Abstract
Due to the complex mathematical structures of the models in engineering, heuristic methods which do not require derivative are developed. This paper improves recently developed Grey Wolf Optimization Algorithm by extending it with three new features: namely presenting a new formulation for evaluating the positions of search agents, applying mirroring distance to the variables violating the limits, and proposing a dynamic decision approach for each agent either in exploration or exploitation phases. The performance of Advanced Grey Wolf Optimization (AGWO) method is tested using several optimization test functions and compared to several heuristic algorithms. Moreover, a planning problem in smart grids is solved by considering different objective functions using 33 and 141 bus distribution test systems. From the numerical simulation results, we observe that, AGWO is able to find the best results compared to other methods from 10 and 9 out of 13 test functions for 30 and 60 variables, respectively. Similar to this, it finds best function values for 5 out of 10 fixed number of variable test functions. Also, the result of the CEC-C06 2019 benchmark functions shows that AGWO outperforms 8 for optimization problems from 10. In power distribution system planning problem, better objective function values were determined by using AGWO, resulting a better voltage profile, less losses, and less emission costs compared to solutions obtained by Grey Wolf Optimization (GWO) and Particle Swarm Optimization (PSO) algorithms.
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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Abdullah JM, Ahmed T (2019) Fitness dependent optimizer: inspired by the bee swarming reproductive process. IEEE Access 7:43473–43486
Abualigah L, Diabat A, Mirjalili S, Elaziz MA, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609
Abualigah L, Yousri D, Elaziz MA, Ewees AA, Al-qaness MAA, Gandomi AH (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Indust Eng 157:107250
Ahmadi B, Ceylan O, Ozdemir A (2021) A multi-objective optimization evaluation framework for integration of distributed energy resources. J Energy Storage 41:103005
Ahmadi B, Ceylan O, Ozdemir A (2021) Distributed energy resource allocation using multi-objective grasshopper optimization algorithm. Electric Power Syst Res 201:107564
Ahmadi B, Ceylan O, Ozdemir A (2019a) Grey wolf optimizer for allocation and sizing of distributed renewable generation. In: 2019 54th international universities power engineering conference (UPEC), pp 1–6, September
Ahmadi B, Ceylan O, Ozdemir A (2019b) Optimal allocation of multi-type distributed generators for minimization of power losses in distribution systems. In: the 20th international conference on intelligent systems applications to power systems, ISAP 2019, New Delhi/India, December
Arabi Nowdeh S, Faraji Davoudkhani I, Moghaddam MJH, Seifi Najmi E, Abdelaziz AY, Ahmadi A, Razavi SE, Gandoman FH (2019) Fuzzy multi-objective placement of renewable energy sources in distribution system with objective of loss reduction and reliability improvement using a novel hybrid method. Appl Soft Comput 77:761–779
Asef F, Majidnezhad V, Feizi-Derakhshi M-R, Parsa S (2021) Heat transfer relation-based optimization algorithm (htoa). Soft Comput, pp 1–30
Baran ME, Wu FF (1989) Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Delivery 4(2):1401–1407
Bavarsad Salehpoor I, Molla-Alizadeh-Zavardehi S (2019) A constrained portfolio selection model at considering risk-adjusted measure by using hybrid meta-heuristic algorithms. Appl Soft Comput 75:233–253
Biswas PP, Mallipeddi R, Suganthan PN, Amaratunga GAJ (2017) A multiobjective approach for optimal placement and sizing of distributed generators and capacitors in distribution network. Appl Soft Comput 60:268–280
Boveiri HR, Elhoseny M (2018) A-coa: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization. Neural Comput Appl 93:1–25
Brest J, Maučec MS, Bošković B (2019) The 100-digit challenge: Algorithm jde100. In: 2019 IEEE congress on evolutionary computation (CEC). IEEE 93:19–26
Burke EK, Kendall G et al (2005) Search methodologies. Springer, Berlin
Ceylan O (2020) Multi-verse optimization algorithm-and salp swarm optimization algorithm-based optimization of multilevel inverters. Neural Comput Appl 93:1–16
Chu X, Cai F, Gao D, Li L, Cui J, Xiu SX, Qin Q (2020) An artificial bee colony algorithm with adaptive heterogeneous competition for global optimization problems. Appl Soft Comput 93:106391
Eberhart R, Kennedy JS (1995) A new optimizer using particle swarm theory. MHS’95. In: Proceedings of the sixth international symposium on micro machine and human science, pp 39–43
Elaziz MA, Heidari AA, Fujita H, Moayedi H (2020) A competitive chain-based harris hawks optimizer for global optimization and multi-level image thresholding problems. Appl Soft Comput 37:106347
Eminoglu U, Hocaoglu M (2009) Distribution systems forward/backward sweep-based power flow algorithms: A review and comparison study. Elect Power Comp Syst 37(91–110):01
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: Harmony search. SIMULATION 76(2):60–68
Gnana Sundari M, Rajaram M, Balaraman S (2016) Application of improved firefly algorithm for programmed pwm in multilevel inverter with adjustable dc sources. Appl Soft Comput 41:169–179
Guner S, Ozdemir A (2020) Reliability improvement of distribution system considering ev parking lots. Elect Power Syst Res 185:106353
Gupta S, Deep K (2020) A memory-based grey wolf optimizer for global optimization tasks. Appl Soft Comput 93:106367
Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with levy flight for optimization tasks. Appl Soft Comput 60:115–134
Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with lévy flight for optimization tasks. Appl Soft Comput 60:115–134
Kansal V, Dhillon JS (2020) Emended salp swarm algorithm for multiobjective electric power dispatch problem. Appl Soft Comput 90:106172
Karthikumar K, Kumar VS (2021) A new opposition crow search optimizer-based two-step approach for controlled intentional islanding in microgrids. Soft Comput 25(4):2575–2588
Ke Q, Zhang J, Wei W, Połap D, Woźniak M, Kośmider L, Damaševĭcius R (2019) A neuro-heuristic approach for recognition of lung diseases from x-ray images. Expert Syst Appl 126:218–232
Khandelwal A, Bhargava A, Sharma A, Sharma H (2018) Modified grey wolf optimization algorithm for transmission network expansion planning problem. Arab J Sci Eng 43(6):2899–2908
Khodr HM, Olsina FG, De Oliveira-De Jesus PM, Yusta JM (2008) Maximum savings approach for location and sizing of capacitors in distribution systems. Elect Power Syst Res 78(7):1192–1203
Liu K, Sheng W, Liu Y, Meng X, Liu Y (2015) Optimal sitting and sizing of dgs in distribution system considering time sequence characteristics of loads and dgs. Int J Elect Power Energy Syst 69:430–440
Mahdad B, Srairi K (2015) Blackout risk prevention in a smart grid based flexible optimal strategy using grey wolf-pattern search algorithms. Energy Convers Manage 98:411–429
Mahesh A, Sushnigdha G (2021) A novel search space reduction optimization algorithm. Soft Comput, pp 1–28
Mirjalili S (2015) How effective is the grey wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161
Mirjalili S (2015) Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98
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, Saremi S, Mirjalili SM, Coelho LS (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47:106–119
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513
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
Nguyen TP, Vo DN (2018) A novel stochastic fractal search algorithm for optimal allocation of distributed generators in radial distribution systems. Appl Soft Comput 70:773–796
Nguyen H, Moayedi H, Foong LK, Husam AH, Najjar A, Jusoh WAW, Rashid ASA, Jamali J (2020) Optimizing ANN models with PSO for predicting short building seismic response. Eng Comput 36(3):823–837
Papadimitrakis M, Giamarelos N, Stogiannos M, Zois EN, Livanos NA-I, Alexandridis A (2021) Metaheuristic search in smart grid: a review with emphasis on planning, scheduling and power flow optimization applications. Renew Sustain Energy Rev 145:111072
Pfenninger S, Staffell I (2016) Long-term patterns of european pv output using 30 years of validated hourly reanalysis and satellite data. Energy 114:1251–1265
Premkumar K, Manikandan BV (2015) Speed control of brushless dc motor using bat algorithm optimized adaptive neuro-fuzzy inference system. Appl Soft Comput 32:403–419
Price KV, Awad NH, Ali MZ, Suganthan PN (2018) The 100-digit challenge: Problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. Nanyang Technological University
Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417
Rahmani R, Langeroudi NMA, Yousefi R, Mahdian M, Seyedmahmoudian M (2014) Fuzzy logic controller and cascade inverter for direct torque control of im. Neural Comput Appl 25(3–4):879–888
Rashid TA, Abbas DK, Turel YK (2019) A multi hidden recurrent neural network with a modified grey wolf optimizer. PLoS ONE 14(3):1–23, 03
Saha A, Bhattacharya A, Das P, Chakraborty AK (2020) Hsos: a novel hybrid algorithm for solving the transient-stability-constrained opf problem. Soft Comput 24(10):7481–7510
Saha S, Mukherjee V (2020) A novel multi-objective modified symbiotic organisms search algorithm for optimal allocation of distributed generation in radial distribution system. Neural Comput Appl 83:1–21
Salgotra R, Singh U, Sharma S (2019) On the improvement in grey wolf optimization. Neural Comput Appl 36:1–40
Sanjay R, Jayabarathi T, Raghunathan T, Ramesh V, Mithulananthan N (2017) Optimal allocation of distributed generation using hybrid grey wolf optimizer. IEEE Access 5:14807–14818
Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26(5):1257–1263
Shehab M, Abualigah L, Hamad HA, Alabool H, Alshinwan M, Khasawneh AM (2019) Moth-flame optimization algorithm: variants and applications. Neural Comput Appl 33:1–26
Staffell I, Pfenninger S (2016) Using bias-corrected reanalysis to simulate current and future wind power output. Energy 114:1224–1239
Sultana U, Khairuddin AB, Mokhtar AS, Zareen N, Sultana B (2016) Grey wolf optimizer based placement and sizing of multiple distributed generation in the distribution system. Energy 111:525–536
Tolba Mohamed A, Hegazy R, Mujahed A-D, Eisa Ayman A (2020) Heuristic optimization techniques for connecting renewable distributed generators on distribution grids. Benefits 3:6
Trelea IC (2003) The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf Process Lett 85(6):317–325
Truong KH, Nallagownden P, Elamvazuthi I, Vo DN (2019) An improved meta-heuristic method to maximize the penetration of distributed generation in radial distribution networks. Neural Comput Appl, pp 1–23
Truong KH, Nallagownden P, Elamvazuthi I, Dieu NV (2020) A quasi-oppositional-chaotic symbiotic organisms search algorithm for optimal allocation of dg in radial distribution networks. Appl Soft Comput 88:106067
Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4:65–85
Yammani C, Maheswarapu S, Matam SK (2016) A multi-objective shuffled bat algorithm for optimal placement and sizing of multi distributed generations with different load models. Int J Elect Power Energy Syst 79:120–131
Yang B, Zhang X, Tao Yu, Shu H, Fang Z (2017) Grouped grey wolf optimizer for maximum power point tracking of doubly-fed induction generator based wind turbine. Energy Convers Manage 133:427–443
Yang X, Deb S (2009) Cuckoo search via lévy flights. In: 2009 world congress on nature biologically inspired computing (NaBIC), pp 210–214
Yeh J-F, Chen T-Y, Chiang T-C (2019) Modified l-shade for single objective real-parameter optimization. In: 2019 IEEE congress on evolutionary computation (CEC). IEEE, pp 381–386
Zhu A, Xu C, Li Z, Wu J, Liu Z (2015) Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3d stacked soc. J Syst Eng Electron 26(2):317–328
Acknowledgements
This research is funded as a part of “117E773 Advanced Evolutionary Computation for Smart Grid and Smart Community” project under the framework of 1001 Project organized by “The Scientific and Technological Research Council of Turkey TUBITAK”.
Funding
This research is funded as a part of “117E773 Advanced Evolutionary Computation for Smart Grid and Smart Community” project under the framework of 1001 Project organized by “The Scientific and Technological Research Council of Turkey TUBITAK”.
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Bahman Ahmadi has made literature review, worked on software development, prepared the original draft, and visualized the simulation results. Soheil Younesi contributed to literature review and helped on preparing the draft. Oguzhan Ceylan contributed to methodology, data curation, review and editing, and formal analysis. Aydogan Ozdemir contributed to conceptualization and validation. He supervised the study and administered the project.
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Ahmadi, B., Younesi, S., Ceylan, O. et al. An advanced Grey Wolf Optimization Algorithm and its application to planning problem in smart grids. Soft Comput 26, 3789–3808 (2022). https://doi.org/10.1007/s00500-022-06767-9
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DOI: https://doi.org/10.1007/s00500-022-06767-9