Advancements in the computation of enclosures for multi-objective optimization problems
•Presents a framework to solve multi-objective optimization problems.•Suitable for convex and mixed-integer quadratic multi-objective optimization problems.•Generalizes the concept of Local Upper Bounds.•Demonstrates how to warm start computations of enclosures.•Includes computational results of alg...
Uložené v:
| Vydané v: | European journal of operational research Ročník 310; číslo 1; s. 315 - 327 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
01.10.2023
|
| Predmet: | |
| ISSN: | 0377-2217, 1872-6860 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | •Presents a framework to solve multi-objective optimization problems.•Suitable for convex and mixed-integer quadratic multi-objective optimization problems.•Generalizes the concept of Local Upper Bounds.•Demonstrates how to warm start computations of enclosures.•Includes computational results of algorithmic framework for selected test instances.
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems. |
|---|---|
| AbstractList | •Presents a framework to solve multi-objective optimization problems.•Suitable for convex and mixed-integer quadratic multi-objective optimization problems.•Generalizes the concept of Local Upper Bounds.•Demonstrates how to warm start computations of enclosures.•Includes computational results of algorithmic framework for selected test instances.
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems. |
| Author | Eichfelder, Gabriele Warnow, Leo |
| Author_xml | – sequence: 1 givenname: Gabriele orcidid: 0000-0002-1938-6316 surname: Eichfelder fullname: Eichfelder, Gabriele email: gabriele.eichfelder@tu-ilmenau.de – sequence: 2 givenname: Leo orcidid: 0000-0002-2177-8466 surname: Warnow fullname: Warnow, Leo email: leo.warnow@tu-ilmenau.de |
| BookMark | eNp9kM1KxDAUhYOM4Dj6Aq7yAq35aZsW3AyDfzDgRnEZkvQGU9qmJJkBfXo71JWLWd3N-Q73fNdoNfoRELqjJKeEVvddDp0POSOM54TlhLMLtKa1YFlVV2SF1oQLkTFGxRW6jrEjhNCSlmv0uW2PajQwwJgidiNOX4CNH6ZDUsn5EXuLYTS9j4cAEVsf8HDok8u87sAkdwTsp-QG97PEp-B1D0O8QZdW9RFu_-4GfTw9vu9esv3b8-tuu88Mr8qUVZxoVRWtrqxhuuRFLRrBgRk7f9gwoEXLlKWmaEijeCvmbFNDSYUFpXXb8A1iS68JPsYAVk7BDSp8S0rkSY3s5EmNPKmRhMlZzQzV_yDjlrkpKNefRx8WFOZRRwdBRuNmQdC6MPuQrXfn8F-qcIQL |
| CitedBy_id | crossref_primary_10_1016_j_cor_2023_106512 crossref_primary_10_1007_s00186_023_00826_z crossref_primary_10_1016_j_ifacol_2025_03_072 crossref_primary_10_1007_s00186_024_00879_8 crossref_primary_10_1007_s10898_024_01440_x crossref_primary_10_1016_j_eswa_2023_121223 |
| Cites_doi | 10.1007/s10898-010-9588-7 10.1016/j.cor.2021.105349 10.1007/s10898-021-01109-9 10.1007/s10107-017-1149-0 10.1016/j.ejor.2016.05.001 10.1007/s001860200217 10.1007/BF00934564 10.1080/10556788.2013.854357 10.1007/s10288-020-00430-5 10.1137/19M1264709 10.1007/s11750-016-0430-3 10.1007/s10898-013-0102-x 10.1016/j.ejor.2015.03.031 10.1287/mnsc.1100.1248 10.1137/S1052623496307510 10.1016/j.ejor.2016.05.029 10.1016/j.ejco.2021.100014 10.1007/s10898-020-00984-y 10.1080/10556788.2021.1880579 10.1007/s10898-019-00798-7 10.1016/j.cor.2005.10.003 10.1007/s10957-005-5494-4 10.1080/0305215X.2021.1939695 |
| ContentType | Journal Article |
| Copyright | 2023 Elsevier B.V. |
| Copyright_xml | – notice: 2023 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.ejor.2023.02.032 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Business |
| EISSN | 1872-6860 |
| EndPage | 327 |
| ExternalDocumentID | 10_1016_j_ejor_2023_02_032 S0377221723001662 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6OB 7-5 71M 8P~ 9JN 9JO AAAKF AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AARIN AAXUO AAYFN ABAOU ABBOA ABFNM ABFRF ABJNI ABMAC ABUCO ABYKQ ACAZW ACDAQ ACGFO ACGFS ACIWK ACNCT ACRLP ACZNC ADBBV ADEZE ADGUI AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIGVJ AIKHN AITUG AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR AXJTR BKOJK BKOMP BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HAMUX IHE J1W KOM LY1 M41 MHUIS MO0 MS~ N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 ROL RPZ RXW SCC SDF SDG SDP SDS SES SEW SPC SPCBC SSB SSD SSV SSW SSZ T5K TAE TN5 U5U XPP ZMT ~02 ~G- 1OL 29G 41~ 9DU AAAKG AAQXK AATTM AAXKI AAYWO AAYXX ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADIYS ADJOM ADMUD ADNMO ADXHL AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AI. AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS EJD FEDTE FGOYB HVGLF HZ~ R2- VH1 WUQ ~HD |
| ID | FETCH-LOGICAL-c365t-630ba64db6fc2b53487973e2cf00092e14d2af1c4909a3d7a6498e517feabbd93 |
| ISICitedReferencesCount | 9 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001006897400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-2217 |
| IngestDate | Sat Nov 29 07:22:17 EST 2025 Tue Nov 18 22:39:05 EST 2025 Fri Feb 23 02:35:09 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Nonlinear programming Enclosure Mixed-integer programming Warm start strategies Multiple objective programming |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c365t-630ba64db6fc2b53487973e2cf00092e14d2af1c4909a3d7a6498e517feabbd93 |
| ORCID | 0000-0002-1938-6316 0000-0002-2177-8466 |
| PageCount | 13 |
| ParticipantIDs | crossref_primary_10_1016_j_ejor_2023_02_032 crossref_citationtrail_10_1016_j_ejor_2023_02_032 elsevier_sciencedirect_doi_10_1016_j_ejor_2023_02_032 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-10-01 |
| PublicationDateYYYYMMDD | 2023-10-01 |
| PublicationDate_xml | – month: 10 year: 2023 text: 2023-10-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | European journal of operational research |
| PublicationYear | 2023 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Ehrgott, Shao, Schöbel (bib0008) 2010; 50 Ruzika, Wiecek (bib0029) 2005; 126 Shao, Ehrgott (bib0030) 2013; 58 Eichfelder, G., & Warnow, L. (2021b). A hybrid patch decomposition approach to compute an enclosure for multi-objective mixed-integer convex optimization problems. Das, Dennis (bib0005) 1998; 8 Göpfert, Riahi, Tammer, Zalinescu (bib0017) 2003 Pascoletti, Serafini (bib0027) 1984; 42 Kirlik, Sayın (bib0020) 2017; 169 Klamroth, Lacour, Vanderpooten (bib0021) 2015; 245 Yang, Emmerich, Deutz, Bäck (bib0032) 2019; 75 Hoai, Thi, Nam (bib0019) 2021; 19 Accessed 2021-07-21. Burachik, Kaya, Rizvi (bib0001) 2021; 54 Shao, Ehrgott (bib0031) 2016; 255 Klamroth, Tind, Wiecek (bib0022) 2003; 56 Paquete, Schulze, Stiglmayr, Lourenço (bib0026) 2022; 137 Przybylski, A., Klamroth, K., & Lacour, R. (2019). A simple and efficient dichotomic search algorithm for multi-objective mixed integer linear programs. Özpeynirci, Köksalan (bib0025) 2010; 56 Eichfelder (bib0010) 2021; 9 Ehrgott, Gandibleux (bib0007) 2007; 34 Dächert, Klamroth, Lacour, Vanderpooten (bib0002) 2017; 260 Dächert, K., & Teichert, K. (2020). An improved hyperboxing algorithm for calculating a Pareto front representation. Eichfelder, Warnow (bib0013) 2021; 83 . Eichfelder, Kirst, Meng, Stein (bib0011) 2021; 80 Eichfelder, G., & Warnow, L. (2021c). On implementation details and numerical experiments for the HyPaD algorithm to solve multi-objective mixed-integer convex optimization problems. Gurobi Optimization LLC Gurobi. Evtushenko, Posypkin (bib0016) 2013; 29 Dörfler, Löhne, Schneider, Weißing (bib0004) 2021; 37 Eichfelder, G., Stein, O., & Warnow, L. (2022). A deterministic solver for multiobjective mixed-integer convex and nonconvex optimization. MATLAB Matlab bench documentation. Eichfelder (bib0009) 2008 Accessed 2021-02-24. Nobakhtian, Shafiei (bib0024) 2017; 25 De Santis, Eichfelder, Niebling, Rocktäschel (bib0006) 2020; 30 Eichfelder (10.1016/j.ejor.2023.02.032_sbref0008) 2008 Pascoletti (10.1016/j.ejor.2023.02.032_bib0027) 1984; 42 Eichfelder (10.1016/j.ejor.2023.02.032_bib0011) 2021; 80 Eichfelder (10.1016/j.ejor.2023.02.032_bib0013) 2021; 83 Ehrgott (10.1016/j.ejor.2023.02.032_bib0008) 2010; 50 10.1016/j.ejor.2023.02.032_bib0015 10.1016/j.ejor.2023.02.032_bib0018 10.1016/j.ejor.2023.02.032_bib0012 Eichfelder (10.1016/j.ejor.2023.02.032_sbref0009) 2021; 9 10.1016/j.ejor.2023.02.032_bib0014 Shao (10.1016/j.ejor.2023.02.032_bib0031) 2016; 255 Paquete (10.1016/j.ejor.2023.02.032_bib0026) 2022; 137 Dächert (10.1016/j.ejor.2023.02.032_bib0002) 2017; 260 Evtushenko (10.1016/j.ejor.2023.02.032_bib0016) 2013; 29 Klamroth (10.1016/j.ejor.2023.02.032_bib0022) 2003; 56 Dörfler (10.1016/j.ejor.2023.02.032_bib0004) 2021; 37 Ruzika (10.1016/j.ejor.2023.02.032_bib0029) 2005; 126 Shao (10.1016/j.ejor.2023.02.032_bib0030) 2013; 58 Yang (10.1016/j.ejor.2023.02.032_bib0032) 2019; 75 Özpeynirci (10.1016/j.ejor.2023.02.032_bib0025) 2010; 56 10.1016/j.ejor.2023.02.032_bib0028 10.1016/j.ejor.2023.02.032_bib0023 Hoai (10.1016/j.ejor.2023.02.032_bib0019) 2021; 19 10.1016/j.ejor.2023.02.032_bib0003 Klamroth (10.1016/j.ejor.2023.02.032_bib0021) 2015; 245 Kirlik (10.1016/j.ejor.2023.02.032_bib0020) 2017; 169 Nobakhtian (10.1016/j.ejor.2023.02.032_bib0024) 2017; 25 Das (10.1016/j.ejor.2023.02.032_bib0005) 1998; 8 Burachik (10.1016/j.ejor.2023.02.032_bib0001) 2021; 54 Göpfert (10.1016/j.ejor.2023.02.032_bib0017) 2003 Ehrgott (10.1016/j.ejor.2023.02.032_bib0007) 2007; 34 De Santis (10.1016/j.ejor.2023.02.032_bib0006) 2020; 30 |
| References_xml | – volume: 75 start-page: 3 year: 2019 end-page: 34 ident: bib0032 article-title: Efficient computation of expected hypervolume improvement using box decomposition algorithms publication-title: Journal of Global Optimization – volume: 255 start-page: 687 year: 2016 end-page: 698 ident: bib0031 article-title: Discrete representation of non-dominated sets in multi-objective linear programming publication-title: European Journal of Operational Research – volume: 9 year: 2021 ident: bib0010 article-title: Twenty years of continuous multiobjective optimization in the twenty-first century publication-title: EURO Journal on Computational Optimization – reference: Eichfelder, G., & Warnow, L. (2021c). On implementation details and numerical experiments for the HyPaD algorithm to solve multi-objective mixed-integer convex optimization problems. – volume: 56 start-page: 413 year: 2003 end-page: 437 ident: bib0022 article-title: Unbiased approximation in multicriteria optimization publication-title: Mathematical Methods of Operations Research (ZOR) – reference: . Accessed 2021-07-21. – volume: 126 start-page: 473 year: 2005 end-page: 501 ident: bib0029 article-title: Approximation methods in multiobjective programming publication-title: Journal of Optimization Theory and Applications – volume: 37 start-page: 1006 year: 2021 end-page: 1026 ident: bib0004 article-title: A Benson-type algorithm for bounded convex vector optimization problems with vertex selection publication-title: Optimization Methods and Software – volume: 169 start-page: 585 year: 2017 end-page: 604 ident: bib0020 article-title: Bilevel programming for generating discrete representations in multiobjective optimization publication-title: Mathematical Programming – volume: 245 start-page: 767 year: 2015 end-page: 778 ident: bib0021 article-title: On the representation of the search region in multi-objective optimization publication-title: European Journal of Operational Research – volume: 58 start-page: 711 year: 2013 end-page: 728 ident: bib0030 article-title: An objective space cut and bound algorithm for convex multiplicative programmes publication-title: Journal of Global Optimization – volume: 25 start-page: 271 year: 2017 end-page: 287 ident: bib0024 article-title: A Benson type algorithm for nonconvex multiobjective programming problems publication-title: TOP – volume: 42 start-page: 499 year: 1984 end-page: 524 ident: bib0027 article-title: Scalarizing vector optimization problems publication-title: Journal of Optimization Theory and Applications – volume: 137 start-page: 105349 year: 2022 ident: bib0026 article-title: Computing representations using hypervolume scalarizations publication-title: Computers & Operations Research – volume: 50 start-page: 397 year: 2010 end-page: 416 ident: bib0008 article-title: An approximation algorithm for convex multi-objective programming problems publication-title: Journal of Global Optimization – year: 2003 ident: bib0017 article-title: Variational methods in partially ordered spaces – reference: Przybylski, A., Klamroth, K., & Lacour, R. (2019). A simple and efficient dichotomic search algorithm for multi-objective mixed integer linear programs. – volume: 260 start-page: 841 year: 2017 end-page: 855 ident: bib0002 article-title: Efficient computation of the search region in multi-objective optimization publication-title: European Journal of Operational Research – volume: 30 start-page: 3122 year: 2020 end-page: 3145 ident: bib0006 article-title: Solving multiobjective mixed integer convex optimization problems publication-title: SIAM Journal on Optimization – reference: MATLAB Matlab bench documentation. – volume: 56 start-page: 2302 year: 2010 end-page: 2315 ident: bib0025 article-title: An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs publication-title: Management Science – volume: 19 start-page: 41 year: 2021 end-page: 70 ident: bib0019 article-title: Half-open polyblock for the representation of the search region in multiobjective optimization problems: Its application and computational aspects publication-title: 4OR – reference: Dächert, K., & Teichert, K. (2020). An improved hyperboxing algorithm for calculating a Pareto front representation. – volume: 34 start-page: 2674 year: 2007 end-page: 2694 ident: bib0007 article-title: Bound sets for biobjective combinatorial optimization problems publication-title: Computers & Operations Research – reference: . – reference: Gurobi Optimization LLC Gurobi. – reference: Eichfelder, G., Stein, O., & Warnow, L. (2022). A deterministic solver for multiobjective mixed-integer convex and nonconvex optimization. – year: 2008 ident: bib0009 article-title: Adaptive scalarization methods in multiobjective optimization – volume: 80 start-page: 195 year: 2021 end-page: 227 ident: bib0011 article-title: A general branch-and-bound framework for continuous global multiobjective optimization publication-title: Journal of Global Optimization – reference: . Accessed 2021-02-24. – volume: 8 start-page: 631 year: 1998 end-page: 657 ident: bib0005 article-title: Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems publication-title: SIAM Journal on Optimization – volume: 83 start-page: 329 year: 2021 end-page: 357 ident: bib0013 article-title: An approximation algorithm for multi-objective optimization problems using a box-coverage publication-title: Journal of Global Optimization – reference: Eichfelder, G., & Warnow, L. (2021b). A hybrid patch decomposition approach to compute an enclosure for multi-objective mixed-integer convex optimization problems. – volume: 54 start-page: 1413 year: 2021 end-page: 1425 ident: bib0001 article-title: Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems publication-title: Engineering Optimization – volume: 29 start-page: 1005 year: 2013 end-page: 1019 ident: bib0016 article-title: A deterministic algorithm for global multi-objective optimization publication-title: Optimization Methods and Software – volume: 50 start-page: 397 issue: 3 year: 2010 ident: 10.1016/j.ejor.2023.02.032_bib0008 article-title: An approximation algorithm for convex multi-objective programming problems publication-title: Journal of Global Optimization doi: 10.1007/s10898-010-9588-7 – volume: 137 start-page: 105349 year: 2022 ident: 10.1016/j.ejor.2023.02.032_bib0026 article-title: Computing representations using hypervolume scalarizations publication-title: Computers & Operations Research doi: 10.1016/j.cor.2021.105349 – volume: 83 start-page: 329 issue: 2 year: 2021 ident: 10.1016/j.ejor.2023.02.032_bib0013 article-title: An approximation algorithm for multi-objective optimization problems using a box-coverage publication-title: Journal of Global Optimization doi: 10.1007/s10898-021-01109-9 – volume: 169 start-page: 585 issue: 2 year: 2017 ident: 10.1016/j.ejor.2023.02.032_bib0020 article-title: Bilevel programming for generating discrete representations in multiobjective optimization publication-title: Mathematical Programming doi: 10.1007/s10107-017-1149-0 – volume: 255 start-page: 687 issue: 3 year: 2016 ident: 10.1016/j.ejor.2023.02.032_bib0031 article-title: Discrete representation of non-dominated sets in multi-objective linear programming publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2016.05.001 – ident: 10.1016/j.ejor.2023.02.032_bib0014 – volume: 56 start-page: 413 issue: 3 year: 2003 ident: 10.1016/j.ejor.2023.02.032_bib0022 article-title: Unbiased approximation in multicriteria optimization publication-title: Mathematical Methods of Operations Research (ZOR) doi: 10.1007/s001860200217 – volume: 42 start-page: 499 issue: 4 year: 1984 ident: 10.1016/j.ejor.2023.02.032_bib0027 article-title: Scalarizing vector optimization problems publication-title: Journal of Optimization Theory and Applications doi: 10.1007/BF00934564 – ident: 10.1016/j.ejor.2023.02.032_bib0012 – volume: 29 start-page: 1005 issue: 5 year: 2013 ident: 10.1016/j.ejor.2023.02.032_bib0016 article-title: A deterministic algorithm for global multi-objective optimization publication-title: Optimization Methods and Software doi: 10.1080/10556788.2013.854357 – volume: 19 start-page: 41 year: 2021 ident: 10.1016/j.ejor.2023.02.032_bib0019 article-title: Half-open polyblock for the representation of the search region in multiobjective optimization problems: Its application and computational aspects publication-title: 4OR doi: 10.1007/s10288-020-00430-5 – volume: 30 start-page: 3122 issue: 4 year: 2020 ident: 10.1016/j.ejor.2023.02.032_bib0006 article-title: Solving multiobjective mixed integer convex optimization problems publication-title: SIAM Journal on Optimization doi: 10.1137/19M1264709 – volume: 25 start-page: 271 year: 2017 ident: 10.1016/j.ejor.2023.02.032_bib0024 article-title: A Benson type algorithm for nonconvex multiobjective programming problems publication-title: TOP doi: 10.1007/s11750-016-0430-3 – volume: 58 start-page: 711 issue: 4 year: 2013 ident: 10.1016/j.ejor.2023.02.032_bib0030 article-title: An objective space cut and bound algorithm for convex multiplicative programmes publication-title: Journal of Global Optimization doi: 10.1007/s10898-013-0102-x – volume: 245 start-page: 767 issue: 3 year: 2015 ident: 10.1016/j.ejor.2023.02.032_bib0021 article-title: On the representation of the search region in multi-objective optimization publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2015.03.031 – ident: 10.1016/j.ejor.2023.02.032_bib0003 – volume: 56 start-page: 2302 issue: 12 year: 2010 ident: 10.1016/j.ejor.2023.02.032_bib0025 article-title: An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs publication-title: Management Science doi: 10.1287/mnsc.1100.1248 – volume: 8 start-page: 631 issue: 3 year: 1998 ident: 10.1016/j.ejor.2023.02.032_bib0005 article-title: Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems publication-title: SIAM Journal on Optimization doi: 10.1137/S1052623496307510 – volume: 260 start-page: 841 issue: 3 year: 2017 ident: 10.1016/j.ejor.2023.02.032_bib0002 article-title: Efficient computation of the search region in multi-objective optimization publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2016.05.029 – ident: 10.1016/j.ejor.2023.02.032_bib0028 – volume: 9 year: 2021 ident: 10.1016/j.ejor.2023.02.032_sbref0009 article-title: Twenty years of continuous multiobjective optimization in the twenty-first century publication-title: EURO Journal on Computational Optimization doi: 10.1016/j.ejco.2021.100014 – ident: 10.1016/j.ejor.2023.02.032_bib0015 – year: 2008 ident: 10.1016/j.ejor.2023.02.032_sbref0008 – volume: 80 start-page: 195 year: 2021 ident: 10.1016/j.ejor.2023.02.032_bib0011 article-title: A general branch-and-bound framework for continuous global multiobjective optimization publication-title: Journal of Global Optimization doi: 10.1007/s10898-020-00984-y – volume: 37 start-page: 1006 issue: 3 year: 2021 ident: 10.1016/j.ejor.2023.02.032_bib0004 article-title: A Benson-type algorithm for bounded convex vector optimization problems with vertex selection publication-title: Optimization Methods and Software doi: 10.1080/10556788.2021.1880579 – ident: 10.1016/j.ejor.2023.02.032_bib0023 – ident: 10.1016/j.ejor.2023.02.032_bib0018 – volume: 75 start-page: 3 year: 2019 ident: 10.1016/j.ejor.2023.02.032_bib0032 article-title: Efficient computation of expected hypervolume improvement using box decomposition algorithms publication-title: Journal of Global Optimization doi: 10.1007/s10898-019-00798-7 – year: 2003 ident: 10.1016/j.ejor.2023.02.032_bib0017 – volume: 34 start-page: 2674 issue: 9 year: 2007 ident: 10.1016/j.ejor.2023.02.032_bib0007 article-title: Bound sets for biobjective combinatorial optimization problems publication-title: Computers & Operations Research doi: 10.1016/j.cor.2005.10.003 – volume: 126 start-page: 473 issue: 3 year: 2005 ident: 10.1016/j.ejor.2023.02.032_bib0029 article-title: Approximation methods in multiobjective programming publication-title: Journal of Optimization Theory and Applications doi: 10.1007/s10957-005-5494-4 – volume: 54 start-page: 1413 issue: 8 year: 2021 ident: 10.1016/j.ejor.2023.02.032_bib0001 article-title: Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems publication-title: Engineering Optimization doi: 10.1080/0305215X.2021.1939695 |
| SSID | ssj0001515 |
| Score | 2.4779866 |
| Snippet | •Presents a framework to solve multi-objective optimization problems.•Suitable for convex and mixed-integer quadratic multi-objective optimization... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 315 |
| SubjectTerms | Enclosure Mixed-integer programming Multiple objective programming Nonlinear programming Warm start strategies |
| Title | Advancements in the computation of enclosures for multi-objective optimization problems |
| URI | https://dx.doi.org/10.1016/j.ejor.2023.02.032 |
| Volume | 310 |
| WOSCitedRecordID | wos001006897400001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-6860 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001515 issn: 0377-2217 databaseCode: AIEXJ dateStart: 19950105 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lj9MwELZgFyE48CigXV7ygVtllNhJHB8rVF5CKw6L6C2KHxGtuskqLav9-YzjSRoKu2IPXKIqSty083n8ZTzfDCFvXBRb3_WIATfIWWK5Y1qkijlY-6NcK1PmodmEPDnJFwv1FYM5m66dgKzr_PJSnf9XU8M5MLaXzt7A3MOgcAI-g9HhCGaH4z8ZfhZ29YN0DbMYTde7YWCH8LjrxocGu2IMIamQNXoVnN-0ATdyhvrMKXac2VwZwkc6CyfaPrCIFYSGSPN8aX5Ubm0DPD6UuvWy9l0sv63DDtMX14yjEHyXzzaor6RknAcdZu9ZBWasjiEU_KQIGk5cckUoD_CHNw-BhdVbt2p86VYuuvKqGA_9rXT23pI2JBr2OWyrwo9R-DGKiBcwxm1yyGWqwJcfzj7NF5-H5dszvG7rCX8QKq1CUuD-k_ydzYwYyukj8gBfLegsQOIxueXqCbnbKxsm5GHfwYOiQ5-Q-6NylE_I9zF06LKmAB06gg5tKrqDDgXo0D3o0DF0aA-dp-Tb-_npu48MG28wI7J0y2Ca6jJLvELTcJ0KeKlVUjhuKk_JuYthTpdVbBIVqVJYCdeq3KWxrFyptVXiGTmom9odEeqUdTLLIqGtSwTwQwucPxK5qTKbKCGOSdz_gYXBqvS-Ocq6uNp0x2Q63HMearJce3Xa26VAVhnYYgEwu-a-5zf6lhfk3m5avCQH2_ane0XumIvtctO-Roz9AhD6nKE |
| linkProvider | Elsevier |
| 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=Advancements+in+the+computation+of+enclosures+for+multi-objective+optimization+problems&rft.jtitle=European+journal+of+operational+research&rft.au=Eichfelder%2C+Gabriele&rft.au=Warnow%2C+Leo&rft.date=2023-10-01&rft.issn=0377-2217&rft.volume=310&rft.issue=1&rft.spage=315&rft.epage=327&rft_id=info:doi/10.1016%2Fj.ejor.2023.02.032&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ejor_2023_02_032 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-2217&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-2217&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-2217&client=summon |