{"id":"https://openalex.org/W2114119858","doi":"https://doi.org/10.1093/comjnl/bxt130","title":"Constructing Constrained-Version of Magic Squares Using Selection Hyper-heuristics","display_name":"Constructing Constrained-Version of Magic Squares Using Selection Hyper-heuristics","publication_year":2013,"publication_date":"2013-11-11","ids":{"openalex":"https://openalex.org/W2114119858","doi":"https://doi.org/10.1093/comjnl/bxt130","mag":"2114119858"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxt130","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxt130","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://nottingham-repository.worktribe.com/output/722514","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017573824","display_name":"Ahmed Kheiri","orcid":"https://orcid.org/0000-0002-6716-2130"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"A. Kheiri","raw_affiliation_strings":["School of Computer Science, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK","School of Computer Science, University of Nottingham Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK","institution_ids":["https://openalex.org/I142263535"]},{"raw_affiliation_string":"School of Computer Science, University of Nottingham Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK#TAB#","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020026827","display_name":"Ender \u00d6zcan","orcid":"https://orcid.org/0000-0003-0276-1391"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. Ozcan","raw_affiliation_strings":["School of Computer Science, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK","School of Computer Science, University of Nottingham Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK","institution_ids":["https://openalex.org/I142263535"]},{"raw_affiliation_string":"School of Computer Science, University of Nottingham Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK#TAB#","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017573824"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":{"value":2635,"currency":"GBP","value_usd":3232},"apc_paid":null,"fwci":1.1786,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82505772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"57","issue":"3","first_page":"469","last_page":"479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/magic-square","display_name":"Magic square","score":0.8601722717285156},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.5989114046096802},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5671433210372925},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.557174563407898},{"id":"https://openalex.org/keywords/library-science","display_name":"Library science","score":0.5113655924797058},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.39921313524246216},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.3295634388923645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1800086796283722},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16747406125068665},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.065501868724823},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.061844825744628906}],"concepts":[{"id":"https://openalex.org/C44201097","wikidata":"https://www.wikidata.org/wiki/Q192089","display_name":"Magic square","level":2,"score":0.8601722717285156},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.5989114046096802},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5671433210372925},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.557174563407898},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.5113655924797058},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.39921313524246216},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.3295634388923645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1800086796283722},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16747406125068665},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.065501868724823},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.061844825744628906}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.1093/comjnl/bxt130","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxt130","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"},{"id":"pmh:oai:http://orca.cardiff.ac.uk:85915","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.637.7800","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.637.7800","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.nott.ac.uk/~exo/docs/publications/msq.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.944.8786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.944.8786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://comjnl.oxfordjournals.org/content/57/3/469.full.pdf","raw_type":"text"},{"id":"pmh:oai:eprints.lancs.ac.uk:133231","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/133231/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:eprints.lancs.ac.uk:133232","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/133232/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:eprints.nottingham.ac.uk:32177","is_oa":false,"landing_page_url":"http://comjnl.oxfordjournals.org/content/57/3/469","pdf_url":null,"source":{"id":"https://openalex.org/S4377196365","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:http://orca-dev.cardiff.ac.uk:85915","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/85915/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:722514","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/722514","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:ore.exeter.ac.uk:10871/15558","is_oa":false,"landing_page_url":"http://hdl.handle.net/10871/15558","pdf_url":null,"source":{"id":"https://openalex.org/S4306401998","display_name":"Open Research Exeter (University of Exeter)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I23923803","host_organization_name":"University of Exeter","host_organization_lineage":["https://openalex.org/I23923803"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/5a18254b-2036-47d7-b273-d0a9ec24ed23","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/5a18254b-2036-47d7-b273-d0a9ec24ed23","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kheiri, A & \u00d6zcan, E 2014, 'Constructing constrained-version of magic squares using selection hyper-heuristics', Computer Journal, vol. 57, no. 3, pp. 469-479. https://doi.org/10.1093/comjnl/bxt130","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:nottingham-repository.worktribe.com:722514","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/722514","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6414137052","display_name":null,"funder_award_id":"EP/H000968/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W86810280","https://openalex.org/W1499849206","https://openalex.org/W1536647479","https://openalex.org/W1567102157","https://openalex.org/W1668207500","https://openalex.org/W1745341198","https://openalex.org/W1970604725","https://openalex.org/W1972291640","https://openalex.org/W1974342535","https://openalex.org/W2056956492","https://openalex.org/W2072441740","https://openalex.org/W2096323754","https://openalex.org/W2102807025","https://openalex.org/W2108910404","https://openalex.org/W2109101401","https://openalex.org/W2112466399","https://openalex.org/W2133734201","https://openalex.org/W3036035835","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3115275600","https://openalex.org/W2389744961","https://openalex.org/W2946016713","https://openalex.org/W265061586","https://openalex.org/W2947016455","https://openalex.org/W2795626499","https://openalex.org/W2350254425","https://openalex.org/W3100758610","https://openalex.org/W2384514444","https://openalex.org/W2381469815"],"abstract_inverted_index":{"A":[0],"square":[1,28],"matrix":[2],"of":[3,29,55,69,82],"distinct":[4],"numbers":[5],"in":[6],"which":[7],"every":[8],"row,":[9],"column":[10],"and":[11],"both":[12],"diagonals":[13],"have":[14],"the":[15,53,79,92,100],"same":[16],"total":[17],"is":[18,33],"referred":[19],"to":[20],"as":[21],"a":[22,26,30,35,59,67],"magic":[23,27,83],"square.":[24],"Constructing":[25],"given":[31,60],"order":[32],"considered":[34],"difficult":[36],"computational":[37],"problem,":[38],"particularly":[39],"when":[40],"additional":[41],"constraints":[42],"are":[43,46],"imposed.":[44],"Hyper-heuristics":[45],"emerging":[47],"high-level":[48],"search":[49],"methodologies":[50],"that":[51,88],"explore":[52],"space":[54],"heuristics":[56,76],"for":[57,77],"solving":[58],"problem.":[61],"In":[62],"this":[63],"study,":[64],"we":[65],"present":[66],"range":[68],"effective":[70],"selection":[71,89],"hyper-heuristics":[72],"mixing":[73],"perturbative":[74],"low-level":[75],"constructing":[78],"constrained":[80],"version":[81],"squares.":[84],"The":[85],"results":[86],"show":[87],"hyper-heuristics,":[90],"even":[91],"non-learning":[93],"ones":[94],"deliver":[95],"an":[96],"outstanding":[97],"performance,":[98],"beating":[99],"best-known":[101],"heuristic":[102],"solution":[103],"on":[104],"average.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}