Multiple k −opt evaluation multiple k −opt moves with GPU high performance local search to large-scale traveling salesman problems
The 2-opt, 3-opt or k –opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while sequential k –opt complete neighborhood examination takes polynomial time complexity which is timeconsuming to approach large scale TSP instance...
Saved in:
| Published in: | Annals of mathematics and artificial intelligence Vol. 88; no. 4; pp. 347 - 365 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cham
Springer International Publishing
01.04.2020
Springer Springer Nature B.V |
| Subjects: | |
| ISSN: | 1012-2443, 1573-7470 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | The 2-opt, 3-opt or
k
–opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while sequential
k
–opt complete neighborhood examination takes polynomial time complexity which is timeconsuming to approach large scale TSP instances. This paper introduces a reasonable methodology called “multiple
k
–opt evaluation, multiple
k
–opt moves” that allows to simultaneously execute, without interference, massive
k
−opt moves that are globally found on the same TSP tour, as well as keep high performance GPU (Graphics Processing Unit) parallel 2-/3-opt evaluation with characteristic of “data parallelism, decentralized control and
O
(1) local memory for each GPU thread”. The methodology is reasonable since intervention of a sequential
O
(
N
) time complexity tour reversal operation is unavoidable for each
k
−opt move when using array of ordered coordinates as TSP tour data structure for high performance GPU
k
−opt local search that considers coalesced memory access and usage of limited on-chip shared memory. Innovation work includes two parts, a sequential non-interacted
k
-opt moves’ set partition algorithm that takes linear time complexity; a new TSP tour representation, array of ordered coordinates-index, that unveils how to combine the advantages of using doubly linked list and array of ordered coordinates data structures for iterative parallel
k
−opt local search based on GPU CUDA. We test this methodology on 22 national TSP instances with up to 71009 cities and with brute initial tour solution. Average maximum 997 non-interacted 2-opt moves are found and executed on the same tour of ch71009.tsp instance after one iteration of complete
N
∗
(
N
−
1
)
2
2-opt checks working in parallel on GPU. And the proposed iterative GPU parallel 2-opt methodology executes average 306631 2-opt moves while only iterates 786 tour reversal operations, in comparison with methods that have to execute tour reversal operation after each 2-opt move. Experimental comparisons show that our proposed methodology gets huge acceleration over both classical sequential and a current state-of-the-art GPU parallel 2-opt implementation. |
|---|---|
| AbstractList | The 2-opt, 3-opt or
k
–opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while sequential
k
–opt complete neighborhood examination takes polynomial time complexity which is timeconsuming to approach large scale TSP instances. This paper introduces a reasonable methodology called “multiple
k
–opt evaluation, multiple
k
–opt moves” that allows to simultaneously execute, without interference, massive
k
−opt moves that are globally found on the same TSP tour, as well as keep high performance GPU (Graphics Processing Unit) parallel 2-/3-opt evaluation with characteristic of “data parallelism, decentralized control and
O
(1) local memory for each GPU thread”. The methodology is reasonable since intervention of a sequential
O
(
N
) time complexity tour reversal operation is unavoidable for each
k
−opt move when using array of ordered coordinates as TSP tour data structure for high performance GPU
k
−opt local search that considers coalesced memory access and usage of limited on-chip shared memory. Innovation work includes two parts, a sequential non-interacted
k
-opt moves’ set partition algorithm that takes linear time complexity; a new TSP tour representation, array of ordered coordinates-index, that unveils how to combine the advantages of using doubly linked list and array of ordered coordinates data structures for iterative parallel
k
−opt local search based on GPU CUDA. We test this methodology on 22 national TSP instances with up to 71009 cities and with brute initial tour solution. Average maximum 997 non-interacted 2-opt moves are found and executed on the same tour of ch71009.tsp instance after one iteration of complete
N
∗
(
N
−
1
)
2
2-opt checks working in parallel on GPU. And the proposed iterative GPU parallel 2-opt methodology executes average 306631 2-opt moves while only iterates 786 tour reversal operations, in comparison with methods that have to execute tour reversal operation after each 2-opt move. Experimental comparisons show that our proposed methodology gets huge acceleration over both classical sequential and a current state-of-the-art GPU parallel 2-opt implementation. The 2-opt, 3-opt or k-opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while sequential k--opt complete neighborhood examination takes polynomial time complexity which is time consuming to approach large scale TSP instances. This paper introduces a reasonable methodology called "multiple k--opt evaluation, multiple k--opt moves" that allows to simultaneously execute, without interference, massive k--opt moves that are globally found on the same TSP tour, as well as keep high performance GPU (Graphics Processing Unit) parallel 2-/3-opt evaluation with characteristic of "data parallelism, decentralized control and O(1) local memory for each GPU thread". The methodology is reasonable since intervention of a sequential O(N) time complexity tour reversal operation is unavoidable for each k--opt move when using array of ordered coordinates as TSP tour data structure for high performance GPU k--opt local search that considers coalesced memory access and usage of limited on-chip shared memory. Innovation work includes two parts, a sequential non-interacted k--opt moves' set partition algorithm that takes linear time complexity; a new TSP tour representation, array of ordered coordinates-index, that unveils how to combine the advantages of using doubly linked list and array of ordered coordinates data structures for iterative parallel k--opt local search based on GPU CUDA. We test this methodology on 22 national TSP instances with up to 71009 cities and with brute initial tour solution. Average maximum 997 non-interacted 2-opt moves are found and executed on the same tour of ch71009.tsp instance after one iteration of complete N * (N-1)/2 2-opt checks working in parallel on GPU. And the proposed iterative GPU parallel 2-opt methodology executes average 306631 2-opt moves while only iterates 786 tour reversal operations, in comparison with methods that have to execute tour reversal operation after each 2-opt move. Experimental comparisons show that our proposed methodology gets huge acceleration over both classical sequential and a current state-of-the-art GPU parallel 2-opt implementation. Keywords Parallel 2-opt * Massive 2-opt moves * Parallel 3-opt * Massive 3-opt moves * TSP * GPU * High performance GPU local search Mathematics Subject Classification (2010) 68 * 68U01 The 2-opt, 3-opt or k–opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while sequential k–opt complete neighborhood examination takes polynomial time complexity which is timeconsuming to approach large scale TSP instances. This paper introduces a reasonable methodology called “multiple k–opt evaluation, multiple k–opt moves” that allows to simultaneously execute, without interference, massive k −opt moves that are globally found on the same TSP tour, as well as keep high performance GPU (Graphics Processing Unit) parallel 2-/3-opt evaluation with characteristic of “data parallelism, decentralized control and O(1) local memory for each GPU thread”. The methodology is reasonable since intervention of a sequential O(N) time complexity tour reversal operation is unavoidable for each k −opt move when using array of ordered coordinates as TSP tour data structure for high performance GPU k −opt local search that considers coalesced memory access and usage of limited on-chip shared memory. Innovation work includes two parts, a sequential non-interacted k-opt moves’ set partition algorithm that takes linear time complexity; a new TSP tour representation, array of ordered coordinates-index, that unveils how to combine the advantages of using doubly linked list and array of ordered coordinates data structures for iterative parallel k −opt local search based on GPU CUDA. We test this methodology on 22 national TSP instances with up to 71009 cities and with brute initial tour solution. Average maximum 997 non-interacted 2-opt moves are found and executed on the same tour of ch71009.tsp instance after one iteration of complete N∗(N−1)2 2-opt checks working in parallel on GPU. And the proposed iterative GPU parallel 2-opt methodology executes average 306631 2-opt moves while only iterates 786 tour reversal operations, in comparison with methods that have to execute tour reversal operation after each 2-opt move. Experimental comparisons show that our proposed methodology gets huge acceleration over both classical sequential and a current state-of-the-art GPU parallel 2-opt implementation. |
| Audience | Academic |
| Author | Qiao, Wen-Bao Créput, Jean-Charles |
| Author_xml | – sequence: 1 givenname: Wen-Bao surname: Qiao fullname: Qiao, Wen-Bao email: rapidbao@outlook.com organization: School of Computer Science, Beijing Information Science and Technology University, CIAD, Univ. Bourgogne Franche-Comté, UTBM – sequence: 2 givenname: Jean-Charles surname: Créput fullname: Créput, Jean-Charles organization: CIAD, Univ. Bourgogne Franche-Comté, UTBM |
| BookMark | eNp9kctu1TAQhi1UJNrCC7CyxNqtLzlxsqwqKJWKYNGuLceZ5Lg4cbB9DuUFqq55RJ6EoUFColLlhe3x_3ku_xE5mOMMhLwV_ERwrk-z4JWWjIuW8bbWLbt7QQ7FRiumK80P8MyFZLKq1CtylPMt5yhr6kNy_2kXil8C0K_018PPuBQKext2tvg40-nJ4xT3kOl3X7b04ssN3fpxSxdIQ0yTnR3QEJ0NNINNbktLpMGmEVjGINCS7B6Cn0ea8ZoRoEuKXYApvyYvBxsyvPm7H5ObD--vzz-yq88Xl-dnV8ypTVOY0m3VgbBcKdt1re2Elti4haruBwFt0zddZYeq58K6Rljhuk3fghr0oGrnKnVM3q3_YuJvO8jF3MZdmjGlka1oJJdSalSdrKoR6zR-HiKW7nD1MHmHkx88xs-00Ior0dQINCvgUsw5wWCcL48jRNAHI7j5Y5NZbTJok3m0ydwhKv9Dl-Qnm348D6kVyiieR0j_2niG-g0oD6yO |
| CitedBy_id | crossref_primary_10_1016_j_eswa_2025_129110 |
| Cites_doi | 10.1016/0377-2217(92)90138-Y 10.1287/moor.2.3.209 10.1002/j.1538-7305.1965.tb04146.x 10.1016/j.jpdc.2017.06.011 10.1016/0167-739X(94)00059-N 10.1287/ijoc.3.4.376 10.1287/ijoc.1.3.190 10.1016/S0893-6080(03)00130-8 10.1287/mnsc.40.10.1276 10.1016/S0305-0548(97)00031-2 10.1016/j.omega.2017.12.003 10.1287/opre.6.6.791 10.1007/978-3-319-59153-7_41 10.1007/s10479-017-2481-8 10.1109/HPCSim.2012.6266963 10.1007/0-306-48056-5_11 10.1109/IPDPSW.2013.227 10.1080/01605682.2018.1464428 10.1007/978-3-030-05348-2_8 |
| ContentType | Journal Article |
| Copyright | Springer Nature Switzerland AG 2020 COPYRIGHT 2020 Springer Springer Nature Switzerland AG 2020. |
| Copyright_xml | – notice: Springer Nature Switzerland AG 2020 – notice: COPYRIGHT 2020 Springer – notice: Springer Nature Switzerland AG 2020. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.1007/s10472-019-09679-x |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection SciTech Premium Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISSN | 1573-7470 |
| EndPage | 365 |
| ExternalDocumentID | A717303186 10_1007_s10472_019_09679_x |
| GrantInformation_xml | – fundername: China Scholarship Council funderid: https://doi.org/10.13039/501100004543 |
| GroupedDBID | -4Z -59 -5G -BR -EM -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 23M 28- 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTD ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K7- KDC KOV KOW LAK LLZTM M4Y M7S MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PT4 PT5 PTHSS QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7X Z81 Z83 Z88 Z92 ZMTXR ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADKFA AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 8FE 8FG AZQEC DWQXO GNUQQ JQ2 L6V P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c358t-3794be1a033abb9ab172047ae46df1e98d8b4af4d01ac81a1cb5d9e3f7f36cc43 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000534791700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1012-2443 |
| IngestDate | Wed Nov 05 14:58:36 EST 2025 Sat Nov 29 09:49:16 EST 2025 Sat Nov 29 05:14:37 EST 2025 Tue Nov 18 22:24:16 EST 2025 Fri Feb 21 02:26:56 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | TSP 68 Parallel 2-opt 68U01 Parallel 3-opt Massive 3-opt moves GPU High performance GPU local search Massive 2-opt moves |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c358t-3794be1a033abb9ab172047ae46df1e98d8b4af4d01ac81a1cb5d9e3f7f36cc43 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2918202227 |
| PQPubID | 2043872 |
| PageCount | 19 |
| ParticipantIDs | proquest_journals_2918202227 gale_infotracacademiconefile_A717303186 crossref_citationtrail_10_1007_s10472_019_09679_x crossref_primary_10_1007_s10472_019_09679_x springer_journals_10_1007_s10472_019_09679_x |
| PublicationCentury | 2000 |
| PublicationDate | 20200400 2020-04-00 20200401 |
| PublicationDateYYYYMMDD | 2020-04-01 |
| PublicationDate_xml | – month: 4 year: 2020 text: 20200400 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Dordrecht |
| PublicationTitle | Annals of mathematics and artificial intelligence |
| PublicationTitleAbbrev | Ann Math Artif Intell |
| PublicationYear | 2020 |
| Publisher | Springer International Publishing Springer Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer – name: Springer Nature B.V |
| References | Laporte (CR1) 1992; 59 Johnson, McGeoch (CR2) 1997; 1 Mladenović, Hansen (CR7) 1997; 24 CR3 Karp (CR15) 1977; 2 Lin (CR19) 1965; 44 CR8 CR17 CR9 CR16 CR13 CR12 Qiao, Créput (CR21) 2017; 11 CR22 Mulder, Wunsch (CR23) 2003; 16 Croes (CR11) 1958; 6 CR20 Pei, Liu, Fan, Pardalos, Lu (CR10) 2019; 82 Rios, Ochi, Boeres, Coelho, Coelho, Farias (CR18) 2018; 111 Reinelt (CR24) 1991; 3 Gendreau, Hertz, Laporte (CR6) 1994; 40 Garey, Johnson (CR4) 1979 Verhoeven, Aarts, Swinkels (CR14) 1995; 11 Glover (CR5) 1989; 1 9679_CR13 E Rios (9679_CR18) 2018; 111 9679_CR12 M Gendreau (9679_CR6) 1994; 40 RM Karp (9679_CR15) 1977; 2 9679_CR17 9679_CR16 G Reinelt (9679_CR24) 1991; 3 SA Mulder (9679_CR23) 2003; 16 DS Johnson (9679_CR2) 1997; 1 F Glover (9679_CR5) 1989; 1 N Mladenović (9679_CR7) 1997; 24 W-B Qiao (9679_CR21) 2017; 11 9679_CR8 9679_CR9 MR Garey (9679_CR4) 1979 G Laporte (9679_CR1) 1992; 59 9679_CR3 J Pei (9679_CR10) 2019; 82 9679_CR20 M Verhoeven (9679_CR14) 1995; 11 GA Croes (9679_CR11) 1958; 6 9679_CR22 S Lin (9679_CR19) 1965; 44 |
| References_xml | – volume: 59 start-page: 231 issue: 2 year: 1992 end-page: 247 ident: CR1 article-title: The traveling salesman problem: An overview of exact and approximate algorithms publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(92)90138-Y – volume: 1 start-page: 215 year: 1997 end-page: 310 ident: CR2 article-title: The traveling salesman problem: A case study in local optimization publication-title: Local Search Comb. Optim. – volume: 2 start-page: 209 issue: 3 year: 1977 end-page: 224 ident: CR15 article-title: Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane publication-title: Math. Oper. Res. doi: 10.1287/moor.2.3.209 – volume: 44 start-page: 2245 issue: 10 year: 1965 end-page: 2269 ident: CR19 article-title: Computer solutions of the traveling salesman problem publication-title: Bell Syst. Tech. J. doi: 10.1002/j.1538-7305.1965.tb04146.x – ident: CR22 – volume: 111 start-page: 39 year: 2018 end-page: 55 ident: CR18 article-title: Exploring parallel multi-gpu local search strategies in a metaheuristic framework publication-title: J. Parallel Distrib. Comput. doi: 10.1016/j.jpdc.2017.06.011 – volume: 11 start-page: 175 issue: 2 year: 1995 end-page: 182 ident: CR14 article-title: A parallel 2-opt algorithm for the traveling salesman problem publication-title: Futur. Gener. Comput. Syst. doi: 10.1016/0167-739X(94)00059-N – volume: 3 start-page: 376 issue: 4 year: 1991 end-page: 384 ident: CR24 article-title: Tsplib—a traveling salesman problem library publication-title: ORSA J. Comput. doi: 10.1287/ijoc.3.4.376 – ident: CR3 – volume: 1 start-page: 190 issue: 3 year: 1989 end-page: 206 ident: CR5 article-title: Tabu search—part i publication-title: ORSA J. Comput. doi: 10.1287/ijoc.1.3.190 – ident: CR16 – ident: CR12 – ident: CR17 – volume: 16 start-page: 827 issue: 5 year: 2003 end-page: 832 ident: CR23 article-title: Million city traveling salesman problem solution by divide and conquer clustering with adaptive resonance neural networks publication-title: Neural Netw. doi: 10.1016/S0893-6080(03)00130-8 – start-page: 70 year: 1979 end-page: 70 ident: CR4 publication-title: A Guide to the Theory of np-Completeness – ident: CR13 – volume: 40 start-page: 1276 issue: 10 year: 1994 end-page: 1290 ident: CR6 article-title: A tabu search heuristic for the vehicle routing problem publication-title: Manag. Sci. doi: 10.1287/mnsc.40.10.1276 – volume: 24 start-page: 1097 issue: 11 year: 1997 end-page: 1100 ident: CR7 article-title: Variable neighborhood search publication-title: Comput. Oper. Res. doi: 10.1016/S0305-0548(97)00031-2 – ident: CR9 – volume: 82 start-page: 55 year: 2019 end-page: 69 ident: CR10 article-title: A hybrid ba-vns algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers publication-title: Omega doi: 10.1016/j.omega.2017.12.003 – volume: 6 start-page: 791 issue: 6 year: 1958 end-page: 812 ident: CR11 article-title: A method for solving traveling-salesman problems publication-title: Oper. Res. doi: 10.1287/opre.6.6.791 – ident: CR8 – volume: 11 start-page: 281 issue: 3 year: 2017 end-page: 285 ident: CR21 article-title: Parallel 2-opt local search on gpu publication-title: World Academy of Science, Engineering and Technology, International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering – ident: CR20 – volume: 1 start-page: 215 year: 1997 ident: 9679_CR2 publication-title: Local Search Comb. Optim. – ident: 9679_CR20 – ident: 9679_CR3 – volume: 6 start-page: 791 issue: 6 year: 1958 ident: 9679_CR11 publication-title: Oper. Res. doi: 10.1287/opre.6.6.791 – volume: 3 start-page: 376 issue: 4 year: 1991 ident: 9679_CR24 publication-title: ORSA J. Comput. doi: 10.1287/ijoc.3.4.376 – ident: 9679_CR13 doi: 10.1007/978-3-319-59153-7_41 – volume: 2 start-page: 209 issue: 3 year: 1977 ident: 9679_CR15 publication-title: Math. Oper. Res. doi: 10.1287/moor.2.3.209 – volume: 40 start-page: 1276 issue: 10 year: 1994 ident: 9679_CR6 publication-title: Manag. Sci. doi: 10.1287/mnsc.40.10.1276 – volume: 24 start-page: 1097 issue: 11 year: 1997 ident: 9679_CR7 publication-title: Comput. Oper. Res. doi: 10.1016/S0305-0548(97)00031-2 – ident: 9679_CR8 doi: 10.1007/s10479-017-2481-8 – start-page: 70 volume-title: A Guide to the Theory of np-Completeness year: 1979 ident: 9679_CR4 – ident: 9679_CR16 doi: 10.1109/HPCSim.2012.6266963 – volume: 1 start-page: 190 issue: 3 year: 1989 ident: 9679_CR5 publication-title: ORSA J. Comput. doi: 10.1287/ijoc.1.3.190 – volume: 111 start-page: 39 year: 2018 ident: 9679_CR18 publication-title: J. Parallel Distrib. Comput. doi: 10.1016/j.jpdc.2017.06.011 – ident: 9679_CR12 doi: 10.1007/0-306-48056-5_11 – volume: 11 start-page: 175 issue: 2 year: 1995 ident: 9679_CR14 publication-title: Futur. Gener. Comput. Syst. doi: 10.1016/0167-739X(94)00059-N – ident: 9679_CR17 doi: 10.1109/IPDPSW.2013.227 – volume: 59 start-page: 231 issue: 2 year: 1992 ident: 9679_CR1 publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(92)90138-Y – volume: 44 start-page: 2245 issue: 10 year: 1965 ident: 9679_CR19 publication-title: Bell Syst. Tech. J. doi: 10.1002/j.1538-7305.1965.tb04146.x – ident: 9679_CR9 doi: 10.1080/01605682.2018.1464428 – volume: 82 start-page: 55 year: 2019 ident: 9679_CR10 publication-title: Omega doi: 10.1016/j.omega.2017.12.003 – volume: 11 start-page: 281 issue: 3 year: 2017 ident: 9679_CR21 publication-title: World Academy of Science, Engineering and Technology, International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering – volume: 16 start-page: 827 issue: 5 year: 2003 ident: 9679_CR23 publication-title: Neural Netw. doi: 10.1016/S0893-6080(03)00130-8 – ident: 9679_CR22 doi: 10.1007/978-3-030-05348-2_8 |
| SSID | ssj0009686 |
| Score | 2.22509 |
| Snippet | The 2-opt, 3-opt or
k
–opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while... The 2-opt, 3-opt or k-opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while... The 2-opt, 3-opt or k–opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area, while... |
| SourceID | proquest gale crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 347 |
| SubjectTerms | Algorithms Analysis Arrays Artificial Intelligence Chips (memory devices) Combinatorial analysis Complex Systems Complexity Computer Science Data structures Decentralized control Efficiency Euclidean space Graphics processing units Management science Mathematics Methodology Polynomials Search algorithms Traveling salesman problem |
| SummonAdditionalLinks | – databaseName: Engineering Database dbid: M7S link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Nb9QwEB1B4QAHCgXEQkFzQOIAFvHGm9gnVCEKl1aVoFJvlr8iIdrNUoeqvwBx5ifyS_B4nUZQ0QvHxLFjaWaeE3vmPYDndStMJbhjtvOSiU4FZprky5VvbCelEN7bLDbR7u_LoyN1UDbcYkmrHDExA7XvHe2Rv54rohqnys03q6-MVKPodLVIaFyHG8SSwHPq3seJdLfJSo9EYcXSMlaXoplSOidaSkqghKGmVez8j4Xpb3i-dE6al5_dzf-d-F24Uz48cWftKffgWlhuweYo6oAlxrfg9t4FkWu8D9_3SsIhfsFfP372qwEnfnA8udR40p-FiLS5i-8PDpHIkHE11SZgXjpxHV449HhMiegsppsBB1JCoup4jOkypg5Y5G7iAzjcfffp7QdWpBuYqxdySLClhA3cVHVtrFXGchLDaU0Qje94UNJLK0wnfMWNk9xwZxdehbpru7pxTtQPYWPZL8MjwMq3QhjBpZ8TN9hCVQmRreOVaRKQu24GfLSbdoXXnOQ1jvXEyEy21snWOttan8_g5UWf1ZrV48qnX5A7aAr5NLIzpXIhzY_Is_QOZTIQODYz2B59QBcsiHpygBm8Gr1oav73ex9fPdoTuDWnn_-cRrQNG8Ppt_AUbrqz4XM8fZYj4TdXnRKJ priority: 102 providerName: ProQuest |
| Title | Multiple k −opt evaluation multiple k −opt moves with GPU high performance local search to large-scale traveling salesman problems |
| URI | https://link.springer.com/article/10.1007/s10472-019-09679-x https://www.proquest.com/docview/2918202227 |
| Volume | 88 |
| WOSCitedRecordID | wos000534791700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1573-7470 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: P5Z dateStart: 19970301 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-7470 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: K7- dateStart: 19970301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-7470 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: M7S dateStart: 19970301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-7470 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: BENPR dateStart: 19970301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLink Contemporary customDbUrl: eissn: 1573-7470 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3LbtQwFL2ClgVdUCggppTRXSCxgEjxxJPYy4JakFBHo5aiio3lVyREOzOq06pfUHXNJ_Il-GacBiggwSZSYjuJnPtI4nPPAXheVFznnNnM1E5kvJY-02W05dyVphaCc-dMKzZRTSbi6EhOU1FY6NDu3ZJkG6l_KHbjFcEICOJTVjKLb46rMd0JEmzYP_jYU-2Wrb4jEVdlMXkVqVTm9-f4KR39GpRvrI62SWd3_f9u9z7cSy-ZuL20igdwy882YL0TcMDkzxuwtndN2hoewuVeAhfiF_x29XW-aLDnAseTG40n83MfkH7k4tvpIRLxMS76OgRs0yQuXQmbOR4T6DwL8aDHhlSPqBIeQ9wNcQAmaZvwCA53dz68eZclmYbMFmPRxBAlufFM50WhjZHaMBK-qbTnpauZl8IJw3XNXc60FUwza8ZO-qKu6qK0lhePYWU2n_kngLmrONecCTciHrCxzGP0NZbluoxB29YDYN3TUjZxmJOUxrHq2Zdp2lWcdtVOu7oYwMvrMYslg8dfe78gI1Dk3vHMVqcqhXh_RJSltgm1QIGwHMBWZycq-X1QI0mE-FRfPIBXnV30zX--7ua_dX8Kd0f04d9CiLZgpTk988_gjj1vPofTIay-3plM94dw-32VDQnOehC30_GnYesp3wFE6g3v |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwEB6VgkQ5UCigLhTwAcQBrMaxN3EOCFVAabXdVQ-t1JvxXyREu1maUMoLIM48CA_Fk-DJOo2gorceOCaOncT5POPYM98H8ITnQieCWWpKJ6koC091FrCcuMyUUgrhnGnFJvLJRB4cFLsL8LPLhcGwys4mtobaVRbXyNfTAqnGMXPz1ewTRdUo3F3tJDTmsBj5r1_CL1v9cvtN-L5P03Tz7d7rLRpVBajlQ9mEEVUI45lOONfGFNow1GnJtReZK5kvpJNG6FK4hGkrmWbWDF3heZmXPLNW8NDuFbgquMxxXI1y2pP8Zq2yJFJm0eA2eUzSial6IscgCAxQyvKCnv7hCP92B-f2ZVt3t7n8v3XULbgZJ9ZkYz4SbsOCn67AcidaQaINW4Eb4zOi2voOfBvHgErykfz6_qOaNaTnPydH5wqPqhNfE1y8Ju929wmSPZNZn3tB2qkBmb8-aSpyiIH2tA4nPWlQ6Qmz_0kdDutQgUQ5n_ou7F9K39yDxWk19atAEpcLoQWTLkXus2GRBI9jLEt0FhyVLQfAOpwoG3nbUT7kUPWM04gtFbClWmyp0wE8P6szm7OWXHj1M4SfQpMWWrY6ZmaE50NyMLWBkRpo_LMBrHWYU9HW1aoH3ABedKjti_993_sXt_YYrm_tjXfUzvZk9ACWUlzoaEOm1mCxOf7sH8I1e9J8qI8ftaOQwPvLRvNvpDJxhw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Nb9QwEB2hglA5UCggFgrMAYkDjRpvvIl9rIAFBF2tBEW9Wf6UKtrdVZNW_QWIMz-RX4In6zSFUiTUYxLbsZyZsWO_9wbgeVFxnXNmMxOcyHiQPtNltOXclSYIwblzpk02UU0mYm9PTs-x-Fu0e3ckueQ0kErTrNlauLB1jvjGK4IUENynrGQWV5HXOQHp6X_905dedrdscz2SiFUWJ7Ii0Wb-3sZvU9OfAfrCSWk7AY3Xrt71O3A7LT5xe2ktd-Gan63DWpfYAZOfr8OtnTMx1_oefNtJoEP8ij-__5gvGuw1wvHwwsPD-YmvkTZ48e10F0kQGRc9PwHb6ROXLobNHA8IjJ7V8abHhrIhEUMe63hZxwqYUt7U92F3_Obzq3dZSt-Q2WIkmhi6JDee6bwotDFSG0YJcSrteekC81I4YbgO3OVMW8E0s2bkpC9CFYrSWl48gJXZfOYfAuau4lxzJtyQ9MFGMo9R2ViW6zIGcxsGwLovp2zSNqcUGweqV2WmYVdx2FU77Op0AC_P6iyWyh7_LP2CDEKR28eWrU7shdg_EtBS24RmoABZDmCjsxmV4kGthpKE8ol3PIDNzkb6x5e_99H_FX8GN6evx-rj-8mHx7A6pL2BFmW0ASvN0bF_AjfsSbNfHz1t3eQXDBoVVQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Multiple+k%E2%80%93opt+evaluation+multiple+k%E2%80%93opt+moves+with+GPU+high+performance+local+search+to+large-scale+traveling+salesman+problems&rft.jtitle=Annals+of+mathematics+and+artificial+intelligence&rft.au=Qiao%2C+Wen-Bao&rft.au=Creput%2C+Jean-Charles&rft.date=2020-04-01&rft.pub=Springer&rft.issn=1012-2443&rft.volume=88&rft.issue=4&rft.spage=347&rft_id=info:doi/10.1007%2Fs10472-019-09679-x&rft.externalDocID=A717303186 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1012-2443&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1012-2443&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1012-2443&client=summon |