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Research Article

Two adaptive nonmonotone trust-region algorithms for solving multiobjective optimization problems

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Received 14 Dec 2021, Accepted 06 May 2023, Published online: 20 Jul 2023

References

  • Carrizosa E, Frenk JBG. Dominating sets for convex functions with some applications. J Optim Theory Appl. 1998;96(2):281–295. doi: 10.1023/A:1022614029984
  • Campana EF, Diez M, Liuzzi G, et al. A multi-objective DIRECT algorithm for ship hull optimization. Comput Optim Appl. 2018;71(1):53–72. doi: 10.1007/s10589-017-9955-0
  • Kasperska R, Ostwald M, Rodak M. Bi-criteria optimization of open cross section of the thin-walled beams with fat fanges. PAMM Proc Appl Math Mech. 2004;4(1):614–615. Berlin: WILEY-VCH Verlag. doi: 10.1002/(ISSN)1617-7061
  • Liuzzi G, Lucidi S, Parasiliti F, et al. Multiobjective optimization techniques for the design of induction motors. IEEE Trans Magn. 2003;39(3):1261–1264. doi: 10.1109/TMAG.2003.810193
  • Sun Y, Ng DWK, Zhu J, et al. Multi-objective optimization for robust power efficient and secure full-duplex wireless communication systems. IEEE Trans Wirel Commun. 2016;15(8):5511–5526. doi: 10.1109/TWC.2016.2560815
  • Evans GW. An overview of techniques for solving multiobjective mathematical programs. Manage Sci. 1984;30(11):1268–1282. doi: 10.1287/mnsc.30.11.1268
  • Gravel M, Martel JM, Nadeau R, et al. A multicriterion view of optimal resource allocation in job-shop production. European J Oper Res. 1992;61(1-2):230–244. doi: 10.1016/0377-2217(92)90284-G
  • Fliege J. OLAF- a general modeling system to evaluate and optimize the location of an air polluting facility. OR-Spektrum. 2001;23(1):117–136. doi: 10.1007/PL00013342
  • Leschine TM, Wallenius H, Verdini WA. Interactive multiobjective analysis and assimilative capacity-based ocean disposal decisions. European J Oper Res. 1992;56(2):278–289. doi: 10.1016/0377-2217(92)90228-2
  • Morovati V, Pourkarimi L. Extension of Zoutendijk method for solving constrained multiobjective optimization problems. European J Oper Res. 2019;273(1):44–57. doi: 10.1016/j.ejor.2018.08.018
  • Fliege J, Drummond LG, Svaiter BF. Newton's method for multiobjective optimization. SIAM J Optim. 2009;20(2):602–626. doi: 10.1137/08071692X
  • Fliege J, Svaiter BF. Steepest descent methods for multicriteria optimization. Math Methods Oper Res. 2000;51(3):479–494. doi: 10.1007/s001860000043
  • Morovati V, Basirzadeh H, Pourkarimi L. Quasi-Newton methods for multiobjective optimization problems. 4OR. 2017;6(3):261–294. doi: 10.1007/s10288-017-0363-1
  • Povalej Z. Quasi-Newtons method for multiobjective optimization. Comput Appl Math. 2014;255:765–777. doi: 10.1016/j.cam.2013.06.045
  • Qu S, Goh M, Chan FT. Quasi-Newton methods for solving multiobjective optimization. Oper Res Lett. 2011;39(5):397–399. doi: 10.1016/j.orl.2011.07.008
  • Morovati V, Pourkarimi L, Basirzadeh H. Barzilai and Borweins method for multiobjective optimization problems. Numer Algorithms. 2016;72(3):539–604. doi: 10.1007/s11075-015-0058-7
  • El Maghri M, Elboulqe Y. Reduced Jacobian method. J Optim Theory Appl. 2018;179(3):917–943. doi: 10.1007/s10957-018-1362-x
  • El Moudden M, El Ghali A. A new reduced gradient method for solving linearly constrained multiobjective optimization problems. Comput Optim Appl. 2018;71(3):719–741. doi: 10.1007/s10589-018-0023-1
  • Fliege J, Vaz AIF. A method for constrained multiobjective optimization based on SQP techniques. SIAM J Optim. 2016;26(4):2091–2119. doi: 10.1137/15M1016424
  • Qu S, Goh M, Lian B. Trust region methods for solving multiobjective optimisation. Optim Methods Softw. 2013;28(4):796–811. doi: 10.1080/10556788.2012.660483
  • Villacorta KD, Oliveira PR, Souberyran A. A trust region method for unconstrained multipbjective problems with applications in satisfying processes. J Optim Theory Appl. 2014;160(3):865–889. doi: 10.1007/s10957-013-0392-7
  • Carrizo GA, Lotito PA, Maciel MC. Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem. Math Program. 2016;159(1-2):339–369. doi: 10.1007/s10107-015-0962-6
  • Qu S, Ji Y, Jiang J, et al. Nonmonotone gradient methods for vector optimization with a Portfolio optimization application. European J Oper Res. 2017;263(2):356–366. doi: 10.1016/j.ejor.2017.05.027
  • Mita K, Fukuda EH, Yamashita N. Nonmonotone line searches for unconstrained multiobjective optimization problems. J Global Optim. 2019;75(1):63–90. doi: 10.1007/s10898-019-00802-0
  • Fazzio NS, Schuverdt ML. Convergence analysis of a nonmonotone projected gradient method for multiobjective optimization problems. Optim Lett. 2019;13(6):1365–1379. doi: 10.1007/s11590-018-1353-8
  • Mahdavi-Amiri N, Salehi Sadaghiani F. A superlinearly convergent nonmonotone quasi-Newton method for unconstrained multiobjective optimization. Optim Methods Softw. 2020;35(6):1223–1247. doi: 10.1080/10556788.2020.1737691
  • Ghalavand N, Khorram E, Morovati V. An adaptive nonmonotone line search for multiobjective optimization problems. Comput Oper Res. 2021;136:Article ID 105506. doi: 10.1016/j.cor.2021.105506
  • Ramirez VA, Sottosanto GN. Nonmonotone trust region algorithm for solving the unconstrained multiobjective optimization problems. Comput Optim Appl. 2022;81(3):769–788. doi: 10.1007/s10589-021-00346-8
  • Deng NY, Xiao Y, Zhou FJ. Nonmonotoic trust region algorithm. J Optim Theory Appl. 1993;76(2):259–285. doi: 10.1007/BF00939608
  • Fu J, Sun W. Nonmonotone adaptive trust-region method for unconstrained optimization problems. Appl Math Comput. 2005;163(1):489–504. doi: 10.1016/j.amc.2004.02.011.
  • Rezaee S, Babaie-Kafaki S. A modified nonmonotone trust region line search method. J Appl Math Comput. 2018;57(1-2):421–436. doi: 10.1007/s12190-017-1113-4
  • Toint P.L. Non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints. Math Program. 1997;77(3):69–94. doi: 10.1007/BF02614518
  • Xiao Y, Zhou F. Nonmonotone trust region methods with curvilinear path in unconstrained optimization. Computing. 1992;48(3-4):303–317. doi: 10.1007/BF02238640
  • Ehrgott M. Multicriteria optimization. 2nd Edition. Berlin: Springer; 2005.
  • Ahookhosh M, Amini K. An efficient nonmonotone trust region method for unconstrained optimization. Numer Algorithms. 2012;59(4):523–540. doi: 10.1007/s11075-011-9502-5
  • Mo J, Liu C, Yan S. A nonmonotone trust region method based on nonincreasing technique of weighted average of the successive function values. Comput Appl Math. 2007;209(1):97–108. doi: 10.1016/j.cam.2006.10.070
  • Zhang H, Hager WW. A nonmonotone line search technique and its application to unconstrained optimization. SIAM J Optim. 2004;14(4):1043–1056. doi: 10.1137/S1052623403428208
  • Conn AR, Gould NI, Toint PL. Trust-region methods. Philadelphia (PA): SIAM-MPS; 2000.
  • Dolan ED, More JJ. Benchmarking optimization software with performance profiles. Math Program. 2002;91(2):201–213. doi: 10.1007/s101070100263
  • Das I, Dennis JE. Normal-boundary intersection: a new method for generating Pareto optimal points in nonlinear multicriteria optimization problems. SIAM J Optim. 1998;8(3):631–657. doi: 10.1137/S1052623496307510
  • Dumitrescu D, Grosan C, Oltean M. A new evolutionary approach for multiobjective optimization. Stud Univ Babes-Bolyai Inform. 2000;XLV(1):51–68.
  • Hillermeier C. Nonlinear multiobjective optimization: a generalized homotopy approach. Basel, Boston, Berlin: Birkauser Verlag; 2001. (International series of numerical mathematics; 25).
  • Huband S, Hingston P, Barone L, et al. A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput. 2006;10(5):477–506. doi: 10.1109/TEVC.2005.861417
  • Jin Y, Olhofer M, Sendhoff B. Dynamic weighted aggregation for evolutionary multiobjective optimization: why does it work and how?. In: Proceedings of the 3rd annual conference on genetic and evolutionary computation; 2001. p. 1042–1049.
  • Kim IY, De Weck OL. Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct Multidiscip Optim. 2005;29(2):149–158. doi: 10.1007/s00158-004-0465-1
  • Preuss M, Naujoks B, Rudolph G. Pareto set and EMOA behavior for simple multimodal multiobjective functions. In: Parallel problem solving from nature-PPSN IX. Berlin, Heidelberg: Springer; 2006. p. 513–522.
  • Socha K, Kisiel-Dorohinicki M. Agent-based evolutionary multiobjective optimisation. In: Proceedings of the congress on evolutionary computation. Vol. 1; 2002. p. 109–114.
  • Sefrioui M, Perlaux J. Nash genetic algorithms: examples and applications. In: Proceedings of the congress on evolutionary computation. Vol. 1; 2000. p. 509–516.
  • Thomann J, Eichfelder G. A trust-region algorithm for heterogeneous multiobjective optimization. SIAM J Optim. 2019;29(2):1017–1047. doi: 10.1137/18M1173277
  • Thomann J, Eichfelder G. Numerical results for the multiobjective trust region algorithm MHT. Data in Brief. 2019;25:Article ID 104103. doi: 10.1016/j.dib.2019.104103
  • Valenzuela-Rendon M, Uresti-Charre E, Monterrey I. A non-generational genetic algorithm for multiobjective optimization. In: Proccedding of 7th international conference genetic algorithms; 1997. p. 658–665.
  • Rau RV, Rai DP, Balic J. . Multi-objective optimization of abrasive waterjet machining process using Jaya algorithm and PROMETHEE method. J Intell Manuf. 2017;30(5):2101–2127. doi: 10.1007/s10845-017-1373-8.

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