Abstract
Surrogate-assisted evolutionary algorithms (SAEAs) are popular for solving expensive optimization problems. However, most existing SAEAs are designed for solving single-objective or multiobjective optimization problems with two or three objectives. Few works had been reported to deal with expensive many-objective optimization problems with more than three objectives because of two difficulties. One is the curse of dimensionality caused by many-objective problems, and the other is the fewer computational resources available in a limited time for expensive optimization problems. Since an effective selection method can better solve the many-objective optimization problems, high-efficiency search and accurate model can save computational resources for expensive optimization problems, this paper proposes a diverse/converged individual competition algorithm, which owns a novel diverse/converged individual competition selection mechanism, a hybrid search mechanism, and a segmentation approach. The diverse/converged individual competition selection mechanism maintains a good balance between the convergence and diversity of the selected solutions for solving many-objective optimization problems. The hybrid search mechanism performs a memetic search and genetic search at different stages of the evolution process to further generate superior solutions. The segmentation approach uses two different populations with small numbers to build two surrogate models which will predict different areas, and it can improve the accuracy of the prediction. The proposed algorithm is compared with several state-of-art algorithms on widely used benchmark functions. The experimental results show that the proposed algorithm performs significantly better than the compared algorithms.
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References
Zhou A et al (2011) Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm. Evol Comput 1:32–49
Schütze O, Lara A, Coello CAC (2011) On the influence of the number of objectives on the hardness of a multiobjective optimization problem. IEEE Trans Evol Comput 15:444–455
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197
Zitzler E, Laumanns M, Thiele L et al (2001) SPEA2: improving the strength Pareto evolutionary algorithm. Proc Evol Methods Des Optimisation Control 103:95–100. https://doi.org/10.3929/ethz-a-004284029
di Pierro F, Khu S-T, Savic DA (2007) An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput 11:17–45
Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems, IEEE Trans. Syst., Man. Cybern. B, Cybern. 38:1402–1412
Hadka D, Reed P (2013) Borg: An auto-adaptive many-objective evolutionary computing framework. Evol Comput 21:231–259
Li M, Yang S, Liu X (2014) Shift-based density estimation for Paretobased algorithms in many-objective optimization. IEEE Trans Evol Comput 18:348–365
Zitzler E, Künzli S (2004) Indicator-based selection in multiobjective search. In: Yao X et al (eds) Parallel problem solving from nature - PPSN VIII. PPSN 2004, Lecture notes in computer science, vol 3242. Springer, Berlin, Heidelberg, pp 832–842. https://doi.org/10.1007/978-3-540-30217-9_84
While L, Hingston P, Barone L, Huband S (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evol Comput 10:29–38
Bader J, Zitzler E (2011) HypE: An algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19:45–76
Sun Y, Yen GG, Yi Z (2019) IGD Indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput 23:173–731
Zhang Q, Li H (2007) MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731
Liu H-L, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18:450–455
Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20:773–455
Shi J, Zhang Q, Sun J (2020) PPLS/D: Parallel pareto local search based on decomposition. IEEE Trans Cybernet 50:1060–1070
Wang H, Jiao L, Yao X (2015) Two_arch2: An improved two-archive algorithm for many-objective optimization. IEEE Trans Evol Comput 19:524–541
Li K, Deb K, Zhang Q, Kwong S (2015) An evolutionary manyobjective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19:694–716
Sun Y, Xue B, Zhang M, Yen GG (2019) A new two-stage evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 23:748–761
Jin Y (2011) Surrogate-assisted evolutionary computation: Recent advances and future challenges, Swarm. Evol Comput 1:61–70
Chugh T, Sindhya K, Hakanen J, Miettien K (2019) A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms. Soft Comput 23:3137–3166
Krige DG (1951) A statistical approach to some mine valuation and allied problems on the Witwatersrand: By DG Krige. Doctoral dissertation, University of the Witwatersrand
Zurada JM (1992) Introduction to Artificial Neural Systems, vol 8. West Publ. Company, St. Paul, MN, USA
Box GEP, Draper NR (1987) Empirical Model-Building and Response Surfaces, vol 424. Wiley, New York, NY, USA
Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297
Broomhead DS, Lowe D (1988) Radial basis functions, multivariable functional interpolation and adaptive networks, document AD-A196 234. Defense Tech Inf Center, Fort Belvoir. https://apps.dtic.mil/sti/citations/ADA196234
Chugh T, Jin Y, Miettinen K, Hakanen J, Sindhya K (2018) A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization. IEEE Trans Evol Comput 22:129–142
Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization. Advanced information and knowledge processing. Springer, London. https://doi.org/10.1007/1-84628-137-7_6
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 10:477–506
Huband S, Barone L, While L, Hingston P (2005) A scalable multi-objective test problem toolkit. In: Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. EMO 2005, Lecture notes in computer science, vol 3410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31880-4_20
Cheng R, Jin Y, Narukawa K, Sendhoff B (2015) A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling. IEEE Trans Evol Comput 19:838–856
Cornell JA (2011) Experiments With Mixtures: Designs, Models, and the Analysis of Mixture Data. Wiley, Hoboken, NJ, USA
Habib A, Singh HK, Chugh T, Ray T, Miettinen K (2019) A multiple surrogate assisted decomposition-based evolutionary algorithm for expensive multi/many-objective optimization. IEEE Trans Evol Comput 23:1000–1013
Schonlau M (1997) Computer experiments and global optimization. Ph.D. dissertation, Department of Statistics & Actuarial Science - The University, Waterloo. https://uwspace.uwaterloo.ca/bitstream/handle/10012/190/nq22234.pdf?sequence=1
Knowles J (2006) ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput 10:50–66
Zhang Q, Liu W, Tsang E, Virginas B (2010) Expensive multiobjective optimization by MOEA/D with Gaussian process model. IEEE Trans Evol Comput 14:456–474
Zhan D, Cheng Y, Liu J (2017) Expected improvement matrix-based infill criteria for expensive multiobjective optimization. IEEE Trans Evol Comput 21:956–975
Akhtar T, Shoemaker CA (2016) Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection. J Glob Optim 64:17–32
Li F, Gao L, Shen W, Cai X, Huang S, A surrogate-assisted offspring generation method for expensive multi-objective optimization problems, (2020) IEEE Congress on Evolutionary Computation (CEC). Glasgow, UK 2020:1–8. https://doi.org/10.1109/CEC48606.2020.9185691
Chugh T, Sindhya K, Miettinen K, Hakanen J, Jin Y (2016) On constraint handling in surrogate-assisted evolutionary many-objective optimization. In: Handl J, Hart E, Lewis P, López-Ibáñez M, Ochoa G, Paechter B (eds) Parallel problem solving from nature – PPSN XIV. PPSN 2016, Lecture notes in computer science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_20
Pan L et al (2019) A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization. IEEE Trans Evol Comput 23:74–88
Hao H, Zhou A, Qian H, Zhang H (2022) Expensive multiobjective optimization by relation learning and prediction. IEEE Trans Evol Comput 26:1157–1170
Mckay MD, Beckman RJ, Conover WJ (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42:55–61
Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9:115–148
Byrd RH, Hribar ME, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. J Optim 9:877–900
McGill R, Tukey J, Larsen WA (1978) Variations of box plots. Am Stat 32:12–16
Tian Ye, Cheng R, Zhang X, Jin Y (2017) PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag 12:73–87
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 7:117–132
Steel RGD, Torrie JH, Dickey DA (1997) Principles and Procedures of Statistics a Biometrical Approach. McGraw-Hill, New York, NY, USA
Lophaven SN, Nielsen HB, Søndergaard J (2002) DACE: a Matlab kriging toolbox, vol 2. IMM, Informatics and Mathematical Modelling, The Technical University of Denmark, Lyngby
Sheskin D (2003) Handbook of Parametric and Nonparametric Statistical Procedures. Chapman & Hall, London, U.K.
Song Z, Wang H, He C, Jin Y (2021) A kriging-assisted two-archive evolutionary algorithm for expensive many-objective optimization. IEEE Trans Evol Comput 25:1013–1027
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Lin, J., Zhang, S.X. & Zheng, S.Y. A diverse/converged individual competition algorithm for computationally expensive many-objective optimization. Appl Intell 54, 2564–2581 (2024). https://doi.org/10.1007/s10489-024-05270-y
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DOI: https://doi.org/10.1007/s10489-024-05270-y