Article
| Title: | A weighted hybrid conjugate gradient method for unconstrained multiobjective optimization problems (English) |
| Author: | Jong, Yunchol |
| Author: | Hwang, Wonchol |
| Author: | Rim, Yungwang |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 537-561 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | We propose a weighted HS (Hestenes-Stiefel)-FR (Fletcher-Reeves) hybrid conjugate gradient method for unconstrained multiobjective optimization problem, in which a new positive coefficient of the multiobjective steepest descent direction is adaptively updated to keep its positiveness. The method takes advantage of a weighted hybrid of our modified HS and FR parameters and under the Armijo-type backtracking line search, it has global convergence to a Pareto critical point (point satisfying the first-order necessary condition for Pareto optimality) without convexity assumption on the objectives. Numerical experiments show that the practical performance of the method is competitive with the existing methods such as conjugate gradient method, steepest descent method, Newton method, and quasi-Newton method for unconstrained multiobjective optimization. (English) |
| Keyword: | multiobjective optimization |
| Keyword: | Pareto optimality |
| Keyword: | conjugate gradient method |
| Keyword: | backtracking line search |
| Keyword: | Armijo condition |
| MSC: | 49M37 |
| MSC: | 65K05 |
| MSC: | 90C29 |
| DOI: | 10.21136/AM.2025.0040-25 |
| . | |
| Date available: | 2025-10-03T12:11:22Z |
| Last updated: | 2025-10-06 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153092 |
| . | |
| Reference: | [1] Ansary, M. A. T., Panda, G.: A modified quasi-Newton method for vector optimization problem.Optimization 64 (2015), 2289-2306. Zbl 1327.90275, MR 3391220, 10.1080/02331934.2014.947500 |
| Reference: | [2] Bandyopadhyay, S., Pal, S. K., Aruna, B.: Multiobjective GAs, quantitative indices, and pattern classification.IEEE Trans. Syst. Man Cybern., Part B 34 (2004), 2088-2099. 10.1109/TSMCB.2004.834438 |
| Reference: | [3] Cabrera-Guerrero, G., Lagos, C.: Comparing multi-objective local search algorithms for the beam angle selection problem.Mathematics 10 (2022), Article ID 159, 25 pages. 10.3390/math10010159 |
| Reference: | [4] Chuong, T. D., Mordukhovich, B. S., Yao, J.-C.: Hybrid approximate proximal algorithms for efficient solutions in vector optimization.J. Nonlinear Convex Anal. 12 (2011), 257-286. Zbl 1223.49033, MR 2858309 |
| Reference: | [5] Coello, C. A. Coello, Lamont, G. B., Veldhuizen, D. A. Van: Evolutionary Algorithms for Solving Multi-Objective Problems.Springer, New York (2007). Zbl 1142.90029, MR 2350880, 10.1007/978-0-387-36797-2 |
| Reference: | [6] Denysiuk, R., Gaspar-Cunha, A.: Multiobjective evolutionary algorithm based on vector angle neighborhood.Swarm Evol. Comput. 37 (2017), 45-57. 10.1016/j.swevo.2017.05.005 |
| Reference: | [7] Dolan, E. D., Moré, J. J.: Benchmarking optimization software with performance profiles.Math. Program. 91 (2002), 201-213. Zbl 1049.90004, MR 1875515, 10.1007/s101070100263 |
| Reference: | [8] Ehrgott, M.: Multicriteria Optimization.Springer, Berlin (2005). Zbl 1132.90001, MR 2143243, 10.1007/3-540-27659-9 |
| Reference: | [9] Eichfelder, G.: Twenty years of continuous multiobjective optimization in the twenty-first century.EURO J. Comput. Optim. 9 (2021), Article ID 100014, 15 pages. Zbl 1530.90091, MR 4397745, 10.1016/j.ejco.2021.100014 |
| Reference: | [10] Eichfelder, G., Kirst, P., Meng, L., Stein, O.: A general branch-and-bound framework for continuous global multiobjective optimization.J. Glob. Optim. 80 (2021), 195-227. Zbl 1470.90114, MR 4260677, 10.1007/s10898-020-00984-y |
| Reference: | [11] Fliege, J., Drummond, L. M. G., Svaiter, B. F.: Newton's method for multiobjective optimization.SIAM J. Optim. 20 (2009), 602-626. Zbl 1195.90078, MR 2515788, 10.1137/08071692X |
| Reference: | [12] Fliege, J., Svaiter, B. F.: Steepest descent methods for multicriteria optimization.Math. Methods Oper. Res. 51 (2000), 479-494. Zbl 1054.90067, MR 1778656, 10.1007/s001860000043 |
| Reference: | [13] Guo, Z., Ersoy, O. K., Yan, X.: A multi-objective differential evolutionary algorithm with angle-based objective space division and parameter adaption for solving sodium gluconate production process and benchmark problems.Swarm Evol. Comput. 55 (2020), Article ID 100670, 12 pages. 10.1016/j.swevo.2020.100670 |
| Reference: | [14] Gupta, S., Srivastava, M.: A new scalarization function and well-posedness of vector optimization problem.Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 83 (2021), 177-192. Zbl 1513.49055, MR 4407132 |
| Reference: | [15] Handl, J., Kell, D. B., Knowles, J.: Multiobjective optimization in bioinformatics and computational biology.IEEE/ACM Trans. Comput. Biolog. Bioinf. 4 (2007), 279-290. 10.1109/TCBB.2007.070203 |
| Reference: | [16] Jahn, J.: Vector Optimization: Theory, Applications, and Extensions.Springer, Berlin (2004). Zbl 1055.90065, MR 2058695, 10.1007/978-3-540-24828-6 |
| Reference: | [17] Jiang, X., Na, J.: Online surrogate multiobjective optimization algorithm for contaminated groundwater remediation designs.Appl. Math. Modelling 78 (2020), 519-538. Zbl 1481.86005, MR 4029067, 10.1016/j.apm.2019.09.053 |
| Reference: | [18] Liang, J., Xu, W., Yue, C., Yu, K., Song, H., Crisalle, O. D., Qu, B.: Multimodal multiobjective optimization with differential evolution.Swarm Evol. Comput. 44 (2019), 1028-1059. 10.1016/j.swevo.2018.10.016 |
| Reference: | [19] Pérez, L. R. Lucambio, Prudente, L. F.: Nonlinear conjugate gradient methods for vector optimization.SIAM J. Optim. 28 (2018), 2690-2720. Zbl 1401.90210, MR 3858809, 10.1137/17M1126588 |
| Reference: | [20] Marcellin, K. N., Ouattara, A., Joseph, S. K.: Multiobjective optimization of micro-gas turbines environmental polluting emissions due to their internal and external thermal losses.Am. J. Environ. Prot. 12 (2023), 1-10. 10.11648/j.ajep.20231201.11 |
| Reference: | [21] Mita, K., Fukuda, E. H., Yamashita, N.: Nonmonotone line searches for unconstrained multiobjective optimization problems.J. Glob. Optim. 75 (2019), 63-90. Zbl 1428.90155, MR 4011712, 10.1007/s10898-019-00802-0 |
| Reference: | [22] Morovati, V., Basirzadeh, H., Pourkarimi, L.: Quasi-Newton methods for multiobjective optimization problems.4OR 16 (2018), 261-294. Zbl 1407.90300, MR 3845793, 10.1007/s10288-017-0363-1 |
| Reference: | [23] Povalej, Ž.: Quasi-Newton's method for multiobjective optimization.J. Comput. Appl. Math. 255 (2014), 765-777. Zbl 1291.90316, MR 3093459, 10.1016/j.cam.2013.06.045 |
| Reference: | [24] Qu, S., Goh, M., Chan, F. T. S.: Quasi-Newton methods for solving multiobjective optimization.Oper. Res. Lett. 39 (2011), 397-399. Zbl 1235.90139, MR 2835535, 10.1016/j.orl.2011.07.008 |
| Reference: | [25] Qu, S., Goh, M., Liang, B.: Trust region methods for solving multiobjective optimization.Optim. Method Softw. 28 (2013), 796-811. Zbl 1278.90365, MR 3175444, 10.1080/10556788.2012.660483 |
| Reference: | [26] Svaiter, B. F.: The multiobjective steepest descent direction is not Lipschitz continuous, but is Hölder continuous.Oper. Res. Lett. 46 (2018), 430-433. Zbl 1525.90389, MR 3827652, 10.1016/j.orl.2018.05.008 |
| Reference: | [27] Thomann, J., Eichfelder, G.: A trust-region algorithm for heterogeneous multiobjective optimization.SIAM J. Optim. 29 (2019), 1017-1047. Zbl 1411.90311, MR 3936040, 10.1137/18M1173277 |
| Reference: | [28] Villacorta, K. D. V., Oliveira, P. R., Soubeyran, A.: A trust-region method for unconstrained multiobjective problems with applications in satisficing processes.J. Optim. Theory Appl. 160 (2014), 865-889. Zbl 1300.90045, MR 3181000, 10.1007/s10957-013-0392-7 |
| Reference: | [29] Wang, J., Hu, Y., Yu, C. K. W., Li, C., Yang, X.: Extended Newton methods for multiobjective optimization: Majorizing function technique and convergence analysis.SIAM J. Optim. 29 (2019), 2388-2421. Zbl 1422.90052, MR 4010766, 10.1137/18M1191737 |
| Reference: | [30] Yang, N.-C., Mehmood, D.: Multi-objective bee swarm optimization algorithm with minimum Manhattan distance for passive power filter optimization problems.Mathematics 10 (2022), Article ID 133, 20 pages. 10.3390/math10010133 |
| Reference: | [31] Zaaraoui, L., Mansouri, A., Smairi, N.: NMOPSO: An improved multiobjective PSO algorithm for permanent magnet motor design.U.P.B. Sci. Bull., Ser. C 84 (2022), 201-214. |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
