pub.1033020271
79 rdf:type schema:PropertyValue
80 N90262f3064ed44edbba80beefd7a36a0 schema:familyName Handl
81 schema:givenName Julia
82 rdf:type schema:Person
83 N94316f02935e46a0bad829f9ac0f383d rdf:first sg:person.010360414373.45
84 rdf:rest N73666179fb424e18bb641872e439f1e0
85 N9574b2388f9a47b499556117b5da2b42 rdf:first sg:person.01327223002.89
86 rdf:rest N94316f02935e46a0bad829f9ac0f383d
87 N9ba16c5fa30446e3ab64255de61562fa schema:name Springer Nature - SN SciGraph project
88 rdf:type schema:Organization
89 Na6a9c05a6491461bb34eaa5de5bb440b schema:familyName Hart
90 schema:givenName Emma
91 rdf:type schema:Person
92 Na8c69117bea3429b9393715980a2cddc schema:name Hasso-Plattner-Institut
93 rdf:type schema:Organization
94 Nb60eeb9be9d945d18c3ed49e559aa946 schema:name doi
95 schema:value 10.1007/978-3-319-45823-6_73
96 rdf:type schema:PropertyValue
97 Nc0cb47efeeff4619b6f61dd95058ea44 rdf:first Na6a9c05a6491461bb34eaa5de5bb440b
98 rdf:rest N1ee7b171786942349e03ee7c542c47be
99 Ncd7bb07e5cee4745adfc66f4f1333d08 schema:familyName Lewis
100 schema:givenName Peter R.
101 rdf:type schema:Person
102 Nfc6bea706739481b8c3dbbfa2454b687 rdf:first N2b694623df0b488998d88b41a8cac9c6
103 rdf:rest N06f8107749fb402dbab5548b8ab58170
104 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
105 schema:name Mathematical Sciences
106 rdf:type schema:DefinedTerm
107 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
108 schema:name Numerical and Computational Mathematics
109 rdf:type schema:DefinedTerm
110 sg:person.010360414373.45 schema:affiliation N35f5a32680cf43f2822384493724a592
111 schema:familyName Doerr
112 schema:givenName Carola
113 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010360414373.45
114 rdf:type schema:Person
115 sg:person.01327223002.89 schema:affiliation https://www.grid.ac/institutes/grid.10877.39
116 schema:familyName Doerr
117 schema:givenName Benjamin
118 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01327223002.89
119 rdf:type schema:Person
120 sg:person.014204051473.89 schema:affiliation Na8c69117bea3429b9393715980a2cddc
121 schema:familyName Kötzing
122 schema:givenName Timo
123 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014204051473.89
124 rdf:type schema:Person
125 sg:pub.10.1007/11513575_14 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014437848
126 https://doi.org/10.1007/11513575_14
127 rdf:type schema:CreativeWork
128 sg:pub.10.1007/3-540-58484-6_258 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013453413
129 https://doi.org/10.1007/3-540-58484-6_258
130 rdf:type schema:CreativeWork
131 sg:pub.10.1007/978-3-540-87744-8_46 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038138435
132 https://doi.org/10.1007/978-3-540-87744-8_46
133 rdf:type schema:CreativeWork
134 sg:pub.10.1007/978-3-642-15844-5_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000452291
135 https://doi.org/10.1007/978-3-642-15844-5_1
136 rdf:type schema:CreativeWork
137 sg:pub.10.1007/978-3-662-05094-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043679011
138 https://doi.org/10.1007/978-3-662-05094-1
139 rdf:type schema:CreativeWork
140 sg:pub.10.1007/s00224-004-1177-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1040195428
141 https://doi.org/10.1007/s00224-004-1177-z
142 rdf:type schema:CreativeWork
143 sg:pub.10.1007/s00453-011-9585-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040023322
144 https://doi.org/10.1007/s00453-011-9585-3
145 rdf:type schema:CreativeWork
146 sg:pub.10.1007/s00453-012-9622-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1017937785
147 https://doi.org/10.1007/s00453-012-9622-x
148 rdf:type schema:CreativeWork
149 sg:pub.10.1007/s00453-015-0048-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004365082
150 https://doi.org/10.1007/s00453-015-0048-0
151 rdf:type schema:CreativeWork
152 https://app.dimensions.ai/details/publication/pub.1043679011 schema:CreativeWork
153 https://doi.org/10.1016/j.tcs.2014.11.028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008296423
154 rdf:type schema:CreativeWork
155 https://doi.org/10.1017/s0963548309990599 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017811806
156 rdf:type schema:CreativeWork
157 https://doi.org/10.1109/4235.771166 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061172023
158 rdf:type schema:CreativeWork
159 https://doi.org/10.1109/icec.1995.489123 schema:sameAs https://app.dimensions.ai/details/publication/pub.1095760180
160 rdf:type schema:CreativeWork
161 https://doi.org/10.1109/tevc.2014.2308294 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061605203
162 rdf:type schema:CreativeWork
163 https://doi.org/10.1145/1967654.1967671 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004292096
164 rdf:type schema:CreativeWork
165 https://doi.org/10.1145/2739480.2754684 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012276676
166 rdf:type schema:CreativeWork
167 https://doi.org/10.1145/2908812.2908891 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040036399
168 rdf:type schema:CreativeWork
169 https://doi.org/10.1145/2908812.2908950 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017940419
170 rdf:type schema:CreativeWork
171 https://www.grid.ac/institutes/grid.10877.39 schema:alternateName École Polytechnique
172 schema:name École Polytechnique
173 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...