Abstract
In this study a recently introduced algorithm, based on foraging process of butterflies known as butterfly optimization algorithm (BOA) is explored and a modified variant is introduced. The framework of BOA is based on the fragrance emitted by the butterflies, which helps other butterflies in searching food as well as in identifying a mating partner. BOA performs both the local and global search while seeking for the global optimal solution for the problem. Despite this BOA sometime stuck in a local optima which results in a slow or poor convergence. This study embeds the bidirectional search in the structure of BOA. This helps to perform the local search in forward as well as backward direction. Greedy selection is performed, while selecting the direction. If the solution improves while traversing backward then backward traverse is adapted otherwise forward. The proposed variant is termed as bidirectional butterfly optimization algorithm (BBOA). This modification facilitate in accelerating the convergence rate of BOA, which is verified and validated by statistical and comparative results on a set of CEC2006 and CEC2014 benchmark problems. Non-parametric statistical tests are performed to analyze the results. Further the method is investigated to solve eight reliability optimization problems. Experimental results demonstrate the competitiveness of BBOA.










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Afonso LD, Mariani VC, Coelho L, dos Santos (2013) Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization. Expert Syst Appl 40(9):3794–3802
Ahandani MA, Shirjoposh NP, Banimahd R (2011) Three modified versions of differential evolution algorithm for continuous optimization. Soft Comput 15:803–830
Arora S, Singh S (2015) Butterfly algorithm with Lèvy Flights for global optimization. In: proceedings of International Conference on Signal Processing, Computing and Control (ISPCC), pp. 220–224
Arora S, Singh S (2019) Butterfly optimization algorithm. Soft Comput 23:715–734
Beji N, Jarboui B, Eddaly M, Chabchoub H (2010) A hybrid particle swarm optimization algorithm for the redundancy allocation problem. J Comput Sci 1(3):159–167
Chang KH, Kuo PY (2018) An efficient simulation optimization method for the generalized redundancy allocation problem. Eur J Oper Res 265(3):1094–1101
Chen TC (2006) IAs based approach for reliability redundancy allocation problems. Appl Math Comput 182(2):1556–1567
Chern MS (1992) On the computational complexity of reliability redundancy allocation in a series system. Oper Res Lett 11(5):309–315
Chidambaram C, Lopes HS (2010) An improved artificial bee colony algorithm for the object recognition problem in complex digital images using template matching. Int J Nat Comput Res 1(2):54–70. https://doi.org/10.4018/jncr.2010040104
Coelho L, dos Santos (2009) An efficient particle swarm approach for mixed-integer programming in reliability–redundancy optimization applications. Reliab Eng Syst Saf 94(4):830–837
Coelho L, dos Santos (2009) Reliability–redundancy optimization by means of a chaotic differential evolution approach. Chaos Solitons Fractals 41(2):594–602
Garcia S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour. J Heuristics 15:617–644
Garg H, RaniSharma S (2013) An efficient two phase approach for solving reliability–redundancy allocation problem using artificial bee colony technique. Comput Oper Res 40(12):2961–2969
Gen M, Ida K, Kobuchi R, Lee C (1998) Hybridized neural network and genetic algorithms for solving nonlinear integer programming. In: Proceedings Second International Conference on Knowledge-Based Intelligent Electronic Systems
Gen M, Yun Y (2006) Soft computing approach for reliability optimization: State-of-the-art survey. Reliab Eng Syst Saf 91(9):1008–1026
Ghambari S, Rahati A (2018) An improved artificial bee colony algorithm and its application to reliability optimization problems. Appl Soft Comput 62:736–767
Li Guocheng, Fei Shuang, Pan Zhao (2019) An improved butterfly optimization algorithm for engineering design problems using the cross-entropy method. Symmetry 11:1049. https://doi.org/10.3390/sym11081049
Hemmati M, Amiri M, Zandieh M (2018) Optimization redundancy allocation problem with non exponential repairable components using simulation approach and artificial neural network. Qual Reliab Eng Int 34(3):278–297
Hsieh YC, Chen TC, Bricker DL (1998) Genetic algorithms for reliability design problems. Microelectron Reliab 38(10):1599–1605
Hsieh YC, Chen TC, Bricker DL (1998) Genetic algorithms for reliability design problems. Microelectronics Reliability 38(10):1599–1605.
Huang X, Coolen FPA, Coolen-Maturi T (2019) A heuristic survival signature based approach for reliability-redundancy allocation. Reliab Eng Syst Saf 185:511–517
Kanagaraj G, Ponnambalam S, Jawahar N (2013) A hybrid cuckoo search and genetic algorithm for reliability–redundancy allocation problems. Comput Ind Eng 66(4):1115–1124
Karaboga D, Akay B (2011) A modified artificial bee colony (abc) algorithm for constrained optimization problems. Appl Soft Comput 11(3):3021–3031
Kemal Aygül, Murat Cikan, Tuğçe Demirdelen, Mehmet Tumay (2019) Butterfly optimization algorithm based maximum power point tracking of photovoltaic systems under partial shading condition. Part A: Recovery, Utilization, and Environmental Effects. J Energy Sour. https://doi.org/10.1080/15567036.2019.1677818
Kim HG, Bae CO, Park DJ (2006) Reliability-redundancy optimization using simulated annealing algorithms. J Qual Maint Eng 12(4):354–363
Kuo W, Lin HH, Xu Z, Zhang W (1987) Reliability optimization with the lagrange-multiplier and branchand-bound technique. IEEE Trans Reliab R 36(5):624–630
Kuo W, Parsad VR, Tillman FA, Hwang CL (2001) Optimal reliability design fundamentals and applications. Cambridge University Press, Cambridge
Kuo W, Prasad VR (2000) An annotated overview of system-reliability optimization. IEEE Trans Reliab 49(2):176–187
Kwo W, Wan R (2007) Recent advances in optimal reliability allocation. IEEE Trans Reliab Man Cybern 37(2):143–156
Lalwani S, Sharma H, Verma A, Kumar R (2019) Efficient discrete firefly algorithm for Ctrie based caching of multiple sequence alignment on optimally scheduled parallel machines. CAAI TransIntell Technol 4(2):92–100
Liang J, Qu B, Suganthan P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Computational intelligence laboratory.
Liang J, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan P, Coello CC, Deb K (2006) Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. J Appl Mech 41:1–8
Liang Y, Wan Z, Fang D (2015) An improved artificial bee colony algorithm for solving constrained optimization problems. Int J Mach Learn Cyber. https://doi.org/10.1007/s13042-015-0357-2
Liao TW (2010) Two hybrid differential evolution algorithms for engineering design optimization. Appl Soft Comput 10(4):1188–1199
Liu Y, Qin G (2015) A DE algorithm combined with Lévy flight for reliability redundancy allocation problems. Int J Hybrid Inf Technol 8(5):113–118
Luus R (1975) Optimization of system reliability by a new nonlinear integer programming procedure. IEEE Trans Reliab 24(1):14–16
Mezura-Montes E, Coello CAC (2005) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evol Comput 9(1):1–17
Munoz Zavala AE, Aguirre AH, Villa Diharce ER (2005) Constrained optimization via particle evolutionary swarm optimization algorithm (peso). In: Proceedings of the 2005 conference on genetic and evolutionary computation, USA, pp 209–216
Nahas N, Thien-My D (2010) Harmony search algorithm. Eng Optim 42(9):845–861
Ouyang HB, Gao LQ, Li S, Kong XY (2015) Improved novel global harmony search with a new relaxation method for reliability optimization problems. Inf Sci 305:14–55
Park YW (2020) MILP models for complex system reliability redundancy allocation with mixed components. INFORMS J Comput
Sahu PC, Prusty RC, Panda S (2020) Improved-GWO designed FO based type-II fuzzy controller for frequency awareness of an AC microgrid under plug in electric vehicle. J Ambient Intell Hum Comput. https://doi.org/10.1007/s12652-020-02260-z
Sangaiah AK, Goli A, Tirkolaee EB, Ranjbar-Bourani M, Pandey HM, Zhang W (2020) Big data-driven cognitive computing system for optimization of social media analytics. IEEE Access 8:82215–82226
Sangaiah AK, Tirkolaee EB, Goli A, Dehnavi-Arani S (2020) Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem. Soft Comput 24:7885–7905
Shakila R, Paramasivan B (2020) An improved range based localization using Whale Optimization Algorithm in underwater wireless sensor network. J Ambient Intell Hum Comput. https://doi.org/10.1007/s12652-020-02263-w
Sharma TK, Abraham A (2020) Artificial bee colony with enhanced food locations for solving mechanical engineering design problems. Ambient Intell Humaniz Comput 11:267–290
Sheikhalishahi M, Ebrahimipour V, Shiri H, Zaman H, Jeihoonian M (2013) A hybrid GA–PSO approach for reliability optimization in redundancy allocation problem. Int J Adv Manuf Technol 68(1–4):317–338
Tavakkoli-Moghaddam R, Safari J, Sassani F (2008) Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliab Eng Syst Saf 93(4):550–556
Tirkolaee EB, Alinaghian M, Asghar A, Hosseinabadi R, Sasi MB, Sangaiah AK (2019) An improved ant colony optimization for the multi-trip Capacitated Arc Routing Problem. Comput Electr Eng 77:457–470
Tirkolaee EB, Mahmoodkhani J, Bourani MR, Tavakkoli-Moghaddam R (2019) A self-learning particle swarm optimization for robust multi-echelon capacitated location–allocation–inventory problem. J Adv Manuf Syst 18(4):677–694
Valian E, Tavakoli S, Mohanna S, Haghi A (2013) Improved cuckoo search for reliability optimization problems. Comput Ind Eng 64(1):459–468
Valian E, Valian E (2013) A cuckoo search algorithm by Lévy flights for solving reliability redundancy allocation problems. Eng Optim 45(11):1273–1286
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82
Wu P, Gao L, Zou D, Li S (2011) An improved particle swarm optimization algorithm for reliability problems. ISA Trans 50(1):71–81
Yeh WC, Hsieh TJ (2011) Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Comput Oper Res 38(11):1465–1473
Zhi Yuan, Weiqing Wang, Haiyun Wang (2019) Improved butterfly optimization algorithm for CCHP driven by PEMFC. Appl Thermal Eng. https://doi.org/10.1016/j.applthermaleng.2019.114766
Yun WY, Song YM, Kim HG (2007) Multiple multi-level redundancy allocation in series systems. Reliab Eng Syst Saf 92(3):308–313
Yun-Chia L, Smith AE (2004) An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Trans Reliab 53(3):417–423
Zou D, Gao L, Li S, Wu (2011) An effective global harmony search algorithm for reliability problems. Expert Syst Appl 38(4):4642–4648
Zou D, Gao L, Wu J, Li S, Li Y (2010) A novel global harmony search algorithm for reliability problems. Comput Ind Eng 58(2):307–316
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Sharma, T.K. Enhanced butterfly optimization algorithm for reliability optimization problems. J Ambient Intell Human Comput 12, 7595–7619 (2021). https://doi.org/10.1007/s12652-020-02481-2
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DOI: https://doi.org/10.1007/s12652-020-02481-2