Abstract
The exposition of any nature-inspired optimization technique relies firmly upon its executed organized framework. Since the regularly utilized backtracking search algorithm (BSA) is a fixed framework, it is not always appropriate for all difficulty levels of problems and, in this manner, probably does not search the entire search space proficiently. To address this limitation, we propose a modified BSA framework, called gQR-BSA, based on the quasi reflection-based initialization, quantum Gaussian mutations, adaptive parameter execution, and quasi-reflection-based jumping to change the coordinate structure of the BSA. In gQR-BSA, a quantum Gaussian mechanism was developed based on the best population information mechanism to boost the population distribution information. As population distribution data can represent characteristics of a function landscape, gQR-BSA has the ability to distinguish the methodology of the landscape in the quasi-reflection-based jumping. The updated automatically managed parameter control framework is also connected to the proposed algorithm. In every iteration, the quasi-reflection-based jumps aim to jump from local optima and are adaptively modified based on knowledge obtained from offspring to global optimum. Herein, the proposed gQR-BSA was utilized to solve three sets of well-known standards of functions, including unimodal, multimodal, and multimodal fixed dimensions, and to solve three well-known engineering optimization problems. The numerical and experimental results reveal that the algorithm can obtain highly efficient solutions to both benchmark and real-life optimization problems.
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References
Audet C, Hare W (2017) Derivative-free and blackbox optimization. https://doi.org/10.1007/978-3-319-68913-5
Belegundu AD (1983) Study of mathematical programming methods for structural optimization. Diss Abstr Int Part B Sci Eng ABST INT PT B- SCI ENG], 43:1983
Bodaghi M, Samieefar K (2019) Meta-heuristic bus transportation algorithm. Iran J Comput Sci 2:23–32. https://doi.org/10.1007/s42044-018-0025-2
Chen Y, He J (2021) Average convergence rate of evolutionary algorithms in continuous optimization. Inf Sci (ny) 562:200–219. https://doi.org/10.1016/j.ins.2020.12.076
Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219:8121–8144. https://doi.org/10.1016/j.amc.2013.02.017
Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6:58–73. https://doi.org/10.1109/4235.985692
de Melo VV, Banzhaf W (2018) Drone Squadron Optimization: a novel self-adaptive algorithm for global numerical optimization. Neural Comput Appl 30:3117–3144. https://doi.org/10.1007/s00521-017-2881-3
Del Ser J, Osaba E, Molina D et al (2019) Bio-inspired computation: where we stand and what’s next. Swarm Evol Comput 48:220–250. https://doi.org/10.1016/j.swevo.2019.04.008
Derrac J, García S, Molina D, Herrera F (2011) 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. https://doi.org/10.1016/j.swevo.2011.02.002
Dhiman G, Kumar V (2019) Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowl Based Syst 165:169–196. https://doi.org/10.1016/j.knosys.2018.11.024
Coelho dos LS (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37:1676–1683. https://doi.org/10.1016/j.eswa.2009.06.044
dos Santos CL, Mariani VC (2008) Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects. Energy Convers Manag 49:3080–3085. https://doi.org/10.1016/j.enconman.2008.06.009
Duan H, Luo Q (2014) Adaptive backtracking search algorithm for induction magnetometer optimization. IEEE Trans Magn. https://doi.org/10.1109/TMAG.2014.2342192
El-Fergany A (2015) Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm. Int J Electr Power Energy Syst 64:1197–1205. https://doi.org/10.1016/j.ijepes.2014.09.020
Ergezer M, Simon D, Du D (2009) Oppositional biogeography-based optimization. In: Conference proceedings—IEEE international conference on systems, man and cybernetics, pp 1009–1014
Fan Q, Chen Z, Xia Z (2020) A novel quasi-reflected Harris hawks optimization algorithm for global optimization problems. Soft Comput. https://doi.org/10.1007/s00500-020-04834-7
Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020a) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377. https://doi.org/10.1016/j.eswa.2020.113377
Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020b) Equilibrium optimizer: a novel optimization algorithm. Knowl Based Syst 191:105190. https://doi.org/10.1016/j.knosys.2019.105190
Gandomi AH (2014) Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans 53:1168–1183. https://doi.org/10.1016/j.isatra.2014.03.018
Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17:4831–4845. https://doi.org/10.1016/j.cnsns.2012.05.010
Gandomi AH, Yang X-S, Talatahari S, Alavi AH (2013a) Metaheuristic algorithms in modeling and optimization. In: Yang X-S, Cui Z, Xiao R, Gandomi AH (eds) Metaheuristic applications in structures and infrastructures, 1st edn. Elsevier, London, pp 1–24
Gandomi AH, Yang XS, Alavi AH (2013b) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35. https://doi.org/10.1007/s00366-011-0241-y
Gao J, Wang J (2011) A hybrid quantum-inspired immune algorithm for multiobjective optimization. Appl Math Comput 217:4754–4770. https://doi.org/10.1016/j.amc.2010.11.030
Gholizadeh S, Salajegheh E (2009) Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel. Comput Methods Appl Mech Eng 198:2936–2949. https://doi.org/10.1016/j.cma.2009.04.010
Gholizadeh S, Danesh M, Gheyratmand C (2020) A new Newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames. Comput Struct 234:106250. https://doi.org/10.1016/j.compstruc.2020.106250
Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13:533–549. https://doi.org/10.1016/0305-0548(86)90048-1
Guha D, Roy P, Banerjee S (2020) Quasi-oppositional backtracking search algorithm to solve load frequency control problem of interconnected power system. Iran J Sci Technol Trans Electr Eng 44:781–804. https://doi.org/10.1007/s40998-019-00260-0
Gupta S, Deep K (2020) A memory-based Grey wolf optimizer for global optimization tasks. Appl Soft Comput J. https://doi.org/10.1016/j.asoc.2020.106367
Gupta S, Deep K, Engelbrecht AP (2020a) A memory guided sine cosine algorithm for global optimization. Eng Appl Artif Intell 93:103718. https://doi.org/10.1016/j.engappai.2020.103718
Gupta S, Deep K, Mirjalili S, Kim JH (2020b) A modified sine cosine algorithm with novel transition parameter and mutation operator for global optimization. Expert Syst Appl 154:113395. https://doi.org/10.1016/j.eswa.2020.113395
Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9:159–195
Holland JH (1992) Genetic algorithms. Sci Am 267:66–72. https://doi.org/10.1038/scientificamerican0792-66
Jamil M, Yang XS (2013) A literature survey of benchmark functions for global optimisation problems. Int J Math Model Numer Optim 4:150. https://doi.org/10.1504/IJMMNO.2013.055204
Jin Y, Yin Z (2020) Enhancement of backtracking search algorithm for identifying soil parameters. Int J Numer Anal Methods Geomech 44:1239–1261. https://doi.org/10.1002/nag.3059
Kallioras NA, Lagaros ND, Avtzis DN (2018) Pity beetle algorithm—a new metaheuristic inspired by the behavior of bark beetles. Adv Eng Softw 121:147–166. https://doi.org/10.1016/j.advengsoft.2018.04.007
Kaur S, Awasthi LK, Sangal AL, Dhiman G (2020) Tunicate Swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell 90:103541. https://doi.org/10.1016/j.engappai.2020.103541
Kennedy J, Eberhart R (1948) Particle swarm optimization. In: Proceedings of ICNN’95—international conference on neural networks. IEEE, pp 1942–1948
Kumar M, Kulkarni AJ, Satapathy SC (2018) Socio evolution & learning optimization algorithm: a socio-inspired optimization methodology. Futur Gener Comput Syst 81:252–272. https://doi.org/10.1016/j.future.2017.10.052
Li S, Chen H, Wang M et al (2020) Slime mould algorithm: a new method for stochastic optimization. Futur Gener Comput Syst 111:300–323. https://doi.org/10.1016/j.future.2020.03.055
Liang J, Qin K, Suganthan PN et al (2006) Comprehensive learning particle swarm optimiser for global optimisation of multimodal functions CEC-31 special session on evolutionary computation for smart city view project evolutionary algorithms for power system optimisation view project comprehensive. IEEE Trans Evol Comput. https://doi.org/10.1109/TEVC.2005.857610
Lin J (2015) Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems. Nonlinear Dyn 80:209–219. https://doi.org/10.1007/s11071-014-1861-8
Liu J, Sun J, Xu W (2006) Quantum-behaved particle swarm optimization with adaptive mutation operator. In: Lecture notes in computer science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, pp 959–967
Liu Z, Wang Y, Yang S, et al An adaptive framework to tune the coordinate systems in nature-inspired optimization algorithms. ieeexplore.ieee.org
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Mirjalili S, Gandomi AH, Mirjalili SZ et al (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
Nama S, Saha AK (2018) A new hybrid differential evolution algorithm with self-adaptation for function optimization. Appl Intell 48:1657–1671. https://doi.org/10.1007/s10489-017-1016-y
Nama S, Saha AK, Ghosh S (2016a) Improved symbiotic organisms search algorithm for solving unconstrained function optimization. Decis Sci Lett. https://doi.org/10.5267/j.dsl.2016.2.004
Nama S, Saha AK, Ghosh S (2016b) A new ensemble algorithm of differential evolution and backtracking s algorithm with adaptive control parameter for function optimization. Int J Ind Eng Comput 7:323–338. https://doi.org/10.5267/j.ijiec.2015.9.003
Nama S, Saha AK, Ghosh S (2016c) Improved symbiotic organisms search algorithm for solving unconstrained function optimization. Decis Sci Lett. https://doi.org/10.5267/j.dsl.2016.2.004
Nama S, Saha AK, Ghosh S (2017) Improved backtracking search algorithm for pseudo dynamic active earth pressure on retaining wall supporting c-Ф backfill. Appl Soft Comput J 52:885–897. https://doi.org/10.1016/j.asoc.2016.09.037
Nowcki H (1974) Optimization in pre-contract ship design. Comput Appl Autom Shipyard Oper Shipyardng Des 2:327–338
Olorunda O, Engelbrecht AP (2008a) Measuring exploration/exploitation in particle swarms using swarm diversity. In: 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence). IEEE, pp 1128–1134
Olorunda O, Engelbrecht AP (2008b) Measuring exploration/exploitation in particle swarms using swarm diversity. In: 2008 IEEE Congress on evolutionary computation, CEC 2008. pp 1128–1134
Qu B, Suganthan P, on SD-IT (2012) undefined A distance-based locally informed particle swarm model for multimodal optimization. ieeexplore.ieee.org
Rahnamayan RS, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12:64–79. https://doi.org/10.1109/TEVC.2007.894200
Rahnamayan S, Tizhoosh HR, Salama MMA (2007) Quasi-oppositional differential evolution. In: 2007 IEEE congress on evolutionary computation, CEC 2007. pp 2229–2236
Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Des 43:303–315. https://doi.org/10.1016/j.cad.2010.12.015
Rao RV, Pawar RB (2020) Constrained design optimization of selected mechanical system components using Rao algorithms. Appl Soft Comput J 89:106141. https://doi.org/10.1016/j.asoc.2020.106141
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (ny) 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004
Sadollah A, Sayyaadi H, Yoo DG et al (2018) Mine blast harmony search: a new hybrid optimization method for improving exploration and exploitation capabilities. Appl Soft Comput J 68:548–564. https://doi.org/10.1016/j.asoc.2018.04.010
Saha A, Chakraborty AK, Das P (2019) Quasi-reflection-based symbiotic organisms search algorithm for solving static optimal power flow problem. Sci Iran 26:1664–1689. https://doi.org/10.24200/sci.2018.20179
Shandilya SK, Shandilya S, Deep K, Nagar AK (2017) Handbook of research on soft computing and nature-inspired algorithms. IGI Global, Hershey
Shi Y (2011) Brain storm optimization algorithm. pp 303–309. ISBN 978-3-319-68912-8
Sriram M, Ravindra K (2020) Backtracking search optimization algorithm based MPPT technique for solar PV system. Springer, Cham, pp 498–506
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328
Tian Z, Ren Y, Wang G (2020) An application of backtracking search optimization-based least squares support vector machine for prediction of short-term wind speed. Wind Eng 44:266–281. https://doi.org/10.1177/0309524X19849843
Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: Proceedings—international conference on computational intelligence for modelling, control and automation, CIMCA 2005 and international conference on intelligent agents, Web Technologies and Internet. pp 695–701
Wang C, Koh JM, Yu T et al (2020) Material and shape optimization of bi-directional functionally graded plates by GIGA and an improved multi-objective particle swarm optimization algorithm. Comput Methods Appl Mech Eng 366:113017. https://doi.org/10.1016/j.cma.2020.113017
Wang L, Tang F, Wu H (2005) Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Appl Math Comput 171:1141–1156. https://doi.org/10.1016/j.amc.2005.01.115
Wang Y, Liu Z, Li J et al (2016) Utilizing cumulative population distribution information in differential evolution. Elsevier, London
Wei F, Shi Y, Li J, Zhang Y (2020) Multi-strategy synergy-based backtracking search optimization algorithm. Soft Comput. https://doi.org/10.1007/s00500-020-05225-8
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893
Xia L, Zhang L, Xia Q, Shi T (2018) Stress-based topology optimization using bi-directional evolutionary structural optimization method. Comput Methods Appl Mech Eng 333:356–370. https://doi.org/10.1016/j.cma.2018.01.035
Yang X, Cui Z, Xiao R, et al (2013) Swarm intelligence and bio-inspired computation: theory and applications. ISBN 978-3-319-68913-5 (eBook)
Yang X, He X (2016) Nature-inspired. Comput Eng 637:1–20. https://doi.org/10.1007/978-3-319-30235-5
Yang XS (2014) Nature-inspired optimization algorithms. Elsevier Inc, London
Yi JH, Lu M, Zhao XJ (2020) Quantum inspired monarch butterfly optimisation for UCAV path planning navigation problem. Int J Bio-Inspir Comput 15:75–89. https://doi.org/10.1504/IJBIC.2020.106428
Zhang Y, Jin Z, Zhao X, Yang Q (2020a) Backtracking search algorithm with Lévy flight for estimating parameters of photovoltaic models. Energy Convers Manag 208:112615. https://doi.org/10.1016/j.enconman.2020.112615
Zhang Y, Ma M, Jin Z (2020b) Backtracking search algorithm with competitive learning for identification of unknown parameters of photovoltaic systems. Expert Syst Appl 160:113750. https://doi.org/10.1016/j.eswa.2020.113750
Zhao J, Tang D, Liu Z et al (2020) Spherical search optimizer: a simple yet efficient meta-heuristic approach. Neural Comput Appl 32:9777–9808. https://doi.org/10.1007/s00521-019-04510-4
Zhao W, Du C, Jiang S (2018) An adaptive multiscale approach for identifying multiple flaws based on XFEM and a discrete artificial fish swarm algorithm. Comput Methods Appl Mech Eng 339:341–357. https://doi.org/10.1016/j.cma.2018.04.037
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Nama, S., Sharma, S., Saha, A.K. et al. A quantum mutation-based backtracking search algorithm. Artif Intell Rev 55, 3019–3073 (2022). https://doi.org/10.1007/s10462-021-10078-0
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DOI: https://doi.org/10.1007/s10462-021-10078-0