Online algorithm configuration for differential evolution algorithm

Springer Science and Business Media LLC - Tập 52 - Trang 9193-9211 - 2022
Changwu Huang1, Hao Bai2, Xin Yao1
1Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China
2Laboratory of Mechanics of Normandy (LMN), INSA Rouen Normandie, Rouen, France

Tóm tắt

The performance of evolutionary algorithms (EAs) is strongly affected by their configurations. Thus, algorithm configuration (AC) problem, that is, to properly set algorithm’s configuration, including the operators and parameter values for maximizing the algorithm’s performance on given problem(s) is an essential and challenging task in the design and application of EAs. In this paper, an online algorithm configuration (OAC) approach is proposed for differential evolution (DE) algorithm to adapt its configuration in a data-driven way. In our proposed OAC, the multi-armed bandit algorithm is adopted to select trial vector generation strategies for DE, and the kernel density estimation method is used to adapt the associated control parameters during the evolutionary search process. The performance of DE algorithm using the proposed OAC (OAC-DE) is evaluated on a benchmark set of 30 bound-constrained numerical optimization problems and compared with several adaptive DE variants. Besides, the influence of OAC’s hyper-parameter on its performance is analyzed. The comparison results show OAC-DE achieves better average performance than the compared algorithms, which validates the effectiveness of the proposed OAC. The sensitivity analysis indicates that the hyper-parameter of OAC has little impact on OAC-DE’s performance.

Tài liệu tham khảo

Aleti A, Moser I (2016) A systematic literature review of adaptive parameter control methods for evolutionary algorithms. ACM Comput Surv 49(3) Ansótegui C, Sellmann M, Tierney K (2009) A gender-based genetic algorithm for the automatic configuration of algorithms. In: Gent IP (ed) Principles and practice of constraint programming - CP 2009. Springer, Berlin, pp 142–157 Auer P, Cesa-Bianchi N, Fischer P (2002) Finite-time analysis of the multiarmed bandit problem. Mach Learn 47(2-3):235–256 Awad NH, Ali MZ, Liang JJ, Qu BY, Suganthan PN (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization. Tech rep. Nanyang Technological University, Singapore Baker JE (1987) Reducing bias and inefficiency in the selection algorithm. In: Proceedings of the second international conference on genetic algorithms on genetic algorithms and their application, L Erlbaum Associates Inc., USA. 14–21 Balaprakash P, Birattari M, Stützle T (2007) Improvement strategies for the F-race algorithm: Sampling design and iterative refinement. In: Bartz-beielstein T, blesa aguilera MJ, Blum C, Naujoks B, Roli A, Rudolph G, Sampels M (eds) Hybrid metaheuristics. Springer, Berlin, pp 108–122 Birattari M, Stützle T, Paquete L, Varrentrapp K (2002) A racing algorithm for configuring metaheuristics. In: Proceedings of the 4th annual conference on genetic and evolutionary computation. Morgan Kaufmann Publishers Inc San Francisco, CA, USA, GECCO’02. 11–18 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 Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31 Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution–an updated survey. Swarm Evol Comput 27:1–30 Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30 Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18 Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141 Fan Q, Wang W, Yan X (2019) Differential evolution algorithm with strategy adaptation and knowledge-based control parameters. Artif Intell Rev 51(2):219–253 Gong W, Fialho Á, Cai Z, Li H (2011) Adaptive strategy selection in differential evolution for numerical optimization: An empirical study. Inf Sci 181(24):5364–5386 Gramacki A (2018) Kernel density estimation. In: Kacprzyk J (ed) Nonparametric kernel density estimation and its computational aspects. Springer International Publishing, Cham, pp 25–62 Hoos HH (2012) Automated algorithm configuration and parameter tuning. In: Hamadi Y, Monfroy E, Saubion F (eds) Autonomous Search. Springer, pp 37–71 Huang C, Yuan B, Li Y, Yao X (2019) Automatic parameter tuning using bayesian optimization method. IEEE Congr. Evol. Comput. Wellington, New Zealand. 2090–2097 Huang C, Li Y, Yao X (2020) A survey of automatic parameter tuning methods for metaheuristics. IEEE Trans Evol Comput 24(2):201–216 Hutter F, Hoos HH, Leytonbrown K, Stutzle T (2009) ParamILS: an automatic algorithm configuration framework. J Artif Intell Res 36(1):267–306 Hutter F, Hoos HH, Leyton-Brown K (2011) Sequential model-based optimization for general algorithm configuration. In: Coello CAC (ed) Learning and intelligent optimization. Springer, Heidelberg, pp 507–523 Iorio AW, Li X (2005) Solving rotated multi-objective optimization problems using differential evolution. In: Webb GI, Yu X (eds) AI: 2004 advances in artificial intelligence. Springer, Berlin, pp 861–872 Jerebic J, Mernik M, Liu SH, Ravber M, Baketarić M, Mernik L, Črepinšek M (2021) A novel direct measure of exploration and exploitation based on attraction basins. Expert Syst Appl 114353:167 Karafotias G, Hoogendoorn M, Eiben AE (2015) Parameter control in evolutionary algorithms: Trends and challenges. IEEE Trans Evol Comput 19(2):167–187 Koulouriotis D, Xanthopoulos A (2008) Reinforcement learning and evolutionary algorithms for non-stationary multi-armed bandit problems. Appl Math Comput 196(2):913–922 Liu SH, Mernik M, Hrnčič D, Črepinšek M (2013) A parameter control method of evolutionary algorithms using exploration and exploitation measures with a practical application for fitting sovova’s mass transfer model. Appl Soft Comput 13(9):3792–3805 Lu X, Tang K, Sendhoff B, Yao X (2014) A new self-adaptation scheme for differential evolution. Neurocomputing 146:2–16 Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696 Mallipeddi R, Wu G, Lee M, Suganthan PN (2014) Gaussian adaptation based parameter adaptation for differential evolution. In: 2014 IEEE congress on evolutionary computation (CEC), pp 1760–1767 Montgomery J, Chen S (2010) An analysis of the operation of differential evolution at high and low crossover rates. IEEE Congr Evol Comput Barcelona, Spain. 1–8 Müller C L, If Sbalzarini (2010) Gaussian adaptation revisited – an entropic view on covariance matrix adaptation. In: Di chio C, Cagnoni S, Cotta C, Ebner M, Ekárt A, Esparcia-Alcazar AI, Goh CK, Merelo JJ, Neri F, Preuß M, Togelius J, Yannakakis GN (eds) Applications of evolutionary computation. Springer, Berlin, pp 432–441 Nannen V, Eiben A (2006) A method for parameter calibration and relevance estimation in evolutionary algorithms. In: Proceedings of the 8th annual conference on genetic and evolutionary computation, association for computing machinery, New York, NY, USA, GECCO ’06. p 183–190 Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimentalanalysis. Artif Intell Rev 33(1-2):61–106 Opara K, Arabas J (2018) Comparison of mutation strategies in differential evolution – a probabilistic perspective. Swarm Evol Comput 39:53–69 Opara KR, Arabas J (2019) Differential evolution: a survey of theoretical analyses. Swarm Evol Comput 44:546–558 Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33 (3):1065–1076 Price KV, Storn RM, Lampinen JA (2005) The differential evolution algorithm. In: Rozenberg G, Bäck T, Eiben A, Kok J, Spaink H (eds). Springer, Berlin, pp 37–134 Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: IEEE Congr. Evol. Comput., Edinburgh, Scotland, UK, vol 2, pp 1785–1791 vol. 2 Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417 Santucci V, Milani A (2011) Covariance-based parameters adaptation in differential evolution. In: Proceedings of the 13th Annual conference companion on genetic and evolutionary computation, association for computing machinery, New York, NY, USA, GECCO ’11. 687–690 Shahriari B, Swersky K, Wang Z, Adams RP, de Freitas N (2016) Taking the human out of the loop: a review of bayesian optimization. Proc IEEE 104(1):148–175 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 Sutton RS, Barto AG (2018) Reinforcement learning: An introduction. MIT Press, Cambridge Swami A, jain R (2013) Scikit-learn: Machine learning in python. J Mach Learn Res 12 (10):2825–2830 Veček N, Mernik M, Filipič B, Črepinšek M (2016) Parameter tuning with chess rating system (CRS-tuning) for meta-heuristic algorithms. Inf Sci 372:446–469 Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66 Yang Z, Tang K, Yao X (2008a) Self-adaptive differential evolution with neighborhood search. IEEE Congr Evol Comput. Hong Kong, China, 1110–1116 Yang Z, Yao X, He J (2008b) Making a difference to differential evolution. In: Siarry P, Michalewicz Z (eds) Advances in metaheuristics for hard optimization. springer, Berlin, pp 397– 414 Yang Z, Tang K, Yao X (2011) Scalability of generalized adaptive differential evolution for large-scale continuous optimization. Soft Comput 15(11):2141–2155 Yu W, Shen M, Chen W, Zhan Z, Gong Y, Lin Y, Liu O, Zhang J (2014) Differential evolution with two-level parameter adaptation. IEEE Trans Cybern 44(7):1080–1099 Zhang J, Sanderson AC (2009) JADE: Adaptive Differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958