# zbMATH — the first resource for mathematics

Single-solution simulated Kalman filter algorithm for global optimisation problems. (English) Zbl 1397.90304
Summary: This paper introduces single-solution simulated Kalman filter (ssSKF), a new single-agent optimisation algorithm inspired by Kalman filter, for solving real-valued numerical optimisation problems. In comparison, the proposed ssSKF algorithm supersedes the original population-based simulated Kalman filter (SKF) algorithm by operating with only a single agent, and having less parameters to be tuned. In the proposed ssSKF algorithm, the initialisation parameters are not constants, but they are produced by random numbers taken from a normal distribution in the range of $$[0,1]$$, thus excluding them from tuning requirement. In order to balance between the exploration and exploitation in ssSKF, the proposed algorithm uses an adaptive neighbourhood mechanism during its prediction step. The proposed ssSKF algorithm is tested using the 30 benchmark functions of CEC 2014, and its performance is compared to that of the original SKF algorithm, black hole (BH) algorithm, particle swarm optimisation (PSO) algorithm, grey wolf optimiser (GWO) algorithm and genetic algorithm (GA). The results show that the proposed ssSKF algorithm is a promising approach and able to outperform GWO and GA algorithms, significantly.
##### MSC:
 90C26 Nonconvex programming, global optimization 65K05 Numerical mathematical programming methods 93E11 Filtering in stochastic control theory 90C59 Approximation methods and heuristics in mathematical programming
CEC 13; KEEL
Full Text:
##### References:
 [1] Talbi E 2009 Metaheuristics. Hoboken, NJ: John Wiley & Sons · Zbl 1190.90293 [2] Droste, S; Jansen, T; Wegener, I, Upper and lower bounds for randomized search heuristics in black-box optimisation, Theor. Comput. Syst., 39, 525-544, (2006) · Zbl 1103.68115 [3] Holland J 1992 Adaptation in natural and artificial systems. Cambridge, MA: The MIT Press [4] Kennedy J and Eberhart R Particle swarm optimisation. In: Proceedings of the IEEE International Conference on Neural Networks, December 1995, pp. 1942-1948 [5] Wolpert, DH; Macready, WG, No free lunch theorems for optimisation, IEEE Trans. Evol. Comput., 1, 67-82, (1997) [6] Boussaid, I; Lepagnot, J; Siarry, P, A survey on optimisation metaheuristics, Inf. Sci., 237, 82-117, (2013) · Zbl 1321.90156 [7] Parejo, JA; Ruiz-Cortes, A; Lozano, S; Fernandez, P, Metaheuristic optimisation frameworks: a survey and benchmarking, Soft Comput., 16, 527-561, (2012) [8] Fister Jr. I, et al 2013 A brief review of nature-inspired algorithms for optimisation. Elektroteh. Vestn. [Engl.] 80(3): 1-7 [9] Hatamlou, A, Black hole: a new heuristic optimisation approach for data clustering, Inf. Sci., 222, 175-184, (2013) [10] Mirjalili, S; Mirjalili, SM; Lewis, A, Grey wolf optimiser, Adv. Eng. Softw., 69, 46-61, (2014) [11] Ibrahim, Z; etal., A Kalman filter approach for solving unimodal optimisation problems, ICIC Express Lett., 9, 3415-3422, (2015) [12] Kirkpatrick, S; Gelatt, CD; Vecchi, M, Optimisation by simulated annealing, Science, 220, 671-680, (1983) · Zbl 1225.90162 [13] Glover, F, Future paths for integer programming and links to artificial intelligence, Comput. Oper. Res., 13, 533-549, (1986) · Zbl 0615.90083 [14] Mladenovic, N; Hansen, P, Variable neighborhood search, Comput. Oper. Res., 24, 1097-1100, (1997) · Zbl 0889.90119 [15] Dorigo M 1992 Optimisation, learning and natural algorithms. Ph.D. dissertation, Politecnico di Milano, Italy [16] Yang, X, Firefly algorithm, stochastic test functions and design optimisation, Int. J. Bio-Inspir. Comput., 2, 78-84, (2010) [17] Yang X and Deb S 2009 Cuckoo search via Levy flights. In: Proceedings of the World Congress on Nature and Biologically Inspired Computing (NaBIC 2009), India, pp. 210-214 [18] Mirjalili, S, SCA: a sine cosine algorithm for solving optimisation problems, Knowl.-Based Syst., 96, 120-133, (2016) [19] Ibrahim, Z; etal., Simulated Kalman filter: a novel estimation-based metaheuristic optimisation algorithm, Adv. Sci. Lett., 22, 2941-2946, (2016) [20] Kalman R E 1960 A new approach to linear filtering and prediction problems. J. Basic Eng. 82(Ser. D): 35-45 [21] Md Yusof, Z; etal., Angle modulated simulated Kalman filter algorithm for combinatorial optimisation problems, ARPN J. Eng. Appl. Sci., 11, 4854-4859, (2016) [22] Md Yusof, Z; etal., Distance evaluated simulated Kalman filter algorithm for combinatorial optimisation problems, ARPN J. Eng. Appl. Sci., 11, 4911-4916, (2016) [23] Md Yusof Z, Ibrahim I, Satiman S N, Ibrahim Z, Abdul Aziz N H and Ab. Aziz N A 2015 BSKF: binary simulated Kalman Filter. In: Proceedings of the 2015 3rd International Conference on Artificial Intelligence, Modelling and Simulation (AIMS), pp. 77-81 [24] Muhammad, B; etal., A new hybrid simulated Kalman filter and particle swarm optimisation for continuous numerical optimisation problems, ARPN J. Eng. Appl. Sci., 10, 17171-17176, (2015) [25] Muhammad B, Ibrahim Z, Mohd Azmi K Z, Abas K H, Ab. Aziz N A, Abdul Aziz N H and Mohamad M S 2016 Four different methods to hybrid simulated Kalman filter (SKF) with gravitational search algorithm (GSA). In: Proceedings of the 3rd National Conference of Postgraduate Research, pp. 854-864 [26] Abdul Aziz N H, Ab. Aziz N A, Ibrahim Z, Razali S, Abas K H and Mohamad M S A Kalman Filter approach to PCB drill path optimisation problem. In: Proceedings of the IEEE Conference on Systems, Process and Control, December 2016, pp. 33-36 [27] Md Yusof Z, Satiman S N, Muhammad B, Razali S, Ibrahim Z, Aspar Z and Ismail S 2015 Solving airport gate allocation problem using simulated Kalman Filter. In: Proceedings of the International Conference on Knowledge Transfer (ICKT’15), Malaysia, December 2015, pp. 121-127 [28] Mohd Azmi K Z, Md Yusof Z, Satiman S N, Ibrahim Z, Ab. Aziz N A and Abdul Aziz N H 2016 Solving airport gate allocation problem using angle modulated simulated Kalman filter. In: Proceedings of the 3rd National Conference of Postgraduate Research, September, pp. 875-885 [29] Adam, A; etal., Feature selection using angle modulated simulated Kalman filter for peak classification of EEG signals, SpringerPlus, 5, 1580-1603, (2016) [30] Hansen N, Ostermeier A and Gawelczyk A 1995 On the adaptation of arbitrary normal mutation distributions in evolution strategies: the generating set adaptation. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 57-64 [31] Storn, R; Price, K, Differential evolution a simple and efficient heuristic for global optimisation over continuous spaces, J. Global Optim., 11, 341-359, (1997) · Zbl 0888.90135 [32] Cheng, M; Prayogo, D, Symbiotic organisms search: a new metaheuristic optimisation algorithm, Comput. Struct., 139, 98-112, (2014) [33] Abdul Aziz N H, Ibrahim Z, Ab. Aziz N A and Razali S 2017 Parameter-less simulated Kalman Filter. Int. J. Softw. Eng. Comput. Syst. (IJSECS) 3(February): 129-137 [34] Abdul Aziz N H, Ibrahim Z, Bakare T A and Ab. Aziz N A 2016 How important the error covariance in simulated Kalman Filter? In: Proceedings of the National Conference for Postgraduate Research, September, pp. 315-320 [35] Liang J J, Qu B Y and Suganthan P N 2013 Problems definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimisation. Tech. Rep. 201311, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China, and Tech. Rep., Nanyang Technological University, Singapore [36] Suganthan P N 2016 Shared documents [online]. Available: http://web.mysites.ntu.edu.sg/epnsugan/PublicSite/Shared%20Documents/CEC-2014/cec14-matlab-code.zip [37] Eberhart R C and Shi Y 2000 Comparing inertia weights and constriction factors in particle swarm optimisation. In: Proceedings of the 2000 Congress on Evolutionary Computation, July, pp. 84-88 [38] Mirjalili S 2016 Seyedali Mirjalili homepage [online]. Available: http://www.alimirjalili.com/GWO.html [39] Haupt R L and Haupt S E 2004 Practical genetic algorithms. Hoboken, NJ: John Wiley & Sons · Zbl 1072.68089 [40] Alcala-Fdez, J; etal., KEEL: a software tool to assess evolutionary algorithms for data mining problems, Soft Comput., 13, 307-318, (2008)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.