zbMATH — the first resource for mathematics

Operational framework for recent advances in backtracking search optimisation algorithm: a systematic review and performance evaluation. (English) Zbl 1433.90201
Summary: Backtracking search optimisation algorithm (BSA) is a commonly used meta-heuristic optimisation algorithm and was proposed by P. Civicioglu [ibid. 219, No. 15, 8121–8144 (2013; Zbl 1288.65092)]. When it was first used, it exhibited its strong potential for solving numerical optimisation problems. Additionally, the experiments conducted in previous studies demonstrated the successful performance of BSA and its non-sensitivity toward the several types of optimisation problems. This success of BSA motivated researchers to work on expanding it, e.g., developing its improved versions or employing it for different applications and problem domains. However, there is a lack of literature review on BSA; therefore, reviewing the aforementioned modifications and applications systematically will aid further development of the algorithm. This paper provides a systematic review and meta-analysis that emphasise on reviewing the related studies and recent developments on BSA. Hence, the objectives of this work are two-fold: (i) first, two frameworks for depicting the main extensions and the uses of BSA are proposed. The first framework is a general framework to depict the main extensions of BSA, whereas the second is an operational framework to present the expansion procedures of BSA to guide the researchers who are working on improving it. (ii) Second, the experiments conducted in this study fairly compare the analytical performance of BSA with four other competitive algorithms: differential evolution (DE), particle swarm optimisation (PSO), artificial bee colony (ABC), and firefly (FF) on 16 different hardness scores of the benchmark functions with different initial control parameters such as problem dimensions and search space. The experimental results indicate that BSA is statistically superior than the aforementioned algorithms in solving different cohorts of numerical optimisation problems such as problems with different levels of hardness score, problem dimensions, and search spaces. This study can act as a systematic and meta-analysis guide for the scholars who are working on improving BSA.

90C59 Approximation methods and heuristics in mathematical programming
65K10 Numerical optimization and variational techniques
90C27 Combinatorial optimization
65K05 Numerical mathematical programming methods
Full Text: DOI
[1] Agarwal, B. L., Basic Statistics (2006), New Age International
[2] Voges, K. E.; Pope, N., Business Applications and Computational Intelligence (2006), Igi Global
[3] Kacprzyk, J.; Pedrycz, W., Springer Handbook of Computational Intelligence (2015), Springer · Zbl 1317.68001
[4] Beni, G.; Wang, J., Swarm intelligence in cellular robotic systems, Robots Biological System Toward A New Bionics?, 703-712 (1993), Springer
[5] Kothari, V.; Anuradha, J.; Shah, S.; Mittal, P., A survey on particle swarm optimization in feature selection, Global Trends in Information Systems and Software Applications, 192-201 (2012), Springer
[6] Kar, A. K., Bio inspired computing-A review of algorithms and scope of applications, Expert Syst. Appl., 59, 20-32 (2016)
[7] Falkenauer, E., Genetic Algorithms and Grouping Problems (1998), Wiley: Wiley New York · Zbl 0803.68037
[8] Storn, R.; Price, K., Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim., 11, 341-359 (1997) · Zbl 0888.90135
[9] Mullen, R. J.; Monekosso, D.; Barman, S.; Remagnino, P., A review of ant algorithms, Expert Syst. Appl., 36, 9608-9617 (2009)
[10] Eberhart, R.; Kennedy, J., A new optimizer using particle swarm theory, (Proceedings of the Sixth International Symposium on Micro Machine and Human (1995), IEEE), 39-43
[11] Civicioglu, P., Backtracking search optimization algorithm for numerical optimization problems, Appl. Math. Comput., 219, 8121-8144 (2013) · Zbl 1288.65092
[12] Ghosh, D.; Bhaduri, U., A simple recursive backtracking algorithm for knight’s tours puzzle on standard 8× 8 chessboard, (Proceedings of the International Conference Advances in Computing, Communications and Informatics (ICACCI) (2017), IEEE), 1195-1200
[13] Güldal, S.; Baugh, V.; Allehaibi, S., N-Queens solving algorithm by sets and backtracking, (Proceedings of the SoutheastCon, 2016 (2016), IEEE), 1-8
[14] Kuswardayan, I.; Suciati, N., Design and implementation of random word generator using backtracking algorithm for gameplay in ambrosia game, Int. J. Comput. Appl., 158 (2017)
[15] Mukherjee, S.; Datta, S.; Chanda, P. B.; Pathak, P., Comparative study of different algorithms to solve N-queens problem, Int. J. Found. Comput. Sci. Technol., 5, 15-27 (2015)
[16] Zhichao, B., Solution for backtracking based on maze problem and algorithm realization, J. Electron. Test., 14, 83 (2013)
[17] Carlson, D., Sophomores meet the traveling salesperson problem, J. Comput. Sci. Coll., 33, 126-133 (2018)
[18] Korte, B.; Vygen, J., Kombinatorische Optimierung: Theorie und Algorithmen (2012), Springer-Verlag · Zbl 1250.90074
[19] Honda, N., Backtrack beam search for multiobjective scheduling problem, Multi-Objective Program Goal Program, 147-152 (2003), Springer · Zbl 1165.90494
[20] Lu, C.; Gao, L.; Li, X.; Pan, Q.; Wang, Q., Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm, J. Clean. Prod., 144, 228-238 (2017)
[21] Dede, T.; Kripka, M.; Togan, V.; Yepes, V., Usage of Optimization Techniques in Civil Engineering During the Last Two Decades, Curr. Trends Civ. Struct. Eng, 2, 1-17 (2019)
[22] Civicioglu, P., Artificial cooperative search algorithm for numerical optimization problems, Inf. Sci. (Ny)., 229, 58-76 (2013)
[23] K.DUSKO, Backtracking Tutorial using C Program Code Example for Programmers, (2014). https://www.thegeekstuff.com/2014/12/backtracking-example/.
[24] Huybers, Backtracking is an implementation of Artificial Intelligence, (n.d.).http://www.huybers.net/backtrack/backe.html(accessed October 6, 2018).
[25] Civicioglu, P.; Besdok, E., A+ Evolutionary search algorithm and QR decomposition based rotation invariant crossover operator, Expert Syst. Appl., 103, 49-62 (2018)
[26] Sheoran, Y.; Kumar, V.; Rana, K. P.S.; Mishra, P.; Kumar, J.; Nair, S. S., Development of backtracking search optimization algorithm toolkit in \(LabView^{TM}\), Procedia Comput. Sci., 57, 241-248 (2015)
[27] Yang, X.-S.; He, X.-S., Mathematical Foundations of Nature-Inspired Algorithms (2019), Springer · Zbl 1426.90004
[28] Sharapov, R. R.; Lapshin, A. V., Convergence of genetic algorithms, Pattern Recognit. Image Anal., 16, 392-397 (2006)
[29] Zhao, L.; Jia, Z.; Chen, L.; Guo, Y., Improved backtracking search algorithm based on population control factor and optimal learning strategy, Math. Probl. Eng., 2017 (2017) · Zbl 1426.90265
[30] Nama, S.; Saha, A. K.; Ghosh, S., Improved backtracking search algorithm for pseudo dynamic active earth pressure on retaining wall supporting c-Ф backfill, Appl. Soft Comput., 52, 885-897 (2017)
[31] Agrawal, P. N.; Mohapatra, R. N.; Singh, U.; Srivastava, H. M., Mathematical Analysis and its Applications (2015), Springer · Zbl 1331.00047
[32] Qi, L., Convergence analysis of some algorithms for solving nonsmooth equations, Math. Oper. Res., 18, 227-244 (1993) · Zbl 0776.65037
[33] Lahaye, D.; Tang, J.; Vuik, K., Modern Solvers for Helmholtz Problems (2017), Springer · Zbl 1367.65005
[34] Brooks, S. P.; Gelman, A., General methods for monitoring convergence of iterative simulations, J. Comput. Graph. Stat., 7, 434-455 (1998)
[35] Wang, H.; Hu, Z.; Sun, Y.; Su, Q.; Xia, X., Modified backtracking search optimization algorithm inspired by simulated annealing for constrained engineering optimization problems, Comput. Intell. Neurosci., 2018 (2018)
[36] Ahmed, M. S.; Mohamed, A.; Khatib, T.; Shareef, H.; Homod, R. Z.; Ali, J. A., Real time optimal schedule controller for home energy management system using new binary backtracking search algorithm, Energy Build, 138, 215-227 (2017)
[37] Akhtar, M.; Hannan, M. A.; Begum, R. A.; Basri, H.; Scavino, E., Backtracking search algorithm in CVRP models for efficient solid waste collection and route optimization, Waste Manag, 61, 117-128 (2017)
[38] H.Wang, Z.Hu, Y.Sun, Q.Su, X.Xia, A novel modified BSA inspired by species evolution rule and simulated annealing principle for constrained engineering optimization problems, Neural Comput. Appl.(n.d.) 1-28.
[39] Chen, D.; Zou, F.; Lu, R.; Wang, P., Learning backtracking search optimisation algorithm and its application, Inf. Sci. (Ny)., 376, 71-94 (2017)
[40] Kartite, J.; Cherkaoui, M., Improved backtracking search algorithm for renewable energy system, Energy Procedia, 141, 126-130 (2017)
[41] Tsai, H.-C., Improving backtracking search algorithm with variable search strategies for continuous optimization, Appl. Soft Comput., 80, 567-578 (2019)
[42] Lu, J.; Ding, J., Construction of prediction intervals for carbon residual of crude oil based on deep stochastic configuration networks, Inf. Sci. (Ny), 486, 119-132 (2019)
[43] Chen, D.; Lu, R.; Zou, F.; Li, S.; Wang, P., A learning and niching based backtracking search optimisation algorithm and its applications in global optimisation and ANN training, Neurocomputing, 266, 579-594 (2017)
[44] Y.Ç.Kuyu, F.Vatansever, The Chaos-Based Approaches for Actual Metaheuristic Algorithms, Uludağ Univ. J. Fac. Eng.23(n.d.)103-116.
[45] Chatzipavlis, A.; Tsekouras, G. E.; Trygonis, V.; Velegrakis, A. F.; Tsimikas, J.; Rigos, A.; Hasiotis, T.; Salmas, C., Modeling beach realignment using a neuro-fuzzy network optimized by a novel backtracking search algorithm, Neural Comput. Appl., 31, 1747-1763 (2019)
[46] Yu, K.; Liang, J. J.; Qu, B. Y.; Cheng, Z.; Wang, H., Multiple learning backtracking search algorithm for estimating parameters of photovoltaic models, Appl. Energy., 226, 408-422 (2018)
[47] Ahandani, M. A.; Ghiasi, A. R.; Kharrati, H., Parameter identification of chaotic systems using a shuffled backtracking search optimization algorithm, Soft Comput, 22, 8317-8339 (2018)
[48] Yang, H.; Yu, J.; Qiu, Y.; Li, Q.; Chen, W., A coordinated optimization method considering time-delay effect of islanded photovoltaic microgrid based on modified backtracking search algorithm, J. Renew. Sustain. Energy., 10, 23503 (2018)
[49] Ali, J. A.; Hannan, M. A.; Mohamed, A., Backtracking search algorithm approach to improve indirect field-oriented control for induction motor drive, (Proceedings of the IEEE 3rd International Conference Smart Instrumentation Measurement and Application (2015), IEEE), 1-6
[50] Xu, Q.; Guo, L.; Wang, N.; Xu, L., Opposition-based backtracking search algorithm for numerical optimization problems, (Proceedings of the International Conference Intelligence Science and Big Data Engineering (2015), Springer), 223-234
[51] Lin, J., Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems, Nonlinear Dyn, 80, 209-219 (2015)
[52] Brévilliers, M.; Abdelkafi, O.; Lepagnot, J.; Idoumghar, L., Idol-guided backtracking search optimization algorithm, (12th International Conference, Evolution Artificielle, EA Lyon, France (2015))
[53] Passos, L. A.; Rodrigues, D.; Papa, J. P., Quaternion-based backtracking search optimization algorithm, (Proceedings of the IEEE Congress on Evolutionary Computation (2019), IEEE), 3014-3021
[54] Vitayasak, S.; Pongcharoen, P.; Hicks, C., A tool for solving stochastic dynamic facility layout problems with stochastic demand using either a Genetic Algorithm or modified Backtracking Search Algorithm, Int. J. Prod. Econ., 190, 146-157 (2017)
[55] Ferradi, H.; Géraud, R.; Maimuţ, D.; Naccache, D.; Zhou, H., Backtracking-assisted multiplication, Cryptogr. Commun., 10, 17-26 (2018) · Zbl 1384.68008
[56] Li, M.; Lin, D.; Kou, J., A hybrid niching PSO enhanced with recombination-replacement crowding strategy for multimodal function optimization, Appl. Soft Comput., 12, 975-987 (2012)
[57] Yu, E. L.; Suganthan, P. N., Ensemble of niching algorithms, Inf. Sci. (Ny), 180, 2815-2833 (2010)
[58] B.Costin, B.Amelia, solving combinatorial optimisation problems using simulated annealing, (n.d.).
[59] Yuan, X.; Wu, X.; Tian, H.; Yuan, Y.; Adnan, R. M., Parameter identification of nonlinear Muskingum model with backtracking search algorithm, Water Resour. Manag, 30, 2767-2783 (2016)
[60] Zou, F.; Chen, D.; Lu, R., Hybrid hierarchical backtracking search optimization algorithm and its application, Arab. J. Sci. Eng., 43, 993-1014 (2018)
[61] Ali, A. F., A memetic backtracking search optimization algorithm for economic dispatch problem, Egypt. Comput. Sci. J., 39, 56-71 (2015)
[62] Hannan, M. A.; Lipu, M. S.H.; Hussain, A.; Saad, M. H.; Ayob, A., Neural network approach for estimating state of charge of lithium-ion battery using backtracking search algorithm, IEEE Access, 6, 10069-10079 (2018)
[63] Lipu, M. S.H.; Hussain, A.; Saad, M. H.M.; Hannan, M. A., Optimal neural network approach for estimating state of energy of lithium-ion battery using heuristic optimization techniques, (Proceedings of the 6th International Conference on Electrical Engineering and Informatics (ICEEI) (2017), IEEE), 1-6
[64] Lin, Q.; Gao, L.; Li, X.; Zhang, C., A hybrid backtracking search algorithm for permutation flow-shop scheduling problem, Comput. Ind. Eng., 85, 437-446 (2015)
[65] Chen, P.; Wen, L.; Li, R.; Li, X., A hybrid backtracking search algorithm for permutation flow-shop scheduling problem minimizing makespan and energy consumption, (Proceedings of the International Conference on Industrial Engineering and Engineering Management (2017), IEEE), 1611-1615
[66] Nama, S.; Saha, A., A novel hybrid backtracking search optimization algorithm for continuous function optimization, Decis. Sci. Lett., 8, 163-174 (2019)
[67] Wang, S.; Da, X.; Li, M.; Han, T., Adaptive backtracking search optimization algorithm with pattern search for numerical optimization, J. Syst. Eng. Electron., 27, 395-406 (2016)
[68] Wang, L.; Zhong, Y.; Yin, Y.; Zhao, W.; Wang, B.; Xu, Y., A hybrid backtracking search optimization algorithm with differential evolution, Math. Probl. Eng., 2015 (2015)
[69] Das, S.; Mandal, D.; Kar, R.; Prasad Ghoshal, S., A new hybridized backtracking search optimization algorithm with differential evolution for sidelobe suppression of uniformly excited concentric circular antenna arrays, Int. J. RF Microw. Comput. Eng., 25, 262-268 (2015)
[70] Brévilliers, M.; Abdelkafi, O.; Lepagnot, J.; Idoumghar, L., Fast Hybrid BSA-DE-SA Algorithm on GPU, (Proceedings of the International Conference on Swarm Intelligence Based Optimization (2016), Springer), 75-86
[71] Su, Z.; Wang, H.; Yao, P., A hybrid backtracking search optimization algorithm for nonlinear optimal control problems with complex dynamic constraints, Neurocomputing, 186, 182-194 (2016)
[72] Askarzadeh, A.; dos Santos Coelho, L., A backtracking search algorithm combined with Burger’s chaotic map for parameter estimation of PEMFC electrochemical model, Int. J. Hydrogen Energy, 39, 11165-11174 (2014)
[73] Agarwal, S. K.; Shah, S.; Kumar, R., Classification of mental tasks from EEG data using backtracking search optimization based neural classifier, Neurocomputing, 166, 397-403 (2015)
[74] Ali, J. A.; Hannan, M. A.; Mohamed, A.; Abdolrasol, M. G.M., Fuzzy logic speed controller optimization approach for induction motor drive using backtracking search algorithm, Measurement, 78, 49-62 (2016)
[75] Pal, P. S.; Kar, R.; Mandal, D.; Ghoshal, S. P., A hybrid backtracking search algorithm with wavelet mutation-based nonlinear system identification of Hammerstein models, Signal, Image Video Process, 11, 929-936 (2017)
[76] Zhao, W.; Wang, L.; Wang, B.; Yin, Y., Best guided backtracking search algorithm for numerical optimization problems, (Proceedings of the International Conference on Knowledge Science, Engineering and Management (2016), Springer), 414-425
[77] Pare, S.; Bhandari, A. K.; Kumar, A.; Bajaj, V., Backtracking search algorithm for color image multilevel thresholding, Signal, Image Video Process, 12, 385-392 (2018)
[78] Toz, G.; Yücedağ, İ.; Erdoğmuş, P., A fuzzy image clustering method based on an improved backtracking search optimization algorithm with an inertia weight parameter, J. King Saud Univ. Inf. Sci. (2018)
[79] Turgut, O. E., Thermal and economical optimization of a shell and tube evaporator using hybrid backtracking search—sine-cosine algorithm, Arab. J. Sci. Eng., 42, 2105-2123 (2017)
[80] Lin, J.; Wang, Z.-J.; Li, X., A backtracking search hyper-heuristic for the distributed assembly flow-shop scheduling problem, Swarm Evol. Comput., 36, 124-135 (2017)
[81] Lin, J., Backtracking search based hyper-heuristic for the flexible job-shop scheduling problem with fuzzy processing time, Eng. Appl. Artif. Intell., 77, 186-196 (2019)
[82] Ao, H.; Thoi, T. N.; Huu, V. H.; Anh-Le, L.; Nguyen, T.; Chau, M. Q., Backtracking search optimization algorithm and its application to roller bearing fault diagnosis, Int. J. Acoust. Vib., 21 (2016)
[83] Nama, S.; Saha, A. K., A new hybrid differential evolution algorithm with self-adaptation for function optimization, Appl. Intell., 48, 1657-1671 (2018)
[84] Nama, S.; Saha, A.; Ghosh, S., A new ensemble algorithm of differential evolution and backtracking search optimization algorithm with adaptive control parameter for function optimization, Int. J. Ind. Eng. Comput., 7, 323-338 (2016)
[85] Khan, W. U.; Ye, Z.; Chaudhary, N. I.; Raja, M. A.Z., Backtracking search integrated with sequential quadratic programming for nonlinear active noise control systems, Appl. Soft Comput., 73, 666-683 (2018)
[86] M.Sriram, K.Ravindra, Backtracking Search Optimization Algorithm Based MPPT Technique for Solar PV System, in: Adv. Decis. Sci. Image Process. Secur. Comput. Vis., Springer, 2020: pp. 498-506.
[87] A.Gosain, K.Sachdeva, Selection of materialized views using stochastic ranking based Backtracking Search Optimization Algorithm, Int. J. Syst. Assur. Eng. Manag.(n.d.) 1-10.
[88] Tian, Z.; Ren, Y.; Wang, G., An application of backtracking search optimization-based least squares support vector machine for prediction of short-term wind speed, Wind Eng (2019), 0309524X19849843
[89] M.Konar, GAO Algoritma tabanlı YSA modeliyle İHA motorunun performansının ve uçuş süresinin maksimizasyonu, Avrupa Bilim ve Teknol. Derg.(n.d.) 360-367.
[90] Wang, Z.; Zeng, Y.-R.; Wang, S.; Wang, L., Optimizing echo state network with backtracking search optimization algorithm for time series forecasting, Eng. Appl. Artif. Intell., 81, 117-132 (2019)
[91] Thai, V.; Cheng, J.; Nguyen, V.; Daothi, P., Optimizing SVM’s parameters based on backtracking search optimization algorithm for gear fault diagnosis, J. Vibroeng., 21, 66-81 (2019)
[92] Sun, S.; Wei, L.; Xu, J.; Jin, Z., A new wind speed forecasting modeling strategy using two-stage decomposition, feature selection and DAWNN, Energies, 12, 334 (2019)
[93] Jia, D.; Tong, Y.; Yu, Y.; Cai, Z.; Gao, S., A novel backtracking search with grey wolf algorithm for optimization, (Proceedings of the 10th International Conference on Intelligent Human-Machine Systems (2018), IEEE), 73-76
[94] Xu, Z.; Lei, Z.; Yang, L.; Li, X.; Gao, S., Negative correlation learning enhanced search behavior in backtracking search optimization, (Proceedings of the International Conference on Intelligent Human-Machine Systems and Cybernetics (2018), IEEE), 310-314
[95] Yan, S.; Zhou, J.; Zheng, Y.; Li, C., An improved hybrid backtracking search algorithm based T-S fuzzy model and its implementation to hydroelectric generating units, Neurocomputing, 275, 2066-2079 (2018)
[96] Zhang, C.; Li, C.; Peng, T.; Xia, X.; Xue, X.; Fu, W.; Zhou, J., Modeling and synchronous optimization of pump turbine governing system using sparse robust least squares support vector machine and hybrid backtracking search algorithm, Energies, 11, 3108 (2018)
[97] Chen, L.; Sun, N.; Zhou, C.; Zhou, J.; Zhou, Y.; Zhang, J.; Zhou, Q., Flood forecasting based on an improved extreme learning machine model combined with the backtracking search optimization algorithm, Water, 10, 1362 (2018)
[98] Pourdaryaei, A.; Mokhlis, H.; Illias, H. A.; Kaboli, S. H.A.; Ahmad, S., Short-term electricity price forecasting via hybrid backtracking search algorithm and anfis approach, IEEE Access, 7, 77674-77691 (2019)
[99] Zhou, J.; Zhang, C.; Peng, T.; Xu, Y., Parameter identification of pump turbine governing system using an improved backtracking search algorithm, Energies, 11, 1668 (2018)
[100] Zhou, J.; Sun, N.; Jia, B.; Peng, T., A novel decomposition-optimization model for short-term wind speed forecasting, Energies, 11, 1752 (2018)
[101] Zhang, W.; Zhang, S.; Zhang, S., Two-factor high-order fuzzy-trend FTS model based on BSO-FCM and improved KA for TAIEX stock forecasting, Nonlinear Dyn, 94, 1429-1446 (2018)
[102] Atasever, U. H.; Ozkan, C., A New SEBAL Approach Modified with Backtracking Search Algorithm for Actual Evapotranspiration Mapping and On-Site Application, J, Indian Soc. Remote Sens., 46, 1213-1222 (2018)
[103] Jothi, G.; Inbarani, H. H.; Azar, A. T.; Devi, K. R., Rough set theory with Jaya optimization for acute lymphoblastic leukemia classification, Neural Comput. Appl., 1-20 (2018)
[104] Li, H.; Pan, L.; Chen, M.; Chen, X.; Zhang, Y., RBM-Based Back Propagation Neural Network with BSASA Optimization for Time Series Forecasting, (Proceedings of the 9th International Conference on Intelligent Human-Machine Systems (2017), IEEE), 218-221
[105] Mohy-ud-din, G., Hybrid dynamic economic emission dispatch of thermal, wind, and photovoltaic power using the hybrid backtracking search algorithm with sequential quadratic programming, J. Renew. Sustain. Energy., 9, 15502 (2017)
[106] Lenin, K.; Ravindhranathreddy, B.; Suryakalavathi, M., Hybridisation of backtracking search optimisation algorithm with differential evolution algorithm for solving reactive power problem, Int. J. Adv. Intell. Paradig., 8, 355-364 (2016)
[107] Wang, B.; Wang, L.; Yin, Y.; Xu, Y.; Zhao, W.; Tang, Y., An improved neural network with random weights using backtracking search algorithm, Neural Process. Lett., 44, 37-52 (2016)
[108] Mallick, S.; Kar, R.; Mandal, D.; Ghoshal, S. P., CMOS analogue amplifier circuits optimisation using hybrid backtracking search algorithm with differential evolution, J. Exp. Theor. Artif. Intell., 28, 719-749 (2016)
[109] Benhala, B.; Kotti, M.; Ahaitouf, A.; Fakhfakh, M., Backtracking ACO for RF-circuit design optimization, Performance Optimization Techniques in Analog, Mixed-Signal, and Radio-Frequency Circuit Design, 158-179 (2015), IGI Global
[110] Aldowaisan, T.; Allahverdi, A., New heuristics for no-wait flowshops to minimize makespan, Comput. Oper. Res., 30, 1219-1231 (2003) · Zbl 1047.90053
[111] Liu, B.; Wang, L.; Jin, Y.-H., An effective PSO-based memetic algorithm for flow shop scheduling, IEEE Trans. Syst. Man, Cybern. Part B., 37, 18-27 (2007)
[112] Pan, Q.-K.; Tasgetiren, M. F.; Liang, Y.-C., A discrete differential evolution algorithm for the permutation flowshop scheduling problem, Comput. Ind. Eng., 55, 795-816 (2008)
[113] Das, S.; Suganthan, P. N., Differential evolution: a survey of the state-of-the-art, IEEE Trans. Evol. Comput., 15, 4-31 (2011)
[114] Civicioglu, P.; Besdok, E., A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms, Artif. Intell. Rev., 39, 315-346 (2013)
[115] Yu, J. X.; Yao, X.; Choi, C.-H.; Gou, G., Materialized view selection as constrained evolutionary optimization, IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.), 33, 458-467 (2003)
[116] Cheng, J.; Wu, X.; Zhou, M.; Gao, S.; Huang, Z.; Liu, C., A novel method for detecting new overlapping community in complex evolving networks, IEEE Trans. Syst. Man, Cybern. Syst. (2018)
[117] Gao, S.; Wang, R.-L.; Tamura, H.; Tang, Z., A multi-layered immune system for graph planarization problem, IEICE Trans. Inf. Syst., 92, 2498-2507 (2009)
[118] Zhou, Y.; Wang, J.; Chen, J.; Gao, S.; Teng, L., Ensemble of many-objective evolutionary algorithms for many-objective problems, Soft Comput, 21, 2407-2419 (2017)
[119] Song, S.; Gao, S.; Chen, X.; Jia, D.; Qian, X.; Todo, Y., AIMOES: Archive information assisted multi-objective evolutionary strategy for ab initio protein structure prediction, Knowledge-Based Syst, 146, 58-72 (2018)
[120] Ji, J.; Gao, S.; Cheng, J.; Tang, Z.; Todo, Y., An approximate logic neuron model with a dendritic structure, Neurocomputing, 173, 1775-1783 (2016)
[121] Zhou, T.; Gao, S.; Wang, J.; Chu, C.; Todo, Y.; Tang, Z., Financial time series prediction using a dendritic neuron model, Knowl. Based Syst, 105, 214-224 (2016)
[122] Abdolrasol, M. G.M.; Hannan, M. A.; Mohamed, A.; Amiruldin, U. A.U.; Abidin, I. B.Z.; Uddin, M. N., An optimal scheduling controller for virtual power plant and microgrid integration using the binary backtracking search algorithm, IEEE Trans. Ind. Appl., 54, 2834-2844 (2018)
[123] Zhao, H.; Min, F.; Zhu, W., A backtracking approach to minimal cost feature selection of numerical data, J. Inf. Comput. Sci., 10, 4105-4115 (2013)
[124] Zhao, H.; Min, F.; Zhu, W., Cost-sensitive feature selection of numeric data with measurement errors, J, Appl. Math., 2013 (2013) · Zbl 1267.68199
[125] Civicioglu, P., Circular antenna array design by using evolutionary search algorithms, Prog. Electromagn. Res., 54, 265-284 (2013)
[126] A.M.SHAHEEN, R.A.EL-SEHIEMY, Binary and Integer Coded Backtracking Search Optimization Algorithm for Transmission Network Expansion Planning, (n.d.).
[127] Zhang, C.; Lin, Q.; Gao, L.; Li, X., Backtracking Search Algorithm with three constraint handling methods for constrained optimization problems, Expert Syst. Appl., 42, 7831-7845 (2015)
[128] Zou, F.; Chen, D.; Li, S.; Lu, R.; Lin, M., Community detection in complex networks: Multi-objective discrete backtracking search optimization algorithm with decomposition, Appl. Soft Comput., 53, 285-295 (2017)
[129] Modiri-Delshad, M.; Rahim, N. A., Multi-objective backtracking search algorithm for economic emission dispatch problem, Appl. Soft Comput., 40, 479-494 (2016)
[130] Bhattacharjee, K.; Bhattacharya, A.; nee Dey, S. H., Backtracking search optimization based economic environmental power dispatch problems, Int. J. Electr. Power Energy Syst, 73, 830-842 (2015)
[131] El Maani, R.; Radi, B.; El Hami, A., Multiobjective backtracking search algorithm: application to FSI, Struct. Multidiscip. Optim., 59, 131-151 (2019)
[132] Zeine, A. T.; El Hami, A.; Ellaia, R.; Pagnacco, E., Backtracking search algorithm for multi-objective design optimisation, Int. J. Math. Model. Numer. Optim., 8, 93-107 (2017)
[133] Lu, C.; Gao, L.; Li, X.; Wang, Q.; Liao, W.; Zhao, Q., An efficient multiobjective backtracking search algorithm for single machine scheduling with controllable processing times, Math. Probl. Eng., 2017 (2017)
[134] Daqaq, F.; Ellaia, R.; Ouassaid, M., Multiobjective backtracking search algorithm for solving optimal power flow, (Proceedings of the International Conference of Information Technologies (2017), IEEE), 1-6
[135] Lu, C.; Gao, L.; Li, X.; Chen, P., Energy-efficient multi-pass turning operation using multi-objective backtracking search algorithm, J. Clean. Prod., 137, 1516-1531 (2016)
[136] bin Mohd Zain, M. Z.; Kanesan, J.; Kendall, G.; Chuah, J. H., Optimization of fed-batch fermentation processes using the backtracking search algorithm, Expert Syst. Appl., 91, 286-297 (2018)
[137] Rosen, K. H.; Krithivasan, K., Discrete Mathematics and its Applications: with Combinatorics and Graph Theory (2012), Tata McGraw-Hill Education
[138] El Sakkout, H.; Wallace, M., Probe backtrack search for minimal perturbation in dynamic scheduling, Constraints, 5, 359-388 (2000) · Zbl 0970.68014
[139] J.Yadav, J.Chandel, N.Gupta, Personnel Scheduling: Comparative Study of Backtracking Approaches and Genetic Algorithms, (2015).
[140] Kumar, V.; Rana, K. P.S.; Kler, D., Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller, Appl. Soft Comput., Article 105531 pp. (2019)
[141] Guha, D.; Roy, P. K.; Banerjee, S., Application of backtracking search algorithm in load frequency control of multi-area interconnected power system, Ain Shams Eng. J., 9, 257-276 (2018)
[142] Boudjefdjouf, H.; Bouchekara, H. R.E. H.; Mehasni, R.; Smail, M. K.; Orlandi, A.; de Paulis, F., Wire fault diagnosis using time-domain reflectometry and backtracking search optimization algorithm, (Proceedings of the 31st International Review of Progress in Applied Computational Electromagnetic (2015), IEEE), 1-2
[143] de Sá, A. O.; Nedjah, N.; Mourelle, L. M. d., Genetic and backtracking search optimisation algorithms applied to localisation problems, Int. J. Innov. Comput. Appl., 6, 223-228 (2015)
[144] Mehmood, A.; Chaudhary, N. I.; Zameer, A.; Raja, M. A.Z., Backtracking search optimization heuristics for nonlinear Hammerstein controlled auto regressive auto regressive systems, ISA Trans (2019)
[145] Goyal, V.; Mishra, P.; Shukla, A.; Deolia, V. K.; Varshney, A., A fractional order parallel control structure tuned with meta-heuristic optimization algorithms for enhanced robustness, J. Electr. Eng., 70, 16-24 (2019)
[146] Dinh, T. X.; Luan, N. P.; Ahn, K. K., A novel inverse modeling control for piezo positioning stage, J. Mech. Sci. Technol., 32, 5875-5888 (2018)
[147] Goyal, V.; Mishra, P.; Deolia, V. K., A robust fractional order parallel control structure for flow control using a pneumatic control valve with nonlinear and uncertain dynamics, Arab. J. Sci. Eng., 44, 2597-2611 (2019)
[148] Mehmood, A.; Zameer, A.; Chaudhary, N. I.; Raja, M. A.Z., Backtracking search heuristics for identification of electrical muscle stimulation models using Hammerstein structure, Appl. Soft Comput., Article 105705 pp. (2019)
[149] El-Fergany, A., Multi-objective allocation of multi-type distributed generators along distribution networks using backtracking search algorithm and fuzzy expert rules, Electr. Power Components Syst., 44, 252-267 (2016)
[150] Guney, K.; Durmus, A., Pattern nulling of linear antenna arrays using backtracking search optimization algorithm, Int. J. Antennas Propag., 2015 (2015)
[151] Chaib, A. E.; Bouchekara, H.; Mehasni, R.; Abido, M. A., Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm, Int. J. Electr. Power Energy Syst., 81, 64-77 (2016)
[152] Bhattacharjee, K., Economic dispatch problems using backtracking search optimization, Int. J. Energy Optim. Eng., 7, 39-60 (2018)
[153] Shafiullah, M.; Abido, M. A.; Coelho, L. S., Design of robust PSS in multimachine power systems using backtracking search algorithm, (Proceedings of the 18th International Conference on Intelligent System Application to Power (2015), IEEE), 1-6
[154] Precup, R.-E.; Balint, A.-D.; Radac, M.-B.; Petriu, E. M., Backtracking Search Optimization Algorithm-based approach to PID controller tuning for torque motor systems, (Proceedings of the 9th Annual IEEE International Systems Conference (SysCon) (2015), IEEE), 127-132
[155] Zhang, C.; Zhou, J.; Li, C.; Fu, W.; Peng, T., A compound structure of ELM based on feature selection and parameter optimization using hybrid backtracking search algorithm for wind speed forecasting, Energy Convers. Manag., 143, 360-376 (2017)
[156] Kılıç, U., Backtracking search algorithm-based optimal power flow with valve point effect and prohibited zones, Electr. Eng., 97, 101-110 (2015)
[157] Shaheen, A. M.; El-Sehiemy, R. A.; Farrag, S. M., Optimal reactive power dispatch using backtracking search algorithm, Aust. J. Electr. Electron. Eng., 13, 200-210 (2016)
[158] Kanth, D. S.K.; Reddy, N. S.R.; Reddy, R. S.G., Optimal placement & sizing of DG’s using backtracking search algorithm in IEEE 33-bus distribution system, (Proceedings of the International Conference Computing Methodologies and Communication : ICCMC (2017), IEEE), 163-169
[159] Gupta, P.; Kumar, V.; Rana, K. P.S.; Mishra, P., Comparative study of some optimization techniques applied to Jacketed CSTR control, (Proceedings of the 4th International Conference on Reliability, Infocom Technologies and Optimization: Trends and Future Directions (2015), IEEE), 1-6
[160] Baadji, B.; Bentarzi, H.; Mati, A., Robust Wide Area Power System Stabilizers Design in Multimachine System based on Backtracking Search Optimization, (Proceedings of the International Conference Applications Smart Systems (2018), IEEE), 1-5
[161] Kartite, J.; Cherkaoui, M., Towards 100% Renewable Production: Dakhla Smart City Electrification, (Proceedings of the Third International Conference on Smart City Applications. (2018), Springer), 1146-1156
[162] Kuyu, Y. C.; Vatansever, F., Analog filter group delay optimization using metaheuristic algorithms: a comparative study, (Proceedings of the International Conference on Artificial Intelligence and Data Processing (2018), IEEE), 1-5
[163] Jordehi, A. R., DG allocation and reconfiguration in distribution systems by metaheuristic optimisation algorithms: a comparative analysis, (Proceedings of the IEEE PES Innovative Smart Grid Technologies Conference Europe (2018), IEEE), 1-6
[164] Shafiullah, M.; Abido, M.; Hossain, M.; Mantawy, A., An improved OPP problem formulation for distribution grid observability, Energies, 11, 3069 (2018)
[165] Khamis, A.; Shareef, H.; Mohamed, A.; Dong, Z. Y., A load shedding scheme for DG integrated islanded power system utilizing backtracking search algorithm, Ain. Shams Eng. J., 9, 161-172 (2018)
[166] Khan, S. S.; Rafiq, M. A.; Shareef, H.; Sultan, M. K., Parameter optimization of PEMFC model using backtracking search algorithm, (Proceedings of the 5th International Conference on Renewable Energy: Generation and Applications (2018), IEEE), 323-326
[167] Islam, N. N.; Hannan, M. A.; Shareef, H.; Mohamed, A., An application of backtracking search algorithm in designing power system stabilizers for large multi-machine system, Neurocomputing, 237, 175-184 (2017)
[168] Elomary, I.; Abbou, A.; Idoumghar, L., Backtracking Search Algorithm Optimization for the Brushless Direct Current (BLDC) Motor Parameter Design, (Proceedings of the International Renewable and Sustainable Energy Conference (2017), IEEE), 1-5
[169] B.Hiçdurmaz, B.Durmuş, H.Temurtaş, S.Özyön, The Prediction of Butterworth Type Active Filter Parameters in Low-Pass Sallen-Key Topology by Backtracking Search Algorithm, (n.d.).
[170] El Maani, R.; Zeine, A. T.; Radi, B.; El Hami, A.; Ellaia, R., Backtracking search optimization algorithm for fluid-structure interaction problems, (Proceedings of the 4th IEEE International Colloquium on Information Science and Technology (2016), IEEE), 690-695
[171] Nguyen, T. T.; Pham, H. N.; Truong, A. V.; Phung, T. A.; Nguyen, T. T., A backtracking search algorithm for distribution network reconfiguration problem, AETA 2015: Recent Advances in Electrical Engineering and Related Sciences, 223-234 (2016), Springer
[172] Dasgupta, K.; Ghorui, S. K., An analysis of economic load dispatch with prohibited zone constraints using BSA algorithm, (Proceedings of the International Conference on Electrical, Computer and Communication Engineering (2016), IEEE), 1-5
[173] Shaheen, A. M.; El-Sehiemy, R. A.; Farrag, S. M., Integrated strategies of backtracking search optimizer for solving reactive power dispatch problem, IEEE Syst. J., 12, 424-433 (2016)
[174] Modiri-Delshad, M.; Kaboli, S. H.A.; Taslimi-Renani, E.; Rahim, N. A., Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options, Energy, 116, 637-649 (2016)
[175] Wei, Z.; Wei, Q., The backtracking search optimization algorithm for frequency band and time segment selection in motor imagery-based brain-computer interfaces, J. Integr. Neurosci., 15, 347-364 (2016)
[176] Tyagi, N.; Dubey, H. M.; Pandit, M., Economic load dispatch of wind-solar-thermal system using backtracking search algorithm, Int. J. Eng. Sci. Technol., 8, 16-27 (2016)
[177] Jianjun, W.; Li, L.; Ding, L., Application of SVR with backtracking search algorithm for long-term load forecasting, J. Intell. Fuzzy Syst., 31, 2341-2347 (2016)
[178] Islam, N. N.; Hannan, M. A.; Mohamed, A.; Shareef, H., Improved power system stability using backtracking search algorithm for coordination design of PSS and TCSC damping controller, PLoS One, 11, Article e0146277 pp. (2016)
[179] El-Fergany, A., Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm, Int. J. Electr. Power Energy Syst., 64, 1197-1205 (2015)
[180] Garbaya, A.; Kotti, M.; Fakhfakh, M.; Siarry, P., The backtracking search for the optimal design of low-noise amplifiers, Computational Intelligence in Analog and Mixed-Signal (AMS) and Radio-Frequency (RF) Circuit Design, 391-412 (2015), Springer
[181] Niu, N.; Fu, F.-F.; Li, H.; Lai, F.-C.; Wang, J.-X., A Novel Topology Reconfiguration Backtracking Algorithm for 2D REmesh Networks-on-Chip, (Proceedings of the International Symposium on Parallel Architecture, Algorithm and Programming (2017), Springer), 51-58
[182] Ayan, K.; Kılıç, U., Optimal power flow of two-terminal HVDC systems using backtracking search algorithm, Int. J. Electr. Power Energy Syst., 78, 326-335 (2016)
[183] Yan, J.; Zhang, J., Backtracking algorithms and search heuristics to generate test suites for combinatorial testing, Null, 385-394 (2006), IEEE
[184] Zaman, F.; Khan, S. U.; Raja, M. A.Z.; Niazi, S. A., Backtracking search optimization paradigm for pattern correction of faulty antenna array in wireless mobile communications, Wirel. Commun. Mob. Comput., 2019 (2019)
[185] Badawy, M. M.; Ali, Z. H.; Ali, H. A., QoS provisioning framework for service-oriented internet of things (IoT), Cluster Comput, 1-17 (2019)
[186] Eskandari, M.; Sharifi, O., Effect of face and ocular multimodal biometric systems on gender classification, IET Biometrics, 8, 243-248 (2019)
[187] Osama, R. A.; Zobaa, A. F.; Abdelaziz, A. Y., A Planning Framework for Optimal Partitioning of Distribution Networks Into Microgrids, IEEE Syst. J. (2019)
[188] Walia, G. S.; Singh, T.; Singh, K.; Verma, N., Robust multimodal biometric system based on optimal score level fusion model, Expert Syst. Appl., 116, 364-376 (2019)
[189] de Sá, A. O.; Casimiro, A.; Machado, R. C.S.; da Costa Carmo, L. F.R., Bio-inspired system identification attacks in noisy networked control systems, (Proceedings of the International Conference on Bio-Inspired Information and Communications (2019), Springer), 28-38
[190] Nazri, N. N.A.; Malik, N. N.N. A.; Idoumghar, L.; Latiff, N. M.A.; Ali, S., Backtracking search optimization for collaborative beamforming in wireless sensor networks, Telkomnika, 16, 1801-1808 (2018)
[191] Gosain, A.; Sachdeva, K., Materialized view selection using backtracking search optimization algorithm, Intell. Eng. Informat., 241-251 (2018)
[192] A.Montanaro, Quantum walk speedup of backtracking algorithms, ArXiv1509.02374. (2015). · Zbl 1417.68046
[193] Lin, Y.-K.; Nguyen, T.-P., Reliability evaluation of a multistate flight network under time and stopover constraints, Comput. Ind. Eng., 115, 620-630 (2018)
[194] Mishra, P.; Kumar, V.; Rana, K. P.S., An efficient method for parameter estimation of a nonlinear system using Backtracking search algorithm, Eng. Sci. Technol. Int. J. (2018)
[195] Zhou, J.; Ye, H.; Ji, X.; Deng, W., An improved backtracking search algorithm for casting heat treatment charge plan problem, J. Intell. Manuf., 1-16 (2017)
[196] Song, X.; Zhang, X.; Zhao, S.; Li, L., Backtracking search algorithm for effective and efficient surface wave analysis, J. Appl. Geophys., 114, 19-31 (2015)
[197] Karaboga, D.; Akay, B., A comparative study of artificial bee colony algorithm, Appl. Math. Comput., 214, 108-132 (2009) · Zbl 1169.65053
[198] Karaboga, D.; Basturk, B., A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm, J. Glob. Optim., 39, 459-471 (2007) · Zbl 1149.90186
[199] Das, S.; Suganthan, P. N., Problem Definitions and Evaluation Criteria For Cec 2011 Competition on Testing Evolutionary Algorithms on Real World Optimization Problems (2010), Jadavpur Univ. Nanyang Technol. Univ. Kolkata.
[200] Adamuthe, A. C.; Bichkar, R. S., Personnel scheduling: Comparative study of backtracking approaches and genetic algorithms, Int. J. Comput. Appl., 38 (2012)
[201] Mandal, S.; Sinha, R. K.; Mittal, K., Comparative analysis of backtrack search optimization algorithm (bsa) with other evolutionary algorithms for global continuous optimization, Int. J. Comput. Sci. Inf. Technol., 6, 3237-3241 (2015)
[202] Agarwal, P.; Mehta, S., Empirical analysis of five nature-inspired algorithms on real parameter optimization problems, Artif. Intell. Rev., 50, 383-439 (2018)
[203] Lindfield, G.; Penny, J., Introduction to Nature-Inspired Optimization (2017), Academic Press · Zbl 1397.90003
[204] M.Jamil, X.-S.Yang, A literature survey of benchmark functions for global optimization problems, ArXiv1308.4008. (2013). · Zbl 1280.65053
[205] Ali, M. M.; Khompatraporn, C.; Zabinsky, Z. B., A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems, J. Glob. Optim., 31, 635-672 (2005) · Zbl 1093.90028
[206] Global optimization benchmarks and AMPGO, (n.d.). http://infinity77.net/global_optimization (accessed November 24, 2018).
[207] Derrac, J.; García, S.; Molina, D.; Herrera, F., A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm Evol. Comput., 1, 3-18 (2011)
[208] Joshi, A. S.; Kulkarni, O.; Kakandikar, G. M.; Nandedkar, V. M., Cuckoo search optimization-a review, Mater. Today Proc., 4, 7262-7269 (2017)
[209] Chen, D.; Zou, F.; Lu, R.; Li, S., Backtracking search optimization algorithm based on knowledge learning, Inf. Sci. (Ny)., 473, 202-226 (2019)
[210] Chakrabarti, D.; Kumar, R.; Tomkins, A., Evolutionary clustering, (Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (2006), ACM), 554-560
[211] Xu, K. S.; Kliger, M.; Hero Iii, A. O., Adaptive evolutionary clustering, Data Min. Knowl. Discov., 28, 304-336 (2014) · Zbl 1281.68200
[212] Freitas, A. A., Data Mining and Knowledge Discovery with Evolutionary Algorithms (2013), Springer Science & Business Media · Zbl 1013.68075
[213] Mohammed, H. M.; Umar, S. U.; Rashid, T. A., A systematic and meta-analysis survey of whale optimization algorithm, Comput. Intell. Neurosci., 2019 (2019)
[214] Shamsaldin, A. S.; Rashid, T. A.; Agha, R. A.A.-R.; Al-Salihi, N. K.; Mohammadi, M., Donkey and smuggler optimization algorithm: a collaborative working approach to path finding, J. Comput. Des. Eng. (2019)
[215] Abdullah, J. M.; Ahmed, T., Fitness dependent optimizer: inspired by the bee swarming reproductive process, IEEE Access, 7, 43473-43486 (2019)
[216] Rashid, T. A.; Abbas, D. K.; Turel, Y. K., A multi hidden recurrent neural network with a modified grey wolf optimizer, PLoS One, 14, Article e0213237 pp. (2019)
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.