Abstract
In this paper, an adaptive version of \(\beta -\)hill climbing is proposed. In the original \(\beta -\)hill climbing, two control parameters are utilized to strike the right balance between a local-nearby exploitation and a global wide-range exploration during the search: \({\mathcal {N}}\) and \(\beta \), respectively. Conventionally, these two parameters require an intensive study to find their suitable values. In order to yield an easy-to-use optimization method, this paper proposes an efficient adaptive strategy for these two parameters in a deterministic way. The proposed adaptive method is evaluated against 23 global optimization functions. The selectivity analysis to determine the optimal progressing values of \({\mathcal {N}}\) and \(\beta \) during the search is carried out. Furthermore, the behavior of the adaptive version is analyzed based on various problems with different complexity levels. For comparative evaluation, the adaptive version is initially compared with the original one as well as with other local search-based methods and other well-regarded methods using the same benchmark functions. Interestingly, the results produced are very competitive with the other methods. In a nutshell, the proposed adaptive \(\beta -\)hill climbing is able to achieve the best results on 10 out of 23 test functions. For more validation, the test functions established in IEEE-CEC2015 are used with various scaling values. The comparative results show the viability of the proposed adaptive method.
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References
Abualigah LM, Khader AT, Al-Betar MA(2017a) \(\beta \)-hill climbing technique for the text document clustering. In: New trends in information technology NTIT2017 conference, Amman, Jordan. IEEE, pp 1–6
Abualigah LM, Khadery AT, Al-Betar MA, Alyasseri ZAA, Alomari OA,Hanandehk ES(2017b) Feature selection with \(\beta \)-hill climbing search for text clustering application. In: Second palestinian international conference on information and communication technology (PICICT 2017), Gaza, Palestine. IEEE, pp 22–27
Al-Betar MA, Awadallah MA, Bolaji AL, Alijla BO (2017) \(\beta \)-hill climbing algorithm for sudoku game. In: Second Palestinian international conference on information and communication technology (PICICT 2017), Gaza, Palestine. IEEE, pp 84–88
Al-Betar MA, Khader AT, Doush IA (2014) Memetic techniques for examination timetabling. Ann Oper Res 218(1):23–50
Al-Betar MA (2017) \(\beta \)-hill climbing: an exploratory local search. Neural Comput Appl 28(1):153–168
Al-Dujaili A, Subramanian K, Suresh S (2015) Humancog: a cognitive architecture for solving optimization problems. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 3220–3227
Aleti A, Moser I (2016) A systematic literature review of adaptive parameter control methods for evolutionary algorithms. ACM Comput Surv (CSUR) 49(3):56
Alsukni E, Arabeyyat OS, Awadallah MA, Alsamarraie L, Abu-Doush I, Al-Betar MA (2017) Multiple-reservoir scheduling using B-hill climbing algorithm. J Intell Syst. https://doi.org/10.1515/jisys-2017-0159
Alyasseri ZAA, Khader AT, Al-Betar MA (2017) Optimal EEG signals denoising using hybrid \(\beta \)-hill climbing algorithm and wavelet transform. In: ICISPC ’17, Penang, Malaysia. ACM, pp 5–11
Alyasseri ZAA, Khader AT, Al-Betar MA, Awadallah MA (2018) Hybridizing \(\beta \)-hill climbing with wavelet transform for denoising ECG signals. Inf Sci 429:229–246
Angeline PJ, Angeline PJ (1995) Adaptive and self-adaptive evolutionary computations. In: Computational intelligence: a dynamic systems perspective. IEEE Press, pp 152–163
Awad N, Ali MZ, Reynolds RG (2015) A differential evolution algorithm with success-based parameter adaptation for cec2015 learning-based optimization. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1098–1105
Awadallah MA, Al-Betar MA, Bolaji AL, Alsukhni EM, Al-Zoubi H (2018) Natural selection methods for artificial bee colony with new versions of onlooker bee. Soft Comput
Aydilek İB (2018) A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Appl Soft Comput 66:232–249
Aydın D, Sffltzle T (2015) A configurable generalized artificial bee colony algorithm with local search strategies. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1067–1074
Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv (CSUR) 35(3):268–308
BoussaïD I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117
Corana A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm corrigenda for this article is available here. ACM Trans Math Softw (TOMS) 13(3):262–280
Cui L, Li G, Luo Y, Chen F, Ming Z, Lu N, Lu J (2018) An enhanced artificial bee colony algorithm with dual-population framework. Swarm Evolut Comput 43:184–206
Dragoi E-N, Dafinescu V (2016) Parameter control and hybridization techniques in differential evolution: a survey. Artif Intell Rev 45(4):447–470
Eiben ÁE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evolut Comput 3(2):124–141
El-Abd M (2015) Hybrid cooperative co-evolution for the cec15 benchmarks. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1053–1058
Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Global Optim 6(2):109–133
Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549
Guo S-M, Tsai JS-H, Yang C-C, Hsu P-H (2015) A self-optimization approach for l-shade incorporated with eigenvector-based crossover and successful-parent-selecting framework on cec 2015 benchmark set. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1003–1010
Guo Z, Liu G, Li D, Wang S (2017) Self-adaptive differential evolution with global neighborhood search. Soft Comput 21(13):3759–3768
Guo Z, Yang H, Wang S, Zhou C, Liu X (2018) Adaptive harmony search with best-based search strategy. Soft Comput 22(4):1335–1349
Hansen P, Mladenovi’c N (1999) An introduction to variable neighborhood search. In: Voß S, Martello S, Osman IH, Roucairol C (eds) Metaheuristics: advances and trends in local search paradigms for optimization, chapter 30. Kluwer Academic Publishers, Dordrecht, pp 433–458
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(1):671–680
Leboucher C, Shin H-S, Chelouah R, Le Menec S, Siarry P, Formoso M, Tsourdos A, Kotenkoff A (2018) An enhanced particle swarm optimisation method integrated with evolutionary game theory. IEEE Transactions on Games, pp 1–11
Liang J, Qu B, Suganthan P, Chen Q (2014) Problem definitions and evaluation criteria for the cec 2015 competition on learning-based real-parameter single objective optimization. Technical Report201411A, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore
Liang J, Guo L, Liu R, Qu B (2015) A self-adaptive dynamic particle swarm optimizer. In: 2015 IEEE Congress on, Evolutionary Computation (CEC). IEEE, pp 3206–3213
Lourenço HR, Martin OC, Stützle T (2003) Iterated local search. In: Glover F, Kochenberger GA (eds) Handbook of Metaheuristics. International series in operations research & management science, vol 57. Springer, Boston, MA, pp 320–353
Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579
Mezura-Montes E, Palomeque-Ortiz AG (2009) Self-adaptive and deterministic parameter control in differential evolution for constrained optimization. Springer, Berlin, pp 95–120
Mirjalili S, Lewis A (2013) S-shaped versus v-shaped transfer functions for binary particle swarm optimization. Swarm Evolut Comput 9:1–14
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513
Molga M, Smutnicki C (2005) Test functions for optimization needs. In: Test functions for optimization needs
Noorbin SFEH, Alfi A (2018) Adaptive parameter control of search group algorithm using fuzzy logic applied to networked control systems. Soft Computing 22(23):7939–7960
Osman IH, Laporte G (1996) Metaheuristics: A bibliography. Ann Oper Res 63(5):511–623
Poláková R, Tvrdík J, Bujok P (2015) Cooperation of optimization algorithms: a simple hierarchical model. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1046–1052
Rueda JL, Erlich I (2015) Testing mvmo on learning-based real-parameter single objective benchmark optimization problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1025–1032
Sallam KM, Sarker RA, Essam DL, Elsayed SM (2015) Neurodynamic differential evolution algorithm and solving cec2015 competition problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1033–1040
Sörensen K (2015) Metaheuristics-the metaphor exposed. Int Trans Oper Res 22(1):3–18
Suganthan P, Hansen N, Liang J, Deb K, CY, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. In: Technical report, Nanyang Technological University, Nanyang
Tanweer MR, Suresh S, Sundararajan N (2017) Development of a higher order cognitive optimization algorithm. In: 2017 IEEE congress on evolutionary computation (CEC), pp 2752–2758
Wang H, Zhou X, Sun H, Yu X, Zhao J, Zhang H, Cui L (2017) Firefly algorithm with adaptive control parameters. Soft Comput 21(17):5091–5102
Wessing S, Preuss M, Rudolph G (2011) When parameter tuning actually is parameter control. In: Proceedings of the 13th annual conference on Genetic and evolutionary computation, ACM, pp 821–828
Xue Y, Jiang J, Zhao B, Ma T (2018) A self-adaptive artificial bee colony algorithm based on global best for global optimization. Soft Comput 22(9):2935–2952
Yu C, Kelley LC, Tan Y (2015) Dynamic search fireworks algorithm with covariance mutation for solving the CEC 2015 learning based competition problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1106–1112
Zhao H, Zhang C, Ning J (2019) A best firework updating information guided adaptive fireworks algorithm. Neural Comput Appl 31(1):79–99
Zheng Y-J, Wu X-B (2015) Tuning maturity model of ecogeography-based optimization on cec 2015 single-objective optimization test problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1018–1024
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Al-Betar, M.A., Aljarah, I., Awadallah, M.A. et al. Adaptive \(\beta -\)hill climbing for optimization. Soft Comput 23, 13489–13512 (2019). https://doi.org/10.1007/s00500-019-03887-7
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DOI: https://doi.org/10.1007/s00500-019-03887-7