An interval multi-objective optimization algorithm based on elite genetic strategy. (English) Zbl 1533.90105
Summary: Multi-objective optimization problems with interval parameter (IMOPs) are among the most critical optimization problems in practical applications. However, in contrast to deterministic multi-objective optimization, few studies have addressed IMOPs. Moreover, the uncertainty in such problems makes the convergence and diversity of the algorithm more challenging. Therefore, this paper proposes an interval multi-objective optimization algorithm based on elite genetic strategy (EG-IMOEA). First, existing interval dominance relations cannot comprehensively determine which of the two intervals is better when their midpoints are equal but their upper and lower limits are unequal. Therefore, a conditional-based interval confidence dominance relation is proposed that considers both the average level of convergence and value of the minimum lower limit of intervals. The interval crowding distance (ICD) applied to multiple objectives is then defined to evaluate the solutions more completely. Furthermore, an elite genetic strategy for crossover and mutation is proposed to generate better offspring. The proposed algorithm was evaluated on nine benchmark test problems and compared with the typical algorithm as well as state-of-the-art algorithms. The results showed that this algorithm outperformed the comparison algorithms in terms of convergence, diversity, imprecision, and uniform distribution.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
evolutionary algorithm; multi-objective optimization; interval non-dominance relation; interval uncertaintyReferences:
| [1] | Li, A-D.; Xue, B.; Zhang, M. J., Multi-objective particle swarm optimization for key quality feature selection in complex manufacturing processes, Inf. Sci., 641 (2023) |
| [2] | Cui, Z. H.; Zhang, J. J.; Wu, D.; Cai, X. J.; Wang, H.; Zhang, W. S.; Chen, J. J., Hybrid many-objective particle swarm optimization algorithm for green coal production problem, Inf. Sci., 518, 256-271 (2020) |
| [3] | Xu, B. J.; Zhao, K. X.; Luo, Q. Z.; Wu, G. H.; Pedrycz, W., A GV-drone arc routing approach for urban traffic patrol by coordinating a ground vehicle and multiple drones, Swarm Evol. Comput., 77 (2023) |
| [4] | Dong, T. T.; Zhou, L.; Chen, L.; Song, Y. X.; Tang, H. L.; Qin, H. L., A hybrid algorithm for workflow scheduling in cloud environment, Int. J. Bio-Inspir. Comput., 21, 48-56 (2023) |
| [5] | Cai, X. J.; Hu, Z. M.; Chen, J. J.; Liu, Y. C., A many-objective optimization recommendation algorithm based on knowledge mining, Inf. Sci., 537, 148-161 (2020) |
| [6] | Flor-Sánchez, C. O.; Reséndiz-Flores, E. O.; García-Calvillo, I. D., Kernel-based hybrid multi-objective optimization algorithm (KHMO), Inf. Sci., 624, 416-434 (2023) · Zbl 1537.90015 |
| [7] | Huang, T.; Tang, X. A.; Zhao, S. Y.; Zhang, Q.; Pedrycz, W., Linguistic information-based granular computing based on a tournament selection operator-guided PSO for supporting multi-attribute group decision-making with distributed linguistic preference relations, Inf. Sci., 610, 488-507 (2022) · Zbl 1537.91073 |
| [8] | Cui, Z. H.; Zhao, P.; Hu, Z. M.; Cai, X. J.; Zhang, W. S.; Chen, J. J., An improved matrix factorization based model for many-objective optimization recommendation, Inf. Sci., 579, 1-14 (2021) |
| [9] | Cui, Z. H.; Xue, Z. Y.; Fan, T.; Cai, X. J.; Zhang, W. S., A many-objective evolutionary algorithm based on constraints for collaborative computation offloading, Swarm Evol. Comput. (2023) |
| [10] | Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 2, 182-197 (2002) |
| [11] | Zitzler, E.; Künzli, S., Indicator-based selection in multiobjective search, (8th International Conference on Parallel Problem Solving from Nature (2004)) |
| [12] | Zhang, Q.; Hui, L., MOEA/D: a multiobjective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput., 11, 6, 712-731 (2008) |
| [13] | Wang, S. Y.; Ma, D. C.; Ren, Z.; Qu, Y. Y.; Wu, M., Adaptive surrogate-based swarm intelligence algorithm and its application in wastewater treatment processes, Int. J. Bio-Inspir. Comput., 20, 209-219 (2022) |
| [14] | Yang, W. S.; Chen, L.; Li, Y. Y.; Abid, F., A many-objective particle swarm optimisation algorithm based on convergence assistant strategy, Int. J. Bio-Inspir. Comput., 20, 104-118 (2022) |
| [15] | Aslan, S.; Arslan, S., A modified artificial bee colony algorithm for classification optimisation, Int. J. Bio-Inspir. Comput., 20, 11-12 (2022) |
| [16] | Chen, Z.; Wu, H.; Chen, Y.; Cheng, L.; Zhang, B., Patrol robot path planning in nuclear power plant using an interval multi-objective particle swarm optimization algorithm, Appl. Soft Comput., 116 (2022) |
| [17] | Luo, S. G.; Guo, X. P., Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization, J. Ind. Manag. Optim., 19, 2, 823-851 (2023) · Zbl 1524.49059 |
| [18] | He, Q. Y.; He, Z. N.; Duan, S. L.; Zhong, Y. Y.Z., Multi-objective interval portfolio optimization modeling and solving for margin trading, Swarm Evol. Comput., 75 (2022) |
| [19] | Wei, S. G.; Luo, R.; Song, H. Y.; Sun, J., High-speed train platoon dynamic interval optimization based on resilience adjustment strategy, IEEE Trans. Intell. Transp. Syst., 23, 5, 4402-4414 (2022) |
| [20] | Gong, D. W.; Qin, N. N.; Sun, X. Y., Evolutionary algorithms for multi-objective optimization problems with interval parameters, (IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA) (2010)) |
| [21] | Gong, D. W.; Qin, N. N.; Sun, X. Y., Evolutionary algorithms for optimization problems with uncertainties and hybrid indices, Inf. Sci. (2011) |
| [22] | Liu, X.; Zhang, Z. Y.; Yin, L. R., A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method, Mech. Based Des. Struct. Mach., 45, 1, 25-42 (2017) |
| [23] | Feng, Y.; Zhang, Z.; Tian, G.; Lv, Z.; Tian, S.; Jia, H., Data-driven accurate design of variable blank holder force in sheet forming under interval uncertainty using sequential approximate multi-objective optimization, Future Gener. Comput. Syst., 86, ESP, 1242-1250 (2017) |
| [24] | Han, Y. Y.; Gong, D. W.; Jin, Y. C.; Pan, Q. K., Evolutionary multi-objective blocking lot-streaming flow shop scheduling with interval processing time, Appl. Soft Comput., 42, 229-245 (2016) |
| [25] | Limbourg, P.; Aponte, D. E.S., An optimization algorithm for imprecise multi-objective problem functions, (IEEE Congress on Evolutionary Computation (2005)) |
| [26] | Eskandari, H.; Geiger, C. D.; Bird, R., Handling uncertainty in evolutionary multiobjective optimization: SPGA, (IEEE Congress on Evolutionary Computation (2007)) |
| [27] | Jiang, C.; Han, X.; Liu, G. R.; Liu, G. P., A nonlinear interval number programming method for uncertain optimization problems, Eur. J. Oper. Res., 188, 1, 1-13 (2008) · Zbl 1135.90044 |
| [28] | Jing, S.; Gong, D. W., Solving interval multi-objective optimization problems using evolutionary algorithms with lower limit of possibility degree, Chin. J. Electron., 22, 2, 269-272 (2013) |
| [29] | Eskandari, H.; Bielza, C.; Larranaga, P., Interval-based ranking in noisy evolutionary multi-objective optimization, Comput. Optim. Appl., 61, 2, 517-555 (2015) · Zbl 1326.90077 |
| [30] | Zhang, P. F.; Xu, R. D.; Sun, X. Y.; Gong, D. W.; Choi, J., A synthesized ranking-assisted NSGA-II for interval multi-objective optimization, (IEEE Congress on Evolutionary Computation (CEC) (2016)) |
| [31] | Alolyan, I., Algorithm for interval linear programming involving interval constraints, (Ifsa World Congress and Nafips Meeting (2013)) |
| [32] | Jun, X.; Zhang, Y.; Fu, C., Comparison between methods of InterVaI number ranking based on Possibility, J. Tianjin Univ., 44, 8, 705-711 (2011) |
| [33] | Sun, J.; Miao, Z.; Gong, D. W.; Zeng, X. J.; Li, J.; Wang, G., Interval multiobjective optimization with memetic algorithms, IEEE Trans. Cybern., 50, 8, 3444-3457 (2020) |
| [34] | Liu, G. P.; Liu, S., Direct method for uncertain multi-objective optimization based on interval non-dominated sorting, Struct. Multidiscip. Optim., 62, 2, 729-745 (2020) |
| [35] | Gan, X. J.; Sun, J.; Gong, D. W.; Jia, D. B.; Dai, H. W.; Zhong, Z. M., An adaptive reference vector-based interval multi-objective evolutionary algorithm, IEEE Trans. Evol. Comput. (2022) |
| [36] | Xu, Y.; Pi, D. C.; Yang, S. X.; Chen, Y.; Qin, S.; Zio, E., An angle-based bi-objective optimization algorithm for redundancy allocation in presence of interval uncertainty, IEEE Trans. Autom. Sci. Eng., 20, 1, 271-284 (2023) |
| [37] | Yi, J.; Bai, J. R.; He, H. B.; Zhou, W.; Yao, L. Z., A multifactorial evolutionary algorithm for multitasking under interval uncertainties, IEEE Trans. Evol. Comput., 24, 5, 908-922 (2020) |
| [38] | Li, X.; Zhang, S. L.; Zhang, M.; Liu, H., Interval number ranking based on new distance measure, J. Xihua Univ. Nat. Sci. Ed., 27, 1, 87-90 (2008) |
| [39] | Wang, X.; Dang, J. G., Dynamic multi-attribute decision-making methods with three-parameter interval grey number, Control Decis., 30, 9, 1623-1629 (2015) · Zbl 1349.90507 |
| [40] | Ahn, B. S., The uncertain OWA aggregation with weighting functions having a constant level of orness, Int. J. Intell. Syst., 21, 5, 469-483 (2006) · Zbl 1094.68090 |
| [41] | Zhou, L. G.; Chen, H. Y.; Merigo, J. M.; Gil-Lafuente, A. M., Uncertain generalized aggregation operators, Expert Syst. Appl., 39, 1, 1105-1117 (2012) |
| [42] | Emmerich, M.; Beume, N.; Naujoks, B., An EMO Algorithm Using the Hypervolume Measure as Selection Criterion (2005), Springer Berlin Heidelberg · Zbl 1109.68595 |
| [43] | Zhang, Z. X.; Zhao, M. K.; Wang, H.; Cui, Z. H.; Zhang, W. S., An efficient interval many-objective evolutionary algorithm for cloud task scheduling problem under uncertainty, Inf. Sci., 583, 56-72 (2022) |
| [44] | Gong, D. W.; Sun, J.; Miao, Z., A set-based genetic algorithm for interval many-objective optimization problems, IEEE Trans. Evol. Comput., 22, 1, 47-60 (2018) |
| [45] | Chen, Z. W.; Chen, L.; Bai, X.; Yang, Q.; Zhao, F. L., Interactive multi-attribute decision-making NSGA-II for constrained multi-objective optimization with interval numbers, Control Decis., 5, 865-870 (2015) |
| [46] | Huband, S.; Hingston, P.; Barone, L.; While, L., A review of multiobjective test problems and a scalable test problem toolkit, IEEE Trans. Evol. Comput., 10, 4, 477-506 (2006) |
| [47] | Sri, R. M.S.; Rammohan, M.; Kedar, N. D., A twin-archive guided decomposition based multi/many-objective evolutionary algorithm, Swarm Evol. Comput. (2023) |
| [48] | Zhang, M. Q.; Wang, L.; Li, W. Z.; Hu, B.; Li, D. Y.; Wu, Q. D., Many-objective evolutionary algorithm with adaptive reference vector, Inf. Sci., 563, 70-90 (2021) · Zbl 1524.90286 |
| [49] | Bao, C. T.; Gao, D. J.; Gu, W.; Xu, L. H.; Goodman, E. D., A new adaptive decomposition-based evolutionary algorithm for multi- and many-objective optimization, Expert Syst. Appl., 213 (2023) |
| [50] | Kouka, N.; BenSaid, F.; Fdhila, R.; Fourati, R.; Hussain, A.; Alimi, A. M., A novel approach of many-objective particle swarm optimization with cooperative agents based on an inverted generational distance indicator, IEEE Trans. Evol. Comput., 623, 220-241 (2023) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
