Abstract
In this paper, we propose EOSMA, an equilibrium optimizer (EO)-guided slime mould algorithm (SMA), to improve efficiency by optimizing the search of SMAs. Firstly, the exploration and exploitation abilities of SMA are adapted to enhance the exploration in the early stage and the exploitation in the later stage. Secondly, the anisotropic search operator of SMA is replaced with the search operator of the equilibrium optimizer (EO) to guide search space of SMAs (EOSMA). Finally, the stochastic difference mutation operator is added to help the SMA algorithm escape from local optima after population location updates and to increase the diversity of the population at the late iteration. The performance of EOSMA is evaluated on CEC2019 and CEC2021 functions and nine engineering design problems. The results show that for the challenging CEC2019 functions, EOSMA significantly outperforms the 15 well-known comparison algorithms in terms of Mean and Min metrics. For the latest CEC2021 functions, EOSMA significantly outperforms IMODE, LSHADE, and LSHADE_cnEpSin in terms of Min metrics. In particular, for all nine engineering problems, EOSMA is able to find feasible solutions satisfying all constraints and significantly outperforms the advanced comparison algorithms such as SMA, EO, MPA, IGWO, AGPSO, MTDE in terms of solution accuracy, speed, and robustness.
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References
Povalej, Ž: Quasi-Newton’s method for multiobjective optimization. J. Comput. Appl. Math. 255, 765–777 (2014)
Zhang, J.; Xiao, Y.; Wei, Z.: Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization. Math. Probl. Eng. 2009, 1–16 (2009). https://doi.org/10.1155/2009/243290
Mohamed, A.W.; Hadi, A.A.; Mohamed, A.K.: Gaining-sharing knowledge based algorithm for solving optimization problems: a novel nature-inspired algorithm. Int. J. Mach. Learn. Cybern. 11(7), 1501–1529 (2020). https://doi.org/10.1007/s13042-019-01053-x
Mirjalili, S.; Mirjalili, S.M.; Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014). https://doi.org/10.1016/j.advengsoft.2013.12.007
Faramarzi, A.; Heidarinejad, M.; Stephens, B.; Mirjalili, S.: Equilibrium optimizer: a novel optimization algorithm. Knowl. Based Syst. 191, 105190 (2020). https://doi.org/10.1016/j.knosys.2019.105190
Goldberg, D.E.; Holland, J.H.: Genetic algorithms and machine learning. Mach. Learn. 3, 95–99 (1988)
Storn, R.; Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)
Yao, X.; Liu, Y.; Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999). https://doi.org/10.1109/4235.771163
Kirkpatrick, S.: Optimization by simulated annealing: quantitative studies. J. Stat. Phys. 34(5–6), 975–986 (1984). https://doi.org/10.1007/BF01009452
Grover, L. K.: A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC ’96, pp. 212–219. Philadelphia, Pennsylvania, United States (1996) doi: https://doi.org/10.1145/237814.237866
Erol, O.K.; Eksin, I.: A new optimization method: big Bang-Big crunch. Adv. Eng. Softw. 37(2), 106–111 (2006). https://doi.org/10.1016/j.advengsoft.2005.04.005
Alatas, B.: ACROA: artificial chemical reaction optimization algorithm for global optimization. Expert Syst. Appl. 38(10), 13170–13180 (2011). https://doi.org/10.1016/j.eswa.2011.04.126
Shareef, H.; Ibrahim, A.A.; Mutlag, A.H.: Lightning search algorithm. Appl. Soft Comput. 36, 315–333 (2015). https://doi.org/10.1016/j.asoc.2015.07.028
Mirjalili, S.; Mirjalili, S.M.; Hatamlou, A.: Multi-Verse Optimizer: a nature-inspired algorithm for global optimization. Neural Comput. Appl. 27(2), 495–513 (2016). https://doi.org/10.1007/s00521-015-1870-7
Rashedi, E.; Nezamabadi-pour, H.; Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009). https://doi.org/10.1016/j.ins.2009.03.004
Patel, V.K.; Savsani, V.J.: Heat transfer search (HTS): a novel optimization algorithm. Inf. Sci. 324, 217–246 (2015). https://doi.org/10.1016/j.ins.2015.06.044
Hashim, F.A.; Houssein, E.H.; Mabrouk, M.S.; Al-Atabany, W.; Mirjalili, S.: Henry gas solubility optimization: a novel physics-based algorithm. Future Gener. Comput. Syst. 101, 646–667 (2019). https://doi.org/10.1016/j.future.2019.07.015
Eskandar, H.; Sadollah, A.; Bahreininejad, A.; Hamdi, M.: Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput. Struct. 110–111, 151–166 (2012). https://doi.org/10.1016/j.compstruc.2012.07.010
Zhao, W.; Wang, L.; Zhang, Z.: Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl. -Based Syst. 163, 283–304 (2019). https://doi.org/10.1016/j.knosys.2018.08.030
Anita; Yadav, A.: AEFA: artificial electric field algorithm for global optimization. Swarm Evol. Comput. 48, 93–108 (2019). https://doi.org/10.1016/j.swevo.2019.03.013
Eberhart, R.; Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. Nagoya, Japan (1995) doi: https://doi.org/10.1109/MHS.1995.494215
Karaboga, D.; Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 459–471 (2007). https://doi.org/10.1007/s10898-007-9149-x
Rao, R.V.; Savsani, V.J.; Vakharia, D.P.: Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303–315 (2011). https://doi.org/10.1016/j.cad.2010.12.015
Mirjalili, S.; Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016). https://doi.org/10.1016/j.advengsoft.2016.01.008
Mirjalili, S.; Gandomi, A.H.; Mirjalili, S.Z.; Saremi, S.; Faris, H.; Mirjalili, S.M.: Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017). https://doi.org/10.1016/j.advengsoft.2017.07.002
Cuevas, E.; Cienfuegos, M.; Zaldívar, D.; Pérez-Cisneros, M.: A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Syst. Appl. 40(16), 6374–6384 (2013). https://doi.org/10.1016/j.eswa.2013.05.041
Dhiman, G.; Kumar, V.: Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl. Based Syst. 165, 169–196 (2019). https://doi.org/10.1016/j.knosys.2018.11.024
Faramarzi, A.; Heidarinejad, M.; Mirjalili, S.; Gandomi, A.H.: Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst. Appl. 152, 113377 (2020). https://doi.org/10.1016/j.eswa.2020.113377
Mirjalili, S.: Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl.- Based Syst. 89, 228–249 (2015). https://doi.org/10.1016/j.knosys.2015.07.006
Yapici, H.; Cetinkaya, N.: A new meta-heuristic optimizer: Pathfinder algorithm. Appl. Soft Comput. 78, 545–568 (2019). https://doi.org/10.1016/j.asoc.2019.03.012
Heidari, A.A.; Mirjalili, S.; Faris, H.; Aljarah, I.; Mafarja, M.; Chen, H.: Harris hawks optimization: algorithm and applications. Future Gener. Comput. Syst. 97, 849–872 (2019). https://doi.org/10.1016/j.future.2019.02.028
Li, S.; Chen, H.; Wang, M.; Heidari, A.A.; Mirjalili, S.: Slime mould algorithm: a new method for stochastic optimization. Future Gener. Comput. Syst. 111, 300–323 (2020). https://doi.org/10.1016/j.future.2020.03.055
Wolpert, D.H.; Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997). https://doi.org/10.1109/4235.585893
Abdel-Basset, M.; Chang, V.; Mohamed, R.: HSMA_WOA: A hybrid novel Slime mould algorithm with whale optimization algorithm for tackling the image segmentation problem of chest X-ray images. Appl. Soft Comput. 95, 106642 (2020). https://doi.org/10.1016/j.asoc.2020.106642
Zhao, S., et al.: Multilevel threshold image segmentation with diffusion association slime mould algorithm and Renyi’s entropy for chronic obstructive pulmonary disease. Comput. Biol. Med. 134, 104427 (2021). https://doi.org/10.1016/j.compbiomed.2021.104427
Naik, M.K.; Panda, R.; Abraham, A.: Normalized square difference based multilevel thresholding technique for multispectral images using leader slime mould algorithm. J. King Saud Univ. - Comput. Inf. Sci. (2020). https://doi.org/10.1016/j.jksuci.2020.10.030
Yousri, D.; Fathy, A.; Rezk, H.; Babu, T.S.; Berber, M.R.: A reliable approach for modeling the photovoltaic system under partial shading conditions using three diode model and hybrid marine predators-slime mould algorithm. Energy Convers. Manag. 243, 114269 (2021). https://doi.org/10.1016/j.enconman.2021.114269
Mostafa, M.; Rezk, H.; Aly, M.; Ahmed, E.M.: A new strategy based on slime mould algorithm to extract the optimal model parameters of solar PV panel. Sustain. Energy Technol. Assess. 42, 100849 (2020). https://doi.org/10.1016/j.seta.2020.100849
El-Fergany, A.A.: Parameters identification of PV model using improved slime mould optimizer and Lambert W-function. Energy Rep. 7, 875–887 (2021). https://doi.org/10.1016/j.egyr.2021.01.093
Liu, Y.; Heidari, A.A.; Ye, X.; Liang, G.; Chen, H.; He, C.: Boosting slime mould algorithm for parameter identification of photovoltaic models. Energy 234, 121164 (2021). https://doi.org/10.1016/j.energy.2021.121164
Kumar, C.; Raj, T.D.; Premkumar, M.; Raj, T.D.: A new stochastic slime mould optimization algorithm for the estimation of solar photovoltaic cell parameters. Optik 223, 165277 (2020). https://doi.org/10.1016/j.ijleo.2020.165277
Premkumar, M.; Jangir, P.; Sowmya, R.; Alhelou, H.H.; Heidari, A.A.; Chen, H.: MOSMA: multi-objective slime mould algorithm based on elitist non-dominated sorting. IEEE Access 9, 3229–3248 (2021). https://doi.org/10.1109/ACCESS.2020.3047936
Abdel-Basset, M.; Mohamed, R.; Chakrabortty, R.K.; Ryan, M.J.; Mirjalili, S.: An efficient binary slime mould algorithm integrated with a novel attacking-feeding strategy for feature selection. Comput. Ind. Eng. 153, 107078 (2021). https://doi.org/10.1016/j.cie.2020.107078
Abdollahzadeh, B.; Barshandeh, S.; Javadi, H.; Epicoco, N.: An enhanced binary slime mould algorithm for solving the 0–1 knapsack problem. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01470-z
Zubaidi, S.L., et al.: Hybridised artificial neural network model with slime mould algorithm: a novel methodology for prediction of urban stochastic water demand. Water 12(10), 2692 (2020). https://doi.org/10.3390/w12102692
Chen, Z.; Liu, W.: An efficient parameter adaptive support vector regression using K-means clustering and chaotic slime mould algorithm. IEEE Access 8, 156851–156862 (2020). https://doi.org/10.1109/ACCESS.2020.3018866
Ekinci, S.; Izci, D.; Zeynelgil, H. L.; Orenc, S.: An application of slime mould algorithm for optimizing parameters of power system stabilizer. In: 2020 4th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), pp. 1–5. Istanbul, Turkey, (2020) doi: https://doi.org/10.1109/ISMSIT50672.2020.9254597
Rizk-Allah, R.M.; Hassanien, A.E.; Song, D.: Chaos-opposition-enhanced slime mould algorithm for minimizing the cost of energy for the wind turbines on high-altitude sites. ISA Trans (2021). https://doi.org/10.1016/j.isatra.2021.04.011
Hassan, M.H.; Kamel, S.; Abualigah, L.; Eid, A.: Development and application of slime mould algorithm for optimal economic emission dispatch. Expert Syst. Appl. 182, 115205 (2021). https://doi.org/10.1016/j.eswa.2021.115205
Wazery, Y.M.; Saber, E.; Houssein, E.H.; Ali, A.A.; Amer, E.: An efficient slime mould algorithm combined with K-nearest neighbor for medical classification tasks. IEEE Access 9, 113666–113682 (2021). https://doi.org/10.1109/ACCESS.2021.3105485
Houssein, E.H.; Mahdy, M.A.; Blondin, M.J.; Shebl, D.; Mohamed, W.M.: Hybrid slime mould algorithm with adaptive guided differential evolution algorithm for combinatorial and global optimization problems. Expert Syst. Appl. 174, 114689 (2021). https://doi.org/10.1016/j.eswa.2021.114689
Yu, C.; Heidari, A.A.; Xue, X.; Zhang, L.; Chen, H.; Chen, W.: Boosting quantum rotation gate embedded slime mould algorithm. Expert Syst. Appl. 181, 115082 (2021). https://doi.org/10.1016/j.eswa.2021.115082
Zhao, W.; Wang, L.; Zhang, Z.: Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm”. Neural Comput. Appl. (2019). https://doi.org/10.1007/s00521-019-04452-x
Zhao, W.; Zhang, Z.; Wang, L.: Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng. Appl. Artif. Intell. 87, 103300 (2020). https://doi.org/10.1016/j.engappai.2019.103300
Ahmadianfar, I.; Bozorg-Haddad, O.; Chu, X.: Gradient-based optimizer: a new metaheuristic optimization algorithm. Inf. Sci. 540, 131–159 (2020). https://doi.org/10.1016/j.ins.2020.06.037
Nadimi-Shahraki, M.H.; Taghian, S.; Mirjalili, S.: An improved grey wolf optimizer for solving engineering problems. Expert Syst. Appl. 166, 113917 (2021). https://doi.org/10.1016/j.eswa.2020.113917
Mirjalili, S.; Lewis, A.; Sadiq, A.S.: Autonomous particles groups for particle swarm optimization. Arab. J. Sci. Eng. 39(6), 4683–4697 (2014). https://doi.org/10.1007/s13369-014-1156-x
Nadimi-Shahraki, M.H.; Taghian, S.; Mirjalili, S.; Faris, H.: MTDE: an effective multi-trial vector-based differential evolution algorithm and its applications for engineering design problems. Appl. Soft Comput. 97, 106761 (2020). https://doi.org/10.1016/j.asoc.2020.106761
Sallam, K. M.; Elsayed, S. M.; Chakrabortty, R. K.; Ryan, M. J.: Improved Multi-operator differential evolution algorithm for solving unconstrained problems. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. Glasgow, United Kingdom (2020) doi: https://doi.org/10.1109/CEC48606.2020.9185577
Biswas, S.; Saha, D.; De, S.; Cobb, A. D.; Das, S.; Jalaian, B. A.: Improving differential evolution through bayesian hyperparameter optimization. In: 2021 IEEE Congress on Evolutionary Computation (CEC), pp. 832–840. Kraków, Poland, (2021), doi: https://doi.org/10.1109/CEC45853.2021.9504792
Tanabe, R.; Fukunaga, A. S.: Improving the search performance of SHADE using linear population size reduction. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 1658–1665. Beijing, China, (2014) doi: https://doi.org/10.1109/CEC.2014.6900380
Awad, N. H.; Ali, M. Z.; Suganthan, P. N.: Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. In 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 372–379. Donostia, San Sebastián, Spain, (2017), doi: https://doi.org/10.1109/CEC.2017.7969336
Niu, P.; Niu, S.; Liu, N.; Chang, L.: The defect of the Grey Wolf optimization algorithm and its verification method. Knowl.- Based Syst. 171, 37–43 (2019). https://doi.org/10.1016/j.knosys.2019.01.018
Tzanetos, A.; Dounias, G.: Nature inspired optimization algorithms or simply variations of metaheuristics? Artif. Intell. Rev. 54(3), 1841–1862 (2021). https://doi.org/10.1007/s10462-020-09893-8
Sörensen, K.: Metaheuristics-the metaphor exposed. Int. Trans. Oper. Res. 22(1), 3–18 (2015). https://doi.org/10.1111/itor.12001
Fan, Q.; Huang, H.; Yang, K.; Zhang, S.; Yao, L.; Xiong, Q.: A modified equilibrium optimizer using opposition-based learning and novel update rules. Expert Syst. Appl. 170, 114575 (2021). https://doi.org/10.1016/j.eswa.2021.114575
Jia, H.; Peng, X.: High equilibrium optimizer for global optimization. J. Intell. Fuzzy Syst. 40(3), 5583–5594 (2021). https://doi.org/10.3233/JIFS-200101
Kumar, A.; Das, S.; Zelinka, I.: A self-adaptive spherical search algorithm for real-world constrained optimization problems. In Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion, pp. 13–14. Cancún Mexico, (2020) doi: https://doi.org/10.1145/3377929.3398186
Gupta, S.; Deep, K.; Engelbrecht, A.P.: A memory guided sine cosine algorithm for global optimization. Eng. Appl. Artif. Intell. 93, 103718 (2020). https://doi.org/10.1016/j.engappai.2020.103718
Sharma, S.; Saha, A.K.; Lohar, G.: Optimization of weight and cost of cantilever retaining wall by a hybrid metaheuristic algorithm. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01294-x
Pant, M.; Thangaraj, R.; Singh, V.P.: Optimization of mechanical design problems using improved differential evolution algorithm. Int. J. Recent Trends Eng. 1(5), 21–25 (2009)
Kumar, A.; Wu, G.; Ali, M.Z.; Mallipeddi, R.; Suganthan, P.N.; Das, S.: A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evol. Comput. 56, 100693 (2020). https://doi.org/10.1016/j.swevo.2020.100693
Jarmai, K.; Snyman, J.A.; Farkas, J.: Minimum cost design of a welded orthogonally stiffened cylindrical shell. Comput. Struct. 84, 787–797 (2006). https://doi.org/10.1016/j.compstruc.2006.01.002
Savsani, P.; Savsani, V.: Passing vehicle search (PVS): a novel metaheuristic algorithm. Appl. Math. Model. 40(5–6), 3951–3978 (2016). https://doi.org/10.1016/j.apm.2015.10.040
Simionescu, P.V.; Beale, D.; Dozier, G.V.: Teeth-Number synthesis of a multispeed planetary transmission using an estimation of distribution algorithm. J. Mech. Des. 128, 108–115 (2006). https://doi.org/10.1115/1.2114867
Singh, N.; Kaur, J.: Hybridizing sine–cosine algorithm with harmony search strategy for optimization design problems. Soft Comput. 25(16), 11053–11075 (2021). https://doi.org/10.1007/s00500-021-05841-y
Abderazek, H.; Sait, S.M.; Yildiz, A.R.: Optimal design of planetary gear train for automotive transmissions using advanced meta-heuristics. Int. J. Veh. Des. 80(2–4), 121–136 (2020). https://doi.org/10.1504/IJVD.2019.109862
Osyczka, A.; Krenich, S.; Karas, K.: Optimum design of robot grippers using genetic algorithms. Buffalo, New York, pp. 241–243 (1999). Accessed: Sep. 17, 2021. [Online]. Available: http://www.lania.mx/~ccoello/EMOO/osyczka99.pdf.gz
Yildiz, B.S.; Pholdee, N.; Bureerat, S.; Yildiz, A.R.; Sait, S.M.: Robust design of a robot gripper mechanism using new hybrid grasshopper optimization algorithm. Expert Syst. (2021). https://doi.org/10.1111/exsy.12666
Yildiz, B.S.; Pholdee, N.; Bureerat, S.; Yildiz, A.R.; Sait, S.M.: Enhanced grasshopper optimization algorithm using elite opposition-based learning for solving real-world engineering problems. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01368-w
Pomrehn, L.P.; Papalambros, P.Y.: Discrete optimal design formulations with application to gear train design. J. Mech. Des. 117(3), 419–424 (1995)
Tanabe, R.; Fukunaga, A.: Success-history based parameter adaptation for differential evolution. In: 2013 IEEE Congress on Evolutionary Computation, pp. 71–78. Cancun, Mexico, (2013), doi: https://doi.org/10.1109/CEC.2013.6557555
Kizilay, D.; Tasgetiren, M. F.; Oztop, H.; Kandiller, L.; Suganthan, P. N.: A differential evolution algorithm with q-learning for solving engineering design problems. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. Glasgow, United Kingdom, (2020), doi: https://doi.org/10.1109/CEC48606.2020.9185743
Gotmare, A.; Bhattacharjee, S.S.; Patidar, R.; George, N.V.: Swarm and evolutionary computing algorithms for system identification and filter design: a comprehensive review. Swarm Evol. Comput. 32, 68–84 (2017). https://doi.org/10.1016/j.swevo.2016.06.007
Zou, D.-X.; Deb, S.; Wang, G.-G.: Solving IIR system identification by a variant of particle swarm optimization. Neural Comput. Appl. 30(3), 685–698 (2018). https://doi.org/10.1007/s00521-016-2338-0
Zhao, R., et al.: Selfish herd optimization algorithm based on chaotic strategy for adaptive IIR system identification problem. Soft Comput. 24(10), 7637–7684 (2020). https://doi.org/10.1007/s00500-019-04390-9
Zhang, L.; Xiao, N.: A novel artificial bee colony algorithm for inverse kinematics calculation of 7-DOF serial manipulators. Soft Comput. 23(10), 3269–3277 (2019). https://doi.org/10.1007/s00500-017-2975-y
Toz, M.: Chaos-based Vortex search algorithm for solving inverse kinematics problem of serial robot manipulators with offset wrist. Appl. Soft Comput. 89, 106074 (2020). https://doi.org/10.1016/j.asoc.2020.106074
Dereli, S.; Köker, R.: A meta-heuristic proposal for inverse kinematics solution of 7-DOF serial robotic manipulator: quantum behaved particle swarm algorithm. Artif. Intell. Rev. 53(2), 949–964 (2020). https://doi.org/10.1007/s10462-019-09683-x
Youn, B.D.; Choi, K.K.; Yang, R.-J.; Gu, L.: Reliability-based design optimization for crashworthiness of vehicle side impact. Struct. Multidiscip. Optim. 26(3–4), 272–283 (2004). https://doi.org/10.1007/s00158-003-0345-0
Wang, Y.; Cai, Z.; Zhou, Y.; Fan, Z.: Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique. Struct. Multidiscip. Optim. 37(4), 395–413 (2009). https://doi.org/10.1007/s00158-008-0238-3
Sadollah, A.; Bahreininejad, A.; Eskandar, H.; Hamdi, M.: Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl. Soft Comput. 13(5), 2592–2612 (2013). https://doi.org/10.1016/j.asoc.2012.11.026
Bala Krishna, A.; Saxena, S.; Kamboj, V.K.: hSMA-PS: a novel memetic approach for numerical and engineering design challenges. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01371-1
Kamboj, V.K.; Nandi, A.; Bhadoria, A.; Sehgal, S.: An intensify Harris Hawks optimizer for numerical and engineering optimization problems. Appl. Soft Comput. 89, 106018 (2020). https://doi.org/10.1016/j.asoc.2019.106018
Abualigah, L.; Diabat, A.; Mirjalili, S.; Abd Elaziz, M.; Gandomi, A.H.: The arithmetic optimization algorithm. Comput. Methods Appl. Mech. Eng. 376, 113609 (2021). https://doi.org/10.1016/j.cma.2020.113609
Abualigah, L.; Yousri, D.; Abd Elaziz, M.; Ewees, A.A.; Al-qaness, M.A.A.; Gandomi, A.H.: Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput. Ind. Eng. 157, 107250 (2021). https://doi.org/10.1016/j.cie.2021.107250
Gandomi, A.H.; Yang, X.-S.; Alavi, A.H.: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng. Comput. 29(1), 17–35 (2013). https://doi.org/10.1007/s00366-011-0241-y
Mohamed, A.W.: A novel differential evolution algorithm for solving constrained engineering optimization problems. J Intell. Manuf. (2017). https://doi.org/10.1007/s10845-017-1294-6
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This work was supported by the National Science Foundation of China under Grant No. 62066005.
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Yin, S., Luo, Q. & Zhou, Y. EOSMA: An Equilibrium Optimizer Slime Mould Algorithm for Engineering Design Problems. Arab J Sci Eng 47, 10115–10146 (2022). https://doi.org/10.1007/s13369-021-06513-7
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DOI: https://doi.org/10.1007/s13369-021-06513-7