Abstract
In this paper, a transfer learning based evolutionary algorithm (TLEA) framework for multi-objective optimization problems (MOPs) is proposed. In the TLEA framework, a complex multi-objective optimization task is decomposed into a set of relatively simple multi-objective optimization subtasks and then optimized collaboratively by parallel subpopulation searches with the proposed transfer learning method. More specifically, neighboring subtasks may have some similar features during parallel searches of corresponding subpopulations, and those similarities can be exploited through the proposed transfer learning strategy to improve the collaboration among these search subpopulations and achieve greater efficiency. To show the generality of the proposed algorithm framework, two implementations of the proposed TLEA framework based on differential evolution (DE) and particle swarm optimization (PSO), i.e., TLPSO and TLDE, are presented and studied in detail. In TLPSO and TLDE, the subproblem features are reflected by the search subpopulations, which are generated by a pair of specific parameters. Therefore, subpopulations can adaptively adjust parameter settings by learning useful information from neighboring subproblems with more appropriate parameters during the search. The experimental results show that TLPSO performs better than other algorithms on at least five out of 12 test problems in terms of the IGD indicator and on at least seven out of 12 test problems in terms of the HV indicator. TLDE has an advantage over the other algorithms on five out of 12 test problems in terms of the IGD indicator and on seven out of 12 test problems in terms of the HV indicator.
Similar content being viewed by others
Data Availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
References
Guan T, Han F, Han H (2019) A modified multi-objective particle swarm optimization based on levy flight and double-archive mechanism. IEEE Access 7:183444–183467
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2018) The social engineering optimizer (SEO). Eng Appl Artif Intel 72:267–293
Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2020) Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft Comput 24(19):14637–14665
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international Conference on Neural Networks, vol 4. IEEE, pp 1942–1948
Jones DF, Mirrazavi SK, Tamiz M (2002) Multi-objective meta-heuristics: An overview of the current state-of-the-art. Eur J Oper Res 137(1):1–9
Zhang Y, Gong D-W, Geng N (2013) Multi-objective optimization problems using cooperative evolvement particle swarm optimizer. J Comput Theor Nanosci 10(3):655–663
Liu H-L, Gu F, Zhang Q (2013) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455
Tran B, Xue B, Zhang M (2018) Variable-length particle swarm optimization for feature selection on high-dimensional classification. IEEE Trans Evol Comput 23(3):473–487
Chen K, Xue B, Zhang M, Zhou F (2021) Correlation-guided updating strategy for feature selection in classification with surrogate-assisted particle swarm optimisation. IEEE Trans Evol Comput
Song X, Zhang Y, Gong D, Liu H, Zhang W (2022) Surrogate sample-assisted particle swarm optimization for feature selection on high-dimensional data. IEEE Trans Evol Comput
Han F, Wang T, Ling Q (2022) An improved feature selection method based on angle-guided multi-objective PSO and feature-label mutual information. Appl Intell: 1–18
Cao Y, Zhang H, Li W, Zhou M, Zhang Y, Chaovalitwongse WA (2018) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23(4):718–731
Ji X, Zhang Y, Gong D, Sun X (2021) Dual-surrogate-assisted cooperative particle swarm optimization for expensive multimodal problems. IEEE Trans Evol Comput 25(4):794–808
Duan X, Zhang X (2021) A hybrid genetic-particle swarm optimizer using precise mutation strategy for computationally expensive problems. Appl Intell: 1–24
Villalón CLC, Dorigo M, Stützle T (2021) PSO-X: A component-based framework for the automatic design of particle swarm optimization algorithms. IEEE Trans Evol Comput
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360). IEEE, pp 69–73
Lei K, Qiu Y, He Y (2006) A new adaptive well-chosen inertia weight strategy to automatically harmonize global and local search ability in particle swarm optimization. In: 2006 1st international symposium on systems and control in aerospace and astronautics. IEEE, p 4
Zhang L, Tang Y, Hua C, Guan X (2015) A new particle swarm optimization algorithm with adaptive inertia weight based on Bayesian techniques. Appl Soft Comput 28:138– 149
Shi Y, Eberhart RC (2001) Fuzzy adaptive particle swarm optimization. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546), vol 1. IEEE, pp 101–106
Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8(3):240–255
Zhan Z-H, Zhang J, Li Y, Chung HS-H (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern Part B (Cybernetics) 39(6):1362–1381
Hu W, Yen GG (2013) Adaptive multiobjective particle swarm optimization based on parallel cell coordinate system. IEEE Trans Evol Comput 19(1):1–18
Han H, Lu W, Qiao J (2017) An adaptive multiobjective particle swarm optimization based on multiple adaptive methods. IEEE Trans Cybern 47(9):2754–2767
Dong J, Li Y, Wang M (2019) Fast multi-objective antenna optimization based on RBF neural network surrogate model optimized by improved PSO algorithm. Appl Sci 9(13):2589
Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126
Mezura-Montes E, Portilla-Flores E-A, Capistran-Gumersindo E (2015) Dynamic parameter control in differential evolution with combined variants to optimize a three-finger end effector. In: 2015 IEEE international autumn meeting on power, electronics and computing (ROPEC). IEEE, pp 1–6
Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: 2005 IEEE congress on evolutionary computation, vol 2. IEEE, pp 1785– 1791
Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657
Qin AK, Huang VL, Suganthan PN (2008) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417
Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958
Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: 2013 IEEE congress on evolutionary computation. IEEE, pp 71–78
Viktorin A, Senkerik R, Pluhacek M, Kadavy T, Zamuda A (2019) Distance based parameter adaptation for success-history based differential evolution. Swarm Evol Comput 50:100462
Biswas PP, Suganthan PN, Wu G, Amaratunga GA (2019) Parameter estimation of solar cells using datasheet information with the application of an adaptive differential evolution algorithm. Renew Energy 132:425–438
Tian M, Gao X (2019) An improved differential evolution with information intercrossing and sharing mechanism for numerical optimization. Swarm Evol Comput 50:100341
Draa A, Chettah K, Talbi H (2019) A compound sinusoidal differential evolution algorithm for continuous optimization. Swarm Evol Comput 50:100450
Sun G, Xu G, Jiang N (2020) A simple differential evolution with time-varying strategy for continuous optimization. Soft Comput 24(4):2727–2747
Pan SJ, Yang Q (2009) A survey on transfer learning. IEEE Trans Knowl Data Eng 22 (10):1345–1359
Gupta A, Ong Y-S, Feng L (2015) Multifactorial evolution: toward evolutionary multitasking. IEEE Trans Evol Comput 20(3):343–357
Chaabani A, Said LB (2019) Transfer of learning with the co-evolutionary decomposition-based algorithm-II: a realization on the bi-level production-distribution planning system. Appl Intell 49(3):963–982
Zhenzhong W, Jiang M, Xing G, Liang F, Weizhen H, Tan KC (2019) Evolutionary dynamic multi-objective optimization via regression transfer learning. In: 2019 IEEE symposium series on computational intelligence (SSCI). IEEE, pp 2375–2381
Jiang M, Huang Z, Qiu L, Huang W, Yen GG (2017) Transfer learning-based dynamic multiobjective optimization algorithms. IEEE Trans Evol Comput 22(4):501–514
Jiang M, Wang Z, Qiu L, Guo S, Gao X, Tan KC (2020) A fast dynamic evolutionary multiobjective algorithm via manifold transfer learning. IEEE Trans Cybern 51(7):3417–3428
Bali KK, Ong Y-S, Gupta A, Tan PS (2019) Multifactorial evolutionary algorithm with online transfer parameter estimation: MFEA-II. IEEE Trans Evol Comput 24(1):69–83
Feng L, Zhou L, Zhong J, Gupta A, Ong Y-S, Tan K-C, Qin AK (2018) Evolutionary multitasking via explicit autoencoding. IEEE Trans Cybern 49(9):3457–3470
Lin J, Liu H-L, Tan KC, Gu F (2020) An effective knowledge transfer approach for multiobjective multitasking optimization. IEEE Trans Cybern 51(6):3238–3248
Huang J, Chen L (2021) Transfer learning based multi-objective particle swarm optimization algorithm. In: 2021 17th international conference on computational intelligence and security (CIS). IEEE, pp 382–386
Zhang Q, Li H (2007) MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731
Hillermeier C, et al. (2001) Nonlinear multiobjective optimization: a generalized Homotopy approach, vol 135. Springer, New York
Jaszkiewicz A (2002) On the performance of multiple-objective genetic local search on the 0/1 knapsack problem-a comparative experiment. IEEE Trans Evol Comput 6(4):402–412
Deb K, Agrawal RB et al (1995) Simulated binary crossover for continuous search space. Complex Syst 9(2):115–148
Deb K, Goyal M et al (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inform 26:30–45
Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: International conference on parallel problem solving from nature. Springer, pp 849–858
Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Proceedings of the 2002 congress on evolutionary computation. CEC’02 (Cat. No. 02TH8600), vol 1. IEEE, pp 825–830
Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10(5):477–506
Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Evolutionary multiobjective optimization. Springer, pp 105–145
Wang R, Purshouse RC, Fleming PJ (2015) Preference-inspired co-evolutionary algorithms using weight vectors. Eur J Oper Res 243(2):423–441
Li K, Deb K, Zhang Q, Kwong S (2014) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694–716
Zitzler E, Thiele L, Laumanns M, Fonseca CM, Da Fonseca VG (2003) Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans Evol Comput 7(2):117–132
Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: International conference on parallel problem solving from nature. Springer, pp 292–301
Fathollahi-Fard AM, Woodward L, Akhrif O (2021) Sustainable distributed permutation flow-shop scheduling model based on a triple bottom line concept. J Indu Inf Integr 24:100233
Tian G, Fathollahi-Fard AM, Ren Y, Li Z, Jiang X (2022) Multi-objective scheduling of priority-based rescue vehicles to extinguish forest fires using a multi-objective discrete gravitational search algorithm. Inform Sci 608:578–596
Deb K, Jain H (2013) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601
Lin Q, Liu S, Zhu Q, Tang C, Song R, Chen J, Coello CAC, Wong K-C, Zhang J (2018) Particle swarm optimization with a balanceable fitness estimation for many-objective optimization problems. IEEE Trans Evol Comput 22:32–46
Li H, Zhang Q (2008) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evolut Comput 13(2):284–302
Wang R, Purshouse RC, Fleming PJ (2012) Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Trans Evol Comput 17(4):474–494
Yu K, Liang JJ, Qu B, Luo Y, Yue C (2022) Dynamic selection preference-assisted constrained multiobjective differential evolution. IEEE Trans Syst Man Cybern Syst 52:2954–2965
Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag 12(4):73–87
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (62006044, 62172110), in part by the Natural Science Foundation of Guangdong Province (2022A1515010130), and in part by the Programme of Science and Technology of Guangdong Province (2021A0505110004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Jiechang Wen, Lei Chen and Hai-Lin Liu contributed equally to this work.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Huang, J., Wen, J., Chen, L. et al. Transfer learning based evolutionary algorithm framework for multi-objective optimization problems. Appl Intell 53, 18085–18104 (2023). https://doi.org/10.1007/s10489-022-04444-w
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-022-04444-w