Abstract
Balancing the exploration and exploitation in any nature-inspired optimization algorithm is an essential task, while solving the real-world global optimization problems. Therefore, the search agents of an algorithm always try to explore the unvisited domains of a search space in a balanced manner. The sine cosine algorithm (SCA) is a recent addition to the field of metaheuristics that finds the solution of an optimization problem using the behavior of sine and cosine functions. However, in some cases, the SCA skips the true solutions and trapped at sub-optimal solutions. These problems lead to the premature convergence, which is harmful in determining the global optima. Therefore, in order to alleviate the above-mentioned issues, the present study aims to establish a comparatively better synergy between exploration and exploitation in the SCA. In this direction, firstly, the exploration ability of the SCA is improved by integrating the social and cognitive component, and secondly, the balance between exploration and exploitation is maintained through the grey wolf optimizer (GWO). The proposed algorithm is named as SC-GWO. For the performance evaluation, a well-known set of benchmark problems and engineering test problems are taken. The dimension of benchmark test problems is varied from 30 to 100 to observe the robustness of the SC-GWO on scalability of problems. In the paper, the SC-GWO is also used to determine the optimal setting for overcurrent relays. The analysis of obtained numerical results and its comparison with other metaheuristic algorithms demonstrate the superior ability of the proposed SC-GWO.
Similar content being viewed by others
References
Goldberg DE (2006) Genetic algorithms. Pearson Education India, Bangalore
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39:459–471
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249
Chen H, Jiao S, Wang M, Heidari AA, Zhao X (2020) Parameters identification of photovoltaic cells and modules using diversification-enriched Harris hawks optimization with chaotic drifts. J Clean Prod 244:118778
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872
Mafarja M, Aljarah I, Heidari AA, Hammouri AI, Faris H, Ala’M A-Z, Mirjalili S (2018) Evolutionary population dynamics and grasshopper optimization approaches for feature selection problems. Knowl-Based Syst 145:25–45
Gupta S, Deep K, Heidari AA, Moayedi H, Chen H (2019) Harmonized salp chain-built optimization. Eng Comput 36: https://doi.org/10.1007/s00366-019-00871-5
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47
Zhang Z, Jiang D, Liu W, Chen J, Li E, Fan J, Xie K (2019) Study on the mechanism of roof collapse and leakage of horizontal cavern in thinly bedded salt rocks. Environ Earth Sci 78:292. https://doi.org/10.1007/s12665-019-8292-2
Qiao W, Yang Z (2019) Modified dolphin swarm algorithm based on chaotic maps for solving high-dimensional function optimization problems. IEEE Access 7:110472–110486. https://doi.org/10.1109/ACCESS.2019.2931910
Qiao W, Yang Z (2019) Solving large-scale function optimization problem by using a new metaheuristic algorithm based on quantum dolphin swarm algorithm. IEEE Access 7:138972–138989. https://doi.org/10.1109/ACCESS.2019.2942169
Qiao W, Tian W, Tian Y, Yang Q, Wang Y, Zhang J (2019) The forecasting of PM2.5 using a hybrid model based on wavelet transform and an improved deep learning algorithm. IEEE Access 7:142814–142825. https://doi.org/10.1109/ACCESS.2019.2944755
Liu W, Zhang X, Fan J, Li Y, Wang L (2020) Evaluation of Potential for Salt Cavern Gas Storage and Integration of Brine Extraction: Cavern Utilization, Yangtze River Delta Region. Nat Resour Res 29. https://doi.org/10.1007/s11053-020-09640-4
Qiao W, Huang K, Azimi M, Han S (2019) A novel hybrid prediction model for hourly gas consumption in supply side based on improved whale optimization algorithm and relevance vector machine. IEEE Access 7:88218–88230. https://doi.org/10.1109/ACCESS.2019.2918156
Fan J, Jiang D, Liu W, Wu F, Chen J, Daemen J (2019) Discontinuous fatigue of salt rock with low-stress intervals. Int J Rock Mech Min Sci 115:77–86. https://doi.org/10.1016/j.ijrmms.2019.01.013
Liu W, Zhang Z, Chen J, Fan J, Jiang D, Jjk D, Li Y (2019) Physical simulation of construction and control of two butted-well horizontal cavern energy storage using large molded rock salt specimens. Energy 185:682–694. https://doi.org/10.1016/j.energy.2019.07.014
Chen J, Lu D, Liu W, Fan J, Jiang D, Yi L, Kang Y (2020) Stability study and optimization design of small-spacing two-well (SSTW) salt caverns for natural gas storages. J Energy Storage 27:101131. https://doi.org/10.1016/j.est.2019.101131
Zhou G, Moayedi H, Foong LK (2020) Teaching-learning-based metaheuristic scheme for modifying neural computing in appraising energy performance of building. Eng Comput. https://doi.org/10.1007/s00366-020-00981-5
Zhou G, Moayedi H, Bahiraei M, Lyu Z (2020) Employing artificial bee colony and particle swarm techniques for optimizing a neural network in prediction of heating and cooling loads of residential buildings. J Clean Prod. https://doi.org/10.1016/j.jclepro.2020.120082
Liu W, Zhang ZX, Fan JY, Jiang DY, Daemen JJK (2020) Research on the stability and treatments of natural gas storage caverns with different shapes in bedded salt rocks. IEEE Access 8:000507. https://doi.org/10.1109/ACCESS.2020.2967078
Jinlong L, Wenjie X, Jianjing Z, Wei L, Xilin S, Chunhe Y (2020) Modeling the mining of energy storage salt caverns using a structural dynamic mesh. Energy 193:116730. https://doi.org/10.1016/j.energy.2019.116730
Gao W, Wu H, Siddiqui MK, Baig AQ (2018) Study of biological networks using graph theory. Saudi J Biol Sci 25:1212–1219
Gao W, Wang W, Dimitrov D, Wang Y (2018) Nano properties analysis via fourth multiplicative ABC indicator calculating. Arab J Chem 11:793–801
Gao W, Guirao JLG, Basavanagoud B, Wu J (2018) Partial multi-dividing ontology learning algorithm. Inf Sci 467:35–58
Gao W, Guirao JLG, Abdel-Aty M, Xi W (2019) An independent set degree condition for fractional critical deleted graphs. Discrete Cont Dyn Syst-S 12:877–886
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102
Rizk-Allah RM (2019) An improved sine–cosine algorithm based on orthogonal parallel information for global optimization. Soft Comput 23:7135–7161
Elaziz MA, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500
Gupta S, Deep K (2019) Improved sine cosine algorithm with crossover scheme for global optimization. Knowl-Based Syst 165:374–406
Nayak DR, Dash R, Majhi B, Wang S (2018) Combining extreme learning machine with modified sine cosine algorithm for detection of pathological brain. Comput Electr Eng 68:366–380
Zhang J, Zhou Y, Luo Q (2018) An improved sine cosine water wave optimization algorithm for global optimization. J Intell Fuzzy Syst 34:2129–2141
Nenavath H, Jatoth RK (2018) Hybridizing sine cosine algorithm with differential evolution for global optimization and object tracking. Appl Soft Comput 62:1019–1043
Zamli KZ, Din F, Ahmed BS, Bures M (2018) A hybrid Q-learning sine-cosine-based strategy for addressing the combinatorial test suite minimization problem. PLoS ONE 13:e0195675
Chen H, Heidari AA, Zhao X, Zhang L, Chen H (2020) Advanced orthogonal learning-driven multi-swarm sine cosine optimization: framework and case studies. Expert Syst Appl 144:113113
Gupta S, Deep K (2019) A novel hybrid sine cosine algorithm for global optimization and its application to train multilayer perceptrons. Appl Intell 50: https://doi.org/10.1007/s10489-019-01570-w
Muangkote N, Sunat K, Chiewchanwattana S (2014) An improved grey wolf optimizer for training q-Gaussian Radial Basis Functional-link nets. In: 2014 international computer science and engineering conference (ICSEC)
Jayabarathi T, Raghunathan T, Adarsh B, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641
Rodríguez L, Castillo O, Soria J, Melin P, Valdez F, Gonzalez CI, Martinez GE, Soto J (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328
Castillo O, Amador-Angulo L (2018) A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design. Inf Sci 460:476–496
Castillo O, Melin P, Ontiveros E, Peraza C, Ochoa P, Valdez F, Soria J (2019) A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics. Eng Appl Artif Intell 85:666–680
Ochoa P, Castillo O, Soria J (2020) Optimization of fuzzy controller design using a Differential Evolution algorithm with dynamic parameter adaptation based on Type-1 and Interval Type-2 fuzzy systems. Soft Comput 24:193–214
Olivas F, Valdez F, Melin P, Sombra A, Castillo O (2019) Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm. Inf Sci 476:159–175
Sánchez D, Melin P, Castillo O (2017) A grey wolf optimizer for modular granular neural networks for human recognition. Comput Intell Neurosci 2017:1–24. https://doi.org/10.1155/2017/4180510
Tawhid MA, Ali AF (2017) A hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function. Memetic Computing 9:347–359
Gupta S, Deep K (2019) Enhanced leadership-inspired grey wolf optimizer for global optimization problems. Eng Comput 36:1–24. https://doi.org/10.1007/s00366-019-00795-0
Gupta S, Deep K (2018) Cauchy Grey Wolf Optimiser for continuous optimisation problems. J Exp Theor Artif Intell 30:1051–1075
Long W, Jiao J, Liang X, Tang M (2018) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Eng Appl Artif Intell 68:63–80
Gupta S, Deep K (2019) An efficient grey wolf optimizer with opposition-based learning and chaotic local search for integer and mixed-integer optimization problems. Arab J Sci Eng 44:7277–7296
Singh N, Singh S (2017) A novel hybrid GWO-SCA approach for optimization problems. Engineering Science and Technology, an International Journal 20:1586–1601
Mittal N, Singh U, Sohi BS (2016) Modified grey wolf optimizer for global engineering optimization. Appl Comput Intell Soft Comput 2016:1–1. https://doi.org/10.1155/2016/7950348
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48:3462–3481
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338
Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In: Proceeding of the ASME design technology conference
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (Cat. No. 98TH8360)
Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35
Wu S-J, Chow P-T (1995) Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization. Eng Optim+ A35 24:137–159
Kannan B, Kramer SN (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des 116(2):405–411. https://doi.org/10.1115/1.2919393
Nowacki H (1973) Optimization in pre-contract ship design, Computer Applications in the Automation of Shipyard Operation and Ship Design, IFIP/IFAC/JSNA, Tokyo, Japan
Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33:735–748
Tsai J-F (2005) Global optimization of nonlinear fractional programming problems in engineering design. Eng Optim 37:399–409
Akhtar S, Tai K, Ray T (2002) A socio-behavioural simulation model for engineering design optimization. Eng Optim 34:341–354
Ku KuJ, Rao SS, Chen L (1998) Taguchi-aided search method for design optimization of engineering systems. Eng Optim 30:1–23
Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37:443–473
Arora J (2004) Optimum design concepts: optimality conditions. Introduction to optimum design. Elsevier, Amsterdam
Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Meth Eng 21:1583–1599
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248
Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41:113–127
He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20:89–99
Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294
Deb K (1997) GeneAS: A Robust Optimal Design Technique for Mechanical Component Design. In: Dasgupta D, Michalewicz Z (eds) Evolutionary Algorithms in Engineering Applications. Springer, Berlin, Heidelberg, pp 497–514. https://doi.org/10.1007/978-3-662-03423-1_27
Huang F-z, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186:340–356
Kaveh A, Talatahari S (2010) An improved ant colony optimization for constrained engineering design problems. Eng Comput 27:155–182. https://doi.org/10.1108/02644401011008577
Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization
Blackburn J, Domin T (2006) Symmetrical components: a review. Protective relaying: principles and applications, CRC Press is an imprint of Taylor & Francis Group, an Informa business, ISBN 10:1-57444-716-5
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359
Chelliah TR, Thangaraj R, Allamsetty S, Pant M (2014) Coordination of directional overcurrent relays using opposition based chaotic differential evolution algorithm. Int J Electr Power Energy Syst 55:341–350
Thangaraj R, Pant M, Abraham A (2010) New mutation schemes for differential evolution algorithm and their application to the optimization of directional over-current relay settings. Appl Math Comput 216:532–544
Thangaraj R, Pant M, Deep K (2010) Optimal coordination of over-current relays using modified differential evolution algorithms. Eng Appl Artif Intell 23:820–829
Birla D, Maheshwari RP, Gupta HO, Deep K, Thakur M (2006) Application of random search technique in directional overcurrent relay coordination. Int J Emerg Electric Power Syst 7:1. https://doi.org/10.2202/1553-779X.1271
Thakur M (2007) New real coded genetic algorithms for global optimization. Ph.D thesis, Department of Mathematics, Indian Institute of Technology
Qiao W, Yang Z (2020) An improved dolphin swarm algorithm based on Kernel Fuzzy C-means in the application of solving the optimal problems of largescalefunction. IEEE Access. https://doi.org/10.1109/ACCESS.2019.2958456
Benmouyal G, Meisinger M, Burnworth J, Elmore W, Freirich K, Kotos P, Leblanc P, Lerley P, McConnell J, Mizener J (1999) IEEE standard inverse-time characteristic equations for overcurrent relays. IEEE Trans Power Delivery 14:868–872
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Gupta, S., Deep, K., Moayedi, H. et al. Sine cosine grey wolf optimizer to solve engineering design problems. Engineering with Computers 37, 3123–3149 (2021). https://doi.org/10.1007/s00366-020-00996-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-020-00996-y