Abstract
The analytical study of large-scale linear time-invariant systems is a very tedious and complicated task in a category of real-life optimization problems. So, simplification procedures for these complex problems are needed. In the solution tactic of this complex problem, Model Order Reduction (MOR) is a novel concept providing a simpler model than the original one based on mathematical approximation. In literature, several meta-heuristics are employed to solve MOR problem. In the same line of order, this chapter presents a technique to solve MOR problem using modified BAT algorithm based on levy flight and opposition based learning. The concept of Levy flight random walk and opposition based learning (OBL) is embedded to BAT algorithm (BA) to avoid local optima trapping and to enhance the exploitation and exploration ability. To evaluate the performance of the proposed methodology, it is tested over three different MOR problems of different transfer functions. The numerical and statistical results confirmed the supremacy of the proposed variant in terms of stability of reduced order systems.
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References
Davison E (1966) A method for simplifying linear dynamic systems. IEEE Trans Autom Control 11(1):93–101
Chidambara MR (1969) Two simple techniques for the simplification of large dynamic systems. Jt Autom Control Conf 7:669–674
Shamash Y (1974) Stable reduced-order models using Padé-type approximations. IEEE Trans Autom Control 19(5):615–616
Hutton M, Friedland B (1975) Routh approximations for reducing order of linear, time-invariant systems. IEEE Trans Autom Control 20(3):329–337
Bistritz Y, Langholz G (1979) Model reduction by Chebyshev polynomial techniques. IEEE Trans Autom Control 24(5):741–747
Sinha NK, Kuszta B (1983) Modelling and identification of dynamic systems. Springer
Krishnamurthy V, Seshadri V (1978) Model reduction using the Routh stability criterion. IEEE Trans Autom Control 23(4):729–731
Lucas TN (1983) Factor division: a useful algorithm in model reduction. IEE Proc D: Control Theory Appl 130(6):362–364 (Institution of Electrical Engineers (IEE))
Prasad R, Pal J, Pant AK (1995) Multivariable system approximation using polynomial derivatives. Inst Eng India Part EL Electr Eng Div 76:186–186
Wilson DA (1970) Optimum solution of model-reduction problem. Proc Inst Electr Eng 117(6):1161–1165 (IET)
Wilson DA, Mishra RN (1979) Optimal reduction of multivariable systems. Int J Control 29(2):267–278
Sivanandam SN, Deepa SN (2009) A comparative study using genetic algorithm and particle swarm optimization for lower order system modelling. Int J Computer Internet Manag 17(3):1–10
Panda S, Yadav JS, Patidar NP, Ardil C (2009) Evolutionary techniques for model order reduction of large scale linear systems. Int J Appl Sci Eng Technol 5(1):22–28
Desai SR, Prasad R (2013) A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation. Appl Math Model 37(16–17):8016–8028
Biradar S, Hote YV, Saxena S (2016) Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method. Appl Math Model 40(15–16):7225–7244
Dinkar SK, Deep K (2019) Accelerated opposition-based antlion optimizer with application to order reduction of linear time-invariant systems. Arab J Sci Eng 44(3):2213–2241
Sikander A, Thakur P (2018) Reduced order modelling of linear time-invariant system using modified cuckoo search algorithm. Soft Comput 22(10):3449–3459
Saxena A (2019) A comprehensive study of chaos embedded bridging mechanisms and crossover operators for grasshopper optimisation algorithm. Expert Syst Appl 132:166–188
Shekhawat S, Saxena A (2019) Development and applications of an intelligent crow search algorithm based on opposition based learning. ISA Trans
Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, Heidelberg, pp 65–74
Bora TC, Coelho LDS, Lebensztajn L (2012) Bat-inspired optimization approach for the brushless DC wheel motor problem. IEEE Trans Magn 48(2):947–950
Mishra S, Shaw K, Mishra D (2012) A new meta-heuristic bat inspired classification approach for microarray data. Procedia Technol 4:802–806
Musikapun P, Pongcharoen P (2012) Solving multi-stage multi-machine multi-product scheduling problem using bat algorithm. In: 2nd international conference on management and artificial intelligence, vol 35. IACSIT Press, Singapore, pp 98–102
Zhang JW, Wang GG (2012) Image matching using a bat algorithm with mutation. Appl Mech Mater 203:88–93 (Trans Tech Publications)
Ali ES (2014) Optimization of power system stabilizers using BAT search algorithm. Int J Electr Power Energy Syst 61:683–690
Sathya MR, Ansari MMT (2015) Load frequency control using Bat inspired algorithm based dual mode gain scheduling of PI controllers for interconnected power system. Int J Electr Power Energy Syst 64:365–374
Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math
Gandomi AH, Yang XS (2014) Chaotic bat algorithm. J Comput Sci 5(2):224–232
Satapathy SC, Raja NSM, Rajinikanth V, Ashour AS, Dey N (2018) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29(12):1285–1307
Adarsh BR, Raghunathan T, Jayabarathi T, Yang XS (2016) Economic dispatch using chaotic bat algorithm. Energy 96:666–675
Reddy KH, Hemakesavulu O (2013) Economic load dispatch problem with valve—point effect using a binary bat algorithm
Sabba S, Chikhi S (2014) A discrete binary version of bat algorithm for multidimensional knapsack problem. Int J Bio-inspired Comput 6(2):140–152
Zhou Y, Xie J, Li L, Ma M (2014) Cloud model bat algorithm. Sci World J
Fister I, Fong S, Brest J, Fister I (2014) A novel hybrid self-adaptive bat algorithm. Sci World J 12
Fister I Jr, Fong S, Brest J, Fister I (2014) Towards the self-adaptation of the bat algorithm. In: Proceedings of the 13th IASTED international conference on artificial intelligence and applications (AIA 2014) Innsbruck. IASTED, pp 400–406, Feb 2014
Raghunathan T, Ghose D (2014) Differential evolution based 3-D guidance law for a realistic interceptor model. Appl Soft Comput 16:20–33
Fister I, Yang XS, Fong S, Zhuang Y (2014) Bat algorithm: recent advances. In: 2014 IEEE 15th international symposium on computational intelligence and informatics (CINTI). IEEE, pp 163–167, Nov 2014
Jayabarathi T, Raghunathan T, Gandomi AH (2018) The bat algorithm, variants and some practical engineering applications: a review. In: Nature-inspired algorithms and applied optimization. Springer, Cham, pp 313–330
Yang XS (2013) Bat algorithm: literature review and applications. arXiv:1308.3900
Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06) vol 1. IEEE, pp 695–701, Nov 2005
Tizhoosh HR, Ventresca M (eds) (2008) Oppositional concepts in computational intelligence, vol 155. Springer
Saxena A, Soni BP, Kumar R, Gupta V (2018) Intelligent grey wolf optimizer—development and application for strategic bidding in uniform price spot energy market. Appl Soft Comput 69:1–13
Sharma P, Saxena A, Soni BP, Kumar R, Gupta V (2018) An intelligent energy bidding strategy based on opposition theory enabled grey wolf optimizer. In: 2018 international conference on power, instrumentation, control and computing (PICC). IEEE, pp 1–6, Jan 2018
Mahdavi S, Rahnamayan S, Deb K (2018) Opposition based learning: a literature review. Swarm Evol Comput 39:1–23
Sahba F, Tizhoosh HR, Salama MM (2007) Application of opposition-based reinforcement learning in image segmentation. In: 2007 IEEE symposium on computational intelligence in image and signal processing. IEEE, pp 246–251, Apr 2007
Wang GG, Deb S, Gandomi AH, Alavi AH (2016) Opposition-based krill herd algorithm with Cauchy mutation and position clamping. Neurocomputing 177:147–157
Alamri HS, Alsariera YA, Zamli KZ (2018) Opposition-based whale optimization algorithm. Adv Sci Lett 24(10):7461–7464
Sarkhel R, Chowdhury TM, Das M, Das N, Nasipuri M (2017) A novel harmony search algorithm embedded with metaheuristic opposition based learning. J Intell Fuzzy Syst 32(4):3189–3199
Reynolds AM, Frye MA (2007) Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PloS One 2(4):e354
Yang XS, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40(6):1616–1624
Haklı H, Uğuz H (2014) A novel particle swarm optimization algorithm with Levy flight. Appl Soft Comput 23:333–345
Candela R, Cottone G, Scimemi GF, Sanseverino ER (2010) Composite laminates buckling optimization through Lévy based ant colony optimization. In: International conference on industrial, engineering and other applications of applied intelligent systems. Springer, Berlin, Heidelberg, pp 288–297, June 2010
Cottone G, Scimemi GF, Pirrotta A, Sanseverino ER (2010) Damage Identification by Lévy ant colony optimization. In: Straub D (ed) Reliability and optimization of structural systems, proceedings of IFIP WG7.5 conference
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Shekhawat, S., Saxena, A., Kumar, R., Singh, V.P. (2021). Levy Flight Opposition Embedded BAT Algorithm for Model Order Reduction. In: Dey, N., Rajinikanth, V. (eds) Applications of Bat Algorithm and its Variants. Springer Tracts in Nature-Inspired Computing. Springer, Singapore. https://doi.org/10.1007/978-981-15-5097-3_6
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