Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems
A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important fea...
Saved in:
| Published in: | Applied soft computing Vol. 165; p. 112001 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.11.2024
|
| Subjects: | |
| ISSN: | 1568-4946 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems.
[Display omitted]
•Two modified Pascoletti-Serafini scalarization approach are proposed.•Six well-known test problems with convex and non-convex Pareto fronts are applied to show effectiveness of the algorithms.•The presented algorithms have acceptable performance with regarding to the other algorithms. |
|---|---|
| AbstractList | A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems.
[Display omitted]
•Two modified Pascoletti-Serafini scalarization approach are proposed.•Six well-known test problems with convex and non-convex Pareto fronts are applied to show effectiveness of the algorithms.•The presented algorithms have acceptable performance with regarding to the other algorithms. |
| ArticleNumber | 112001 |
| Author | Dolatnezhadsomarin, Azam Yousefikhoshbakht, Majid Khorram, Esmaile |
| Author_xml | – sequence: 1 givenname: Azam surname: Dolatnezhadsomarin fullname: Dolatnezhadsomarin, Azam organization: Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Avenue, Tehran 15914, Iran – sequence: 2 givenname: Esmaile surname: Khorram fullname: Khorram, Esmaile organization: Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Avenue, Tehran 15914, Iran – sequence: 3 givenname: Majid orcidid: 0000-0003-1965-1594 surname: Yousefikhoshbakht fullname: Yousefikhoshbakht, Majid email: khoshbakht@basu.ac.ir organization: Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran |
| BookMark | eNp9kM1OwzAMgHMYEtvgBTjlBVqS_kfigib-pAk4wDlKU2dL1SZVkk3AC_DaZIwThx0sW7Y-y_4WaGasAYSuKEkpodV1nwpvZZqRrEgpzQihMzSnZdUkBSuqc7Twvo_NimXNHH0_70ZwWooBi2FjnQ7b0WNlHd6AASeCNhssTByO1gcMe4j1NDn7occ4tAZbhcMW8KtwECxWzpqAtcHxqEEbEA6PuyHoxLY9yKD3gO0U9Ki_jnTc1A4w-gt0psTg4fIvL9H7_d3b6jFZvzw8rW7XicwJCUmX5bVogYIqaVnXFWRFV7Yto8CoLAhRsskpq0omRU6qGF1FKGN13rUtoSrLl6g57pXOeu9AcanD7ynBCT1wSvhBIu_5QSI_SORHiRHN_qGTixLc52no5ghBfGqvwXEvNRgJnXbRB--sPoX_AEX5kxs |
| CitedBy_id | crossref_primary_10_3390_s25175524 crossref_primary_10_3390_buildings15071150 crossref_primary_10_1080_00295450_2025_2507976 |
| Cites_doi | 10.1016/j.apm.2015.03.022 10.1137/060672029 10.1007/s00158-013-0946-1 10.1023/A:1021179727569 10.1007/s00186-015-0510-4 10.1142/13488 10.1007/s00158-011-0729-5 10.1007/s00158-004-0465-1 10.1080/02331934.2011.587006 10.1109/4235.996017 10.1080/0305215X.2010.497185 10.2514/1.8977 10.1016/j.ejor.2006.08.002 10.1137/08071692X 10.1140/epjs/s11734-021-00206-w 10.1007/s11750-016-0430-3 10.1137/S0036144599352836 10.1109/TEVC.2016.2521175 10.1016/j.cam.2013.11.007 10.1007/s10957-020-01788-6 10.1007/s00158-012-0797-1 10.1109/TSMCB.2004.834438 10.1007/BF01197559 10.1137/080729013 10.2514/2.1071 10.1007/s10957-013-0346-0 10.1007/978-3-540-79159-1 10.1137/S1052623496307510 10.1007/s00158-002-0276-1 10.1007/s10489-017-1019-8 10.1109/TEVC.2014.2378512 10.1016/j.ejor.2018.08.018 10.1007/1-84628-137-7_6 10.1007/s00158-005-0557-6 10.1080/23311916.2018.1502242 10.1002/nav.3800020106 |
| ContentType | Journal Article |
| Copyright | 2024 Elsevier B.V. |
| Copyright_xml | – notice: 2024 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.asoc.2024.112001 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| ExternalDocumentID | 10_1016_j_asoc_2024_112001 S1568494624007750 |
| GroupedDBID | --K --M .DC .~1 0R~ 1B1 1~. 1~5 23M 4.4 457 4G. 53G 5GY 5VS 6J9 7-5 71M 8P~ AABNK AACTN AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXKI AAXUO AAYFN ABBOA ABFNM ABFRF ABJNI ABMAC ABXDB ACDAQ ACGFO ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD ADTZH AEBSH AECPX AEFWE AEKER AENEX AFJKZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HVGLF HZ~ IHE J1W JJJVA KOM M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SES SEW SPC SPCBC SST SSV SSZ T5K UHS UNMZH ~G- 9DU AATTM AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKYEP ANKPU APXCP CITATION EFKBS EFLBG ~HD |
| ID | FETCH-LOGICAL-c300t-d237abe1ef515776e24d5bb91e91c400fc8319659ca306a30d6019973dbb01f23 |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001294227700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1568-4946 |
| IngestDate | Tue Nov 18 22:33:17 EST 2025 Sat Nov 29 03:06:05 EST 2025 Tue Dec 03 03:45:07 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Pareto optimal solution Pareto front Pascoletti-Serafini scalarization approach Multi-objective optimization problem Hyperplane |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c300t-d237abe1ef515776e24d5bb91e91c400fc8319659ca306a30d6019973dbb01f23 |
| ORCID | 0000-0003-1965-1594 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_asoc_2024_112001 crossref_primary_10_1016_j_asoc_2024_112001 elsevier_sciencedirect_doi_10_1016_j_asoc_2024_112001 |
| PublicationCentury | 2000 |
| PublicationDate | November 2024 2024-11-00 |
| PublicationDateYYYYMMDD | 2024-11-01 |
| PublicationDate_xml | – month: 11 year: 2024 text: November 2024 |
| PublicationDecade | 2020 |
| PublicationTitle | Applied soft computing |
| PublicationYear | 2024 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Dutta, Kaya (bib26) 2011; 60 Das, Dennis (bib3) 1997; 14 Bandyopadhyay, Pal, Aruna (bib40) 2004; 34 Deb, Pratap, Agarwal, Meyarivan (bib12) 2002 Wang, Zhang, Zhang (bib33) 2016; 20 Khorram, Khaledian, Khaledyan (bib17) 2014; 261 Saini, Sriparna (bib35) 2021; 230 Erfani, Utyuzhnikov, Kolo (bib25) 2013; 48 Wang, Liu, Zhao, Wang, Zhang, Chen, Guan, Liu, Shi, Zi (bib32) 2019 Messac, Mattson (bib11) 2004; 42 Burachik, Kaya, Rizvi (bib27) 2014; 162 Bandyopadhyay, Pal, Aruna (bib38) 2004; 34 Deb, Thiele, Laumanns, Zitzler (bib42) 2005 Ehrgott (bib1) 2005 Siddiqui, Azarm, Gabriel (bib14) 2012; 46 Messac, Ismail-Yahaya, Mattson (bib10) 2003; 25 Motta, Afonso, Lyra (bib20) 2012; 46 Khaledian, Soleimani-damaneh (bib22) 2015; 82 Ghane-Kanafi, Khorram (bib15) 2015; 39 Erfani, Utyuzhnikov (bib24) 2011; 43 Wang, Min (bib34) 2018 Zhang, Tian, Jin (bib29) 2015; 19 Mueller-Gritschneder, Graeb, Schlichtmann (bib19) 2009; 20 Fliege, Drummond, Svaiter (bib28) 2009; 20 Morovati, Pourkarimi (bib39) 2019; 273 Das, Dennis (bib9) 1999; 2 Das, Dennis (bib8) 1998; 8 Mirjalili, Mirjalili, Saremi, Faris, Aljarah (bib31) 2017; 48 Gass, Saaty (bib2) 1955; 2 Kim, Weck (bib6) 2005; 29 Messac, Sundararaj, Tappeta, Renaud (bib5) 2000; 38 Shukla, Deb (bib13) 2007; 181 Messac, Mattson (bib23) 2002; 3 Pan, Shaokai, Kaiwen, Shengkun (bib36) 2021; 188 Eichfelder (bib16) 2009; 19 Nobakhtian, Shafiei (bib18) 2017; 25 Koski (bib4) 1985; 1 Du, Faber, Gunzburger (bib21) 1999; 41 Kim, Weck (bib7) 2006; 31 Gunantara (bib30) 2018; 5 G. Eichfelder, 2008, Adaptive scalarization methods in multiobjective optimization436, Springer, Berlin. G. Chen, 2023, , Nonlinear Systems, Stability, Dynamics and Control236. Burachik (10.1016/j.asoc.2024.112001_bib27) 2014; 162 Bandyopadhyay (10.1016/j.asoc.2024.112001_bib38) 2004; 34 10.1016/j.asoc.2024.112001_bib41 Das (10.1016/j.asoc.2024.112001_bib8) 1998; 8 Messac (10.1016/j.asoc.2024.112001_bib23) 2002; 3 Khaledian (10.1016/j.asoc.2024.112001_bib22) 2015; 82 Das (10.1016/j.asoc.2024.112001_bib3) 1997; 14 Eichfelder (10.1016/j.asoc.2024.112001_bib16) 2009; 19 Messac (10.1016/j.asoc.2024.112001_bib11) 2004; 42 Messac (10.1016/j.asoc.2024.112001_bib5) 2000; 38 Du (10.1016/j.asoc.2024.112001_bib21) 1999; 41 Dutta (10.1016/j.asoc.2024.112001_bib26) 2011; 60 10.1016/j.asoc.2024.112001_bib37 Mirjalili (10.1016/j.asoc.2024.112001_bib31) 2017; 48 Zhang (10.1016/j.asoc.2024.112001_bib29) 2015; 19 Bandyopadhyay (10.1016/j.asoc.2024.112001_bib40) 2004; 34 Mueller-Gritschneder (10.1016/j.asoc.2024.112001_bib19) 2009; 20 Deb (10.1016/j.asoc.2024.112001_bib42) 2005 Morovati (10.1016/j.asoc.2024.112001_bib39) 2019; 273 Wang (10.1016/j.asoc.2024.112001_bib33) 2016; 20 Ehrgott (10.1016/j.asoc.2024.112001_bib1) 2005 Ghane-Kanafi (10.1016/j.asoc.2024.112001_bib15) 2015; 39 Gunantara (10.1016/j.asoc.2024.112001_bib30) 2018; 5 Saini (10.1016/j.asoc.2024.112001_bib35) 2021; 230 Koski (10.1016/j.asoc.2024.112001_bib4) 1985; 1 Fliege (10.1016/j.asoc.2024.112001_bib28) 2009; 20 Kim (10.1016/j.asoc.2024.112001_bib6) 2005; 29 Motta (10.1016/j.asoc.2024.112001_bib20) 2012; 46 Erfani (10.1016/j.asoc.2024.112001_bib25) 2013; 48 Gass (10.1016/j.asoc.2024.112001_bib2) 1955; 2 Siddiqui (10.1016/j.asoc.2024.112001_bib14) 2012; 46 Wang (10.1016/j.asoc.2024.112001_bib34) 2018 Deb (10.1016/j.asoc.2024.112001_bib12) 2002; 6 Khorram (10.1016/j.asoc.2024.112001_bib17) 2014; 261 Pan (10.1016/j.asoc.2024.112001_bib36) 2021; 188 Kim (10.1016/j.asoc.2024.112001_bib7) 2006; 31 Messac (10.1016/j.asoc.2024.112001_bib10) 2003; 25 Wang (10.1016/j.asoc.2024.112001_bib32) 2019 Das (10.1016/j.asoc.2024.112001_bib9) 1999; 2 Erfani (10.1016/j.asoc.2024.112001_bib24) 2011; 43 Nobakhtian (10.1016/j.asoc.2024.112001_bib18) 2017; 25 Shukla (10.1016/j.asoc.2024.112001_bib13) 2007; 181 |
| References_xml | – volume: 2 start-page: 39 year: 1955 end-page: 45 ident: bib2 article-title: The computational algorithm for the parametric objective function publication-title: Nav. Res. Logist. Q. – volume: 261 start-page: 158 year: 2014 end-page: 171 ident: bib17 article-title: A numerical method for constructing the Pareto front of multi-objective optimization problems publication-title: J. Comput. Appl. Math. – volume: 29 start-page: 149 year: 2005 end-page: 158 ident: bib6 article-title: Adaptive weighted-sum method for bi-objective optimization: Pareto front generation publication-title: Struct. Multidiscip. Optim. – volume: 181 start-page: 1630 year: 2007 end-page: 1652 ident: bib13 article-title: On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods publication-title: Eur. J. Oper. Res. – volume: 82 start-page: 211 year: 2015 end-page: 228 ident: bib22 article-title: A new approach to approximate the bounded Pareto front publication-title: Math. Methods Oper. Res. – volume: 41 start-page: 637 year: 1999 end-page: 676 ident: bib21 article-title: Centroidal Voronoi tessellations: applications and algorithms publication-title: SIAM Rev. – start-page: 182 year: 2002 end-page: 197 ident: bib12 article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II publication-title: Evolut. Comput., IEEE Trans. – volume: 20 start-page: 602 year: 2009 end-page: 626 ident: bib28 article-title: Newton's method for multiobjective optimization publication-title: SIAM J. Optim. – volume: 46 start-page: 239 year: 2012 end-page: 259 ident: bib20 article-title: A modified NBI and NC method for the solution of N-multiobjective optimization problems publication-title: Struct. Multidisclinary Optim. – start-page: 1 year: 2018 end-page: 11 ident: bib34 article-title: Robust optimization model for uncertain multiobjective linear programs publication-title: J. Inequalities Appl. – volume: 162 start-page: 428 year: 2014 end-page: 446 ident: bib27 article-title: A new scalarization technique to approximate Pareto fronts of problems with disconnected feasible sets publication-title: J. Optim. Theory Appl. – reference: G. Eichfelder, 2008, Adaptive scalarization methods in multiobjective optimization436, Springer, Berlin. – volume: 20 start-page: 821 year: 2016 end-page: 837 ident: bib33 article-title: Decomposition-based algorithms using Pareto adaptive scalarizing methods publication-title: IEEE Trans. Evolut. Comput. – volume: 8 start-page: 631 year: 1998 end-page: 657 ident: bib8 article-title: Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems publication-title: SIAM J. Optim. – volume: 42 start-page: 2101 year: 2004 end-page: 2111 ident: bib11 article-title: Normal constraint method with guarantee of even representation of complete Pareto frontier publication-title: AIAA J. – volume: 48 start-page: 1129 year: 2013 end-page: 1141 ident: bib25 article-title: A modified directed search domain algorithm for multiobjective engineering and design optimization publication-title: Struct. Multidiscip. Optim. – volume: 25 start-page: 271 year: 2017 end-page: 287 ident: bib18 article-title: A Benson type algorithm for nonconvex multiobjective programming problems publication-title: TOP: Off. J. Span. Soc. Stat. Oper. Res. – volume: 19 start-page: 761 year: 2015 end-page: 776 ident: bib29 article-title: A knee point-driven evolutionary algorithm for many-objective optimization publication-title: IEEE Trans. Evolut. Comput. – volume: 38 start-page: 1084 year: 2000 end-page: 1091 ident: bib5 article-title: Ability of objective functions to generate points on nonconvex Pareto frontiers publication-title: AIAA J. – volume: 188 start-page: 402 year: 2021 end-page: 419 ident: bib36 article-title: Trade-off ratio functions for linear and piecewise linear multi-objective optimization problems publication-title: J. Optim. Theory Appl. – volume: 2 start-page: 411 year: 1999 end-page: 413 ident: bib9 article-title: An improved technique for choosing parameters for Pareto surface generation using normal-boundary intersection publication-title: Short. Pap. Proc. Third World Congr. Struct. Multidiscip. Optim. – volume: 1 start-page: 333 year: 1985 end-page: 337 ident: bib4 article-title: Defectiveness of weighting method in multicriterion optimization of structures publication-title: Int. J. Numer. Methods Biomed. Eng. – volume: 19 start-page: 1694 year: 2009 end-page: 1718 ident: bib16 article-title: An adaptive scalarization method in multiobjective optimization publication-title: SIAM J. Optim. – reference: G. Chen, 2023, , Nonlinear Systems, Stability, Dynamics and Control236. – volume: 31 start-page: 105 year: 2006 end-page: 116 ident: bib7 article-title: Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation publication-title: Struct. Multidiscip. Optim. – volume: 60 start-page: 1091 year: 2011 end-page: 1104 ident: bib26 article-title: A new scalarization and numerical method for constructing the weak Pareto front of multi-objective optimization problems publication-title: Optimization – volume: 273 start-page: 44 year: 2019 end-page: 57 ident: bib39 article-title: Extension of Zoutendijk method for solving constrained multiobjective optimization problems publication-title: Eur. J. Oper. Res. – volume: 20 start-page: 915 year: 2009 end-page: 934 ident: bib19 article-title: A successive approach to compute the bounded Pareto front of practical multiobjective optimization problems publication-title: SIAM J. Optim. – start-page: 1 year: 2019 end-page: 6 ident: bib32 article-title: Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum publication-title: Nat. Photonics – start-page: 105 year: 2005 end-page: 145 ident: bib42 article-title: Scalable test problems for evolutionary multiobjective optimization publication-title: Evolut. Multiobjective Optim. Theor. Adv. Appl. – volume: 43 start-page: 467 year: 2011 end-page: 484 ident: bib24 article-title: Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization publication-title: Eng. Optim. – volume: 48 start-page: 805 year: 2017 end-page: 820 ident: bib31 article-title: Grasshopper optimization algorithm for multi-objective optimization problems publication-title: Appl. Intell. – volume: 14 start-page: 63 year: 1997 end-page: 69 ident: bib3 article-title: A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems publication-title: Struct. Optim. – volume: 39 start-page: 7483 year: 2015 end-page: 7498 ident: bib15 article-title: A new scalarization method for finding the efficient frontier in non-convex multi-objective problems publication-title: Appl. Math. Model. – volume: 25 start-page: 86 year: 2003 end-page: 98 ident: bib10 article-title: The normalized normal constraint method for generating the Pareto frontier publication-title: Struct. Multidiscip. Optim. – year: 2005 ident: bib1 article-title: Multicriteria Optimization – volume: 230 start-page: 2319 year: 2021 end-page: 2335 ident: bib35 article-title: Multi-objective optimization techniques: a survey of the state-of-the-art and applications: Multi-objective optimization techniques publication-title: Eur. Phys. J. Spec. Top. – volume: 34 start-page: 2088 year: 2004 end-page: 2099 ident: bib38 article-title: Multiobjective GAs, quantitative indices, and pattern classification publication-title: IEEE Trans. Syst., Man, Cybern., Part B (Cybern. ) – volume: 3 start-page: 431 year: 2002 end-page: 450 ident: bib23 article-title: Generating well-distributed sets of Pareto points for engineering design using physical programming publication-title: Optim. Eng. – volume: 46 start-page: 839 year: 2012 end-page: 852 ident: bib14 article-title: On improving normal boundary intersection method for generation of Pareto frontier publication-title: Struct. Multidiscip. Optim. – volume: 34 start-page: 2088 year: 2004 end-page: 2099 ident: bib40 article-title: Multiobjective GAs, quantitative indices, and pattern classification publication-title: IEEE Trans. Syst., Man, Cybern., Part B – volume: 5 start-page: 1 year: 2018 end-page: 16 ident: bib30 article-title: A review of multi-objective optimization: methods and its applications publication-title: Cogent Eng. – volume: 39 start-page: 7483 issue: 23 year: 2015 ident: 10.1016/j.asoc.2024.112001_bib15 article-title: A new scalarization method for finding the efficient frontier in non-convex multi-objective problems publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2015.03.022 – volume: 19 start-page: 1694 issue: 14 year: 2009 ident: 10.1016/j.asoc.2024.112001_bib16 article-title: An adaptive scalarization method in multiobjective optimization publication-title: SIAM J. Optim. doi: 10.1137/060672029 – volume: 48 start-page: 1129 issue: 6 year: 2013 ident: 10.1016/j.asoc.2024.112001_bib25 article-title: A modified directed search domain algorithm for multiobjective engineering and design optimization publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-013-0946-1 – volume: 3 start-page: 431 issue: 4 year: 2002 ident: 10.1016/j.asoc.2024.112001_bib23 article-title: Generating well-distributed sets of Pareto points for engineering design using physical programming publication-title: Optim. Eng. doi: 10.1023/A:1021179727569 – volume: 82 start-page: 211 issue: 2 year: 2015 ident: 10.1016/j.asoc.2024.112001_bib22 article-title: A new approach to approximate the bounded Pareto front publication-title: Math. Methods Oper. Res. doi: 10.1007/s00186-015-0510-4 – ident: 10.1016/j.asoc.2024.112001_bib37 doi: 10.1142/13488 – volume: 46 start-page: 239 issue: 2 year: 2012 ident: 10.1016/j.asoc.2024.112001_bib20 article-title: A modified NBI and NC method for the solution of N-multiobjective optimization problems publication-title: Struct. Multidisclinary Optim. doi: 10.1007/s00158-011-0729-5 – volume: 29 start-page: 149 issue: 2 year: 2005 ident: 10.1016/j.asoc.2024.112001_bib6 article-title: Adaptive weighted-sum method for bi-objective optimization: Pareto front generation publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-004-0465-1 – volume: 60 start-page: 1091 issue: 8-9 year: 2011 ident: 10.1016/j.asoc.2024.112001_bib26 article-title: A new scalarization and numerical method for constructing the weak Pareto front of multi-objective optimization problems publication-title: Optimization doi: 10.1080/02331934.2011.587006 – volume: 6 start-page: 182 issue: 2 year: 2002 ident: 10.1016/j.asoc.2024.112001_bib12 article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II publication-title: Evolut. Comput., IEEE Trans. doi: 10.1109/4235.996017 – volume: 43 start-page: 467 issue: 5 year: 2011 ident: 10.1016/j.asoc.2024.112001_bib24 article-title: Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization publication-title: Eng. Optim. doi: 10.1080/0305215X.2010.497185 – volume: 42 start-page: 2101 issue: 10 year: 2004 ident: 10.1016/j.asoc.2024.112001_bib11 article-title: Normal constraint method with guarantee of even representation of complete Pareto frontier publication-title: AIAA J. doi: 10.2514/1.8977 – volume: 181 start-page: 1630 issue: 3 year: 2007 ident: 10.1016/j.asoc.2024.112001_bib13 article-title: On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2006.08.002 – volume: 20 start-page: 602 issue: 2 year: 2009 ident: 10.1016/j.asoc.2024.112001_bib28 article-title: Newton's method for multiobjective optimization publication-title: SIAM J. Optim. doi: 10.1137/08071692X – volume: 230 start-page: 2319 issue: 10 year: 2021 ident: 10.1016/j.asoc.2024.112001_bib35 article-title: Multi-objective optimization techniques: a survey of the state-of-the-art and applications: Multi-objective optimization techniques publication-title: Eur. Phys. J. Spec. Top. doi: 10.1140/epjs/s11734-021-00206-w – volume: 25 start-page: 271 issue: 2 year: 2017 ident: 10.1016/j.asoc.2024.112001_bib18 article-title: A Benson type algorithm for nonconvex multiobjective programming problems publication-title: TOP: Off. J. Span. Soc. Stat. Oper. Res. doi: 10.1007/s11750-016-0430-3 – volume: 41 start-page: 637 issue: 4 year: 1999 ident: 10.1016/j.asoc.2024.112001_bib21 article-title: Centroidal Voronoi tessellations: applications and algorithms publication-title: SIAM Rev. doi: 10.1137/S0036144599352836 – volume: 20 start-page: 821 year: 2016 ident: 10.1016/j.asoc.2024.112001_bib33 article-title: Decomposition-based algorithms using Pareto adaptive scalarizing methods publication-title: IEEE Trans. Evolut. Comput. doi: 10.1109/TEVC.2016.2521175 – volume: 261 start-page: 158 year: 2014 ident: 10.1016/j.asoc.2024.112001_bib17 article-title: A numerical method for constructing the Pareto front of multi-objective optimization problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2013.11.007 – volume: 188 start-page: 402 year: 2021 ident: 10.1016/j.asoc.2024.112001_bib36 article-title: Trade-off ratio functions for linear and piecewise linear multi-objective optimization problems publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-020-01788-6 – volume: 46 start-page: 839 issue: 6 year: 2012 ident: 10.1016/j.asoc.2024.112001_bib14 article-title: On improving normal boundary intersection method for generation of Pareto frontier publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-012-0797-1 – volume: 34 start-page: 2088 issue: 5 year: 2004 ident: 10.1016/j.asoc.2024.112001_bib38 article-title: Multiobjective GAs, quantitative indices, and pattern classification publication-title: IEEE Trans. Syst., Man, Cybern., Part B (Cybern. ) doi: 10.1109/TSMCB.2004.834438 – start-page: 1 year: 2018 ident: 10.1016/j.asoc.2024.112001_bib34 article-title: Robust optimization model for uncertain multiobjective linear programs publication-title: J. Inequalities Appl. – volume: 14 start-page: 63 issue: 1 year: 1997 ident: 10.1016/j.asoc.2024.112001_bib3 article-title: A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems publication-title: Struct. Optim. doi: 10.1007/BF01197559 – volume: 2 start-page: 411 year: 1999 ident: 10.1016/j.asoc.2024.112001_bib9 article-title: An improved technique for choosing parameters for Pareto surface generation using normal-boundary intersection publication-title: Short. Pap. Proc. Third World Congr. Struct. Multidiscip. Optim. – volume: 20 start-page: 915 issue: 2 year: 2009 ident: 10.1016/j.asoc.2024.112001_bib19 article-title: A successive approach to compute the bounded Pareto front of practical multiobjective optimization problems publication-title: SIAM J. Optim. doi: 10.1137/080729013 – volume: 38 start-page: 1084 issue: 6 year: 2000 ident: 10.1016/j.asoc.2024.112001_bib5 article-title: Ability of objective functions to generate points on nonconvex Pareto frontiers publication-title: AIAA J. doi: 10.2514/2.1071 – volume: 162 start-page: 428 issue: 2 year: 2014 ident: 10.1016/j.asoc.2024.112001_bib27 article-title: A new scalarization technique to approximate Pareto fronts of problems with disconnected feasible sets publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0346-0 – ident: 10.1016/j.asoc.2024.112001_bib41 doi: 10.1007/978-3-540-79159-1 – volume: 34 start-page: 2088 issue: 5 year: 2004 ident: 10.1016/j.asoc.2024.112001_bib40 article-title: Multiobjective GAs, quantitative indices, and pattern classification publication-title: IEEE Trans. Syst., Man, Cybern., Part B doi: 10.1109/TSMCB.2004.834438 – volume: 8 start-page: 631 issue: 3 year: 1998 ident: 10.1016/j.asoc.2024.112001_bib8 article-title: Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems publication-title: SIAM J. Optim. doi: 10.1137/S1052623496307510 – volume: 25 start-page: 86 issue: 2 year: 2003 ident: 10.1016/j.asoc.2024.112001_bib10 article-title: The normalized normal constraint method for generating the Pareto frontier publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-002-0276-1 – volume: 48 start-page: 805 year: 2017 ident: 10.1016/j.asoc.2024.112001_bib31 article-title: Grasshopper optimization algorithm for multi-objective optimization problems publication-title: Appl. Intell. doi: 10.1007/s10489-017-1019-8 – volume: 19 start-page: 761 year: 2015 ident: 10.1016/j.asoc.2024.112001_bib29 article-title: A knee point-driven evolutionary algorithm for many-objective optimization publication-title: IEEE Trans. Evolut. Comput. doi: 10.1109/TEVC.2014.2378512 – volume: 273 start-page: 44 issue: 1 year: 2019 ident: 10.1016/j.asoc.2024.112001_bib39 article-title: Extension of Zoutendijk method for solving constrained multiobjective optimization problems publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2018.08.018 – year: 2005 ident: 10.1016/j.asoc.2024.112001_bib1 – start-page: 105 year: 2005 ident: 10.1016/j.asoc.2024.112001_bib42 article-title: Scalable test problems for evolutionary multiobjective optimization publication-title: Evolut. Multiobjective Optim. Theor. Adv. Appl. doi: 10.1007/1-84628-137-7_6 – volume: 31 start-page: 105 issue: 2 year: 2006 ident: 10.1016/j.asoc.2024.112001_bib7 article-title: Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-005-0557-6 – start-page: 1 year: 2019 ident: 10.1016/j.asoc.2024.112001_bib32 article-title: Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum publication-title: Nat. Photonics – volume: 1 start-page: 333 issue: 6 year: 1985 ident: 10.1016/j.asoc.2024.112001_bib4 article-title: Defectiveness of weighting method in multicriterion optimization of structures publication-title: Int. J. Numer. Methods Biomed. Eng. – volume: 5 start-page: 1 issue: 1 year: 2018 ident: 10.1016/j.asoc.2024.112001_bib30 article-title: A review of multi-objective optimization: methods and its applications publication-title: Cogent Eng. doi: 10.1080/23311916.2018.1502242 – volume: 2 start-page: 39 issue: 1-2 year: 1955 ident: 10.1016/j.asoc.2024.112001_bib2 article-title: The computational algorithm for the parametric objective function publication-title: Nav. Res. Logist. Q. doi: 10.1002/nav.3800020106 |
| SSID | ssj0016928 |
| Score | 2.4455864 |
| Snippet | A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 112001 |
| SubjectTerms | Hyperplane Multi-objective optimization problem Pareto front Pareto optimal solution Pascoletti-Serafini scalarization approach |
| Title | Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems |
| URI | https://dx.doi.org/10.1016/j.asoc.2024.112001 |
| Volume | 165 |
| WOSCitedRecordID | wos001294227700001&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: ScienceDirect issn: 1568-4946 databaseCode: AIEXJ dateStart: 20010601 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0016928 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb5tAEF65SQ-9tOlLSdtEe-jNwuINe4wqV20PVg6p5BtalqXgGIgAR1b-QH9I_2hnmQUTt4maQw9GFrDrlefjm5llHoR8BEdHBDJwDTt1lIMimMGBCA3u8zCxXT8VDJtNBItFuFyyi8nkV58Lc7MOyjLcbtn1fxU1nANhq9TZR4h7mBROwHcQOhxB7HD8J8EvNvgSRoUe_6jA98-w5oJqlqwqKGNWIlwsqqadqgJOWFh8mxeD-ais0QvV_7ZS-Sdl10agxKIavMYgRKOKV0iW0wpop9D5nFPdoaYZW729qdsA53dB7Ju215jKhgbvui3lbcaTpirAd8eqBre8GLRBVtU1InfeFDxfyxFZNTLNr7KqyWJ-len8o5WO09fbGbar8_pGDOyHhsv0vmRP0b43IlkwEU0c8gf_41bEasYB2jM1_Wx3891i23tKcAhN7KPeVpGaI1JzRDjHE3JoBx4D9j88_zpffhteVvmsa-E7rFznZmEY4f5K_m7_jGyayyPyXDsj9BxB9JJMZPmKvOgbfVDN-6_JzwFTdIcpCpiiO0xRXlLEFFWYoncwRauUAqYoYop2mKJ5SQdM0T1M0TGmaI-pN-T75_nlpy-G7uBhCMc0WyOxnYDH0pIpmM1B4EvbTbw4ZpZklgDtkYrQ6UpaCg6uK3wS31SRT04Sx6aV2s5bcgArkceECm75iZU6NlMNGiyHh4EdJ6BvJCglz0lOiNX_r5HQ5e1Vl5V1dL9ET8h0GHONxV0evNvrxRVp8xTNzgjQ98C4d4_6lffk2e6x-EAO2nojT8lTcdPmTX2mofcbpYC42g |
| 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=Numerical+algorithms+for+generating+an+almost+even+approximation+of+the+Pareto+front+in+nonlinear+multi-objective+optimization+problems&rft.jtitle=Applied+soft+computing&rft.au=Dolatnezhadsomarin%2C+Azam&rft.au=Khorram%2C+Esmaile&rft.au=Yousefikhoshbakht%2C+Majid&rft.date=2024-11-01&rft.issn=1568-4946&rft.volume=165&rft.spage=112001&rft_id=info:doi/10.1016%2Fj.asoc.2024.112001&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_asoc_2024_112001 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1568-4946&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1568-4946&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1568-4946&client=summon |