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Sine cosine grey wolf optimizer to solve engineering design problems

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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.

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References

  1. Goldberg DE (2006) Genetic algorithms. Pearson Education India, Bangalore

    Google Scholar 

  2. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks

  3. 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

    MathSciNet  MATH  Google Scholar 

  4. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Google Scholar 

  5. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  6. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Google Scholar 

  7. 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

    Google Scholar 

  8. 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

    Google Scholar 

  9. 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

    Google Scholar 

  10. 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

    Article  Google Scholar 

  11. 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

    Google Scholar 

  12. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47

    Google Scholar 

  13. 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

    Article  Google Scholar 

  14. 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

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. 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

    Article  Google Scholar 

  18. 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

    Article  Google Scholar 

  19. 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

    Article  Google Scholar 

  20. 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

    Article  Google Scholar 

  21. 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

    Article  Google Scholar 

  22. 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

    Article  Google Scholar 

  23. 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

    Article  Google Scholar 

  24. 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

    Article  Google Scholar 

  25. 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

    Article  Google Scholar 

  26. Gao W, Wu H, Siddiqui MK, Baig AQ (2018) Study of biological networks using graph theory. Saudi J Biol Sci 25:1212–1219

    Google Scholar 

  27. Gao W, Wang W, Dimitrov D, Wang Y (2018) Nano properties analysis via fourth multiplicative ABC indicator calculating. Arab J Chem 11:793–801

    Google Scholar 

  28. Gao W, Guirao JLG, Basavanagoud B, Wu J (2018) Partial multi-dividing ontology learning algorithm. Inf Sci 467:35–58

    MathSciNet  MATH  Google Scholar 

  29. 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

    MathSciNet  MATH  Google Scholar 

  30. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82

    Google Scholar 

  31. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102

    Google Scholar 

  32. Rizk-Allah RM (2019) An improved sine–cosine algorithm based on orthogonal parallel information for global optimization. Soft Comput 23:7135–7161

    Google Scholar 

  33. Elaziz MA, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500

    Google Scholar 

  34. Gupta S, Deep K (2019) Improved sine cosine algorithm with crossover scheme for global optimization. Knowl-Based Syst 165:374–406

    Google Scholar 

  35. 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

    Google Scholar 

  36. 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

    Google Scholar 

  37. Nenavath H, Jatoth RK (2018) Hybridizing sine cosine algorithm with differential evolution for global optimization and object tracking. Appl Soft Comput 62:1019–1043

    Google Scholar 

  38. 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

    Google Scholar 

  39. 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

    Google Scholar 

  40. 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

    Article  Google Scholar 

  41. 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)

  42. Jayabarathi T, Raghunathan T, Adarsh B, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641

    Google Scholar 

  43. 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

    Google Scholar 

  44. 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

    Google Scholar 

  45. 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

    Google Scholar 

  46. 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

    Google Scholar 

  47. 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

    Google Scholar 

  48. 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

    Article  Google Scholar 

  49. Tawhid MA, Ali AF (2017) A hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function. Memetic Computing 9:347–359

    Google Scholar 

  50. 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

    Article  Google Scholar 

  51. Gupta S, Deep K (2018) Cauchy Grey Wolf Optimiser for continuous optimisation problems. J Exp Theor Artif Intell 30:1051–1075

    Google Scholar 

  52. 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

    Google Scholar 

  53. 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

    Google Scholar 

  54. Singh N, Singh S (2017) A novel hybrid GWO-SCA approach for optimization problems. Engineering Science and Technology, an International Journal 20:1586–1601

    Google Scholar 

  55. 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

    Article  Google Scholar 

  56. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Google Scholar 

  57. Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48:3462–3481

    Google Scholar 

  58. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338

    MATH  Google Scholar 

  59. Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In: Proceeding of the ASME design technology conference

  60. 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)

  61. Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35

    Google Scholar 

  62. 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

    Google Scholar 

  63. 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

    Article  Google Scholar 

  64. 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

  65. Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33:735–748

    Google Scholar 

  66. Tsai J-F (2005) Global optimization of nonlinear fractional programming problems in engineering design. Eng Optim 37:399–409

    MathSciNet  Google Scholar 

  67. Akhtar S, Tai K, Ray T (2002) A socio-behavioural simulation model for engineering design optimization. Eng Optim 34:341–354

    Google Scholar 

  68. Ku KuJ, Rao SS, Chen L (1998) Taguchi-aided search method for design optimization of engineering systems. Eng Optim 30:1–23

    Google Scholar 

  69. 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

    MathSciNet  MATH  Google Scholar 

  70. Arora J (2004) Optimum design concepts: optimality conditions. Introduction to optimum design. Elsevier, Amsterdam

    Google Scholar 

  71. 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

    MATH  Google Scholar 

  72. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248

    MATH  Google Scholar 

  73. Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41:113–127

    Google Scholar 

  74. He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20:89–99

    Google Scholar 

  75. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294

    Google Scholar 

  76. 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

  77. Huang F-z, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186:340–356

    MathSciNet  MATH  Google Scholar 

  78. 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

    Article  MATH  Google Scholar 

  79. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization

  80. 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

  81. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359

    MathSciNet  MATH  Google Scholar 

  82. 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

    Google Scholar 

  83. 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

    MathSciNet  MATH  Google Scholar 

  84. 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

    Google Scholar 

  85. 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

    Article  Google Scholar 

  86. Thakur M (2007) New real coded genetic algorithms for global optimization. Ph.D thesis, Department of Mathematics, Indian Institute of Technology

  87. 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

    Article  Google Scholar 

  88. 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

    Google Scholar 

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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

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