## Abstract

Original language | English |
---|---|

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 398 |

DOIs | |

Publication status | Published - 2022 |

## Keywords

- Artificial hummingbird algorithm
- Convergence and diversity
- Dynamic elimination-based crowding distance
- Engineering design problems
- Multi-objective optimization
- Non-dominated sorting
- HTTP
- Optimal systems
- Pareto principle
- Crowding distance
- Multi objective
- Multi-objectives optimization
- Non-dominated Sorting
- Pareto optimal solutions
- Real-world
- Multiobjective optimization

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*Computer Methods in Applied Mechanics and Engineering*,

*398*. https://doi.org/10.1016/j.cma.2022.115223

**An effective multi-objective artificial hummingbird algorithm with dynamic elimination-based crowding distance for solving engineering design problems : Computer Methods in Applied Mechanics and Engineering**. In: Computer Methods in Applied Mechanics and Engineering. 2022 ; Vol. 398.

}

*Computer Methods in Applied Mechanics and Engineering*, vol. 398. https://doi.org/10.1016/j.cma.2022.115223

**An effective multi-objective artificial hummingbird algorithm with dynamic elimination-based crowding distance for solving engineering design problems: Computer Methods in Applied Mechanics and Engineering.**/ Zhao, W.; Zhang, Z.; Mirjalili, S. et al.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 398, 2022.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - An effective multi-objective artificial hummingbird algorithm with dynamic elimination-based crowding distance for solving engineering design problems

T2 - Computer Methods in Applied Mechanics and Engineering

AU - Zhao, W.

AU - Zhang, Z.

AU - Mirjalili, S.

AU - Wang, L.

AU - Khodadadi, N.

AU - Mirjalili, S.

N1 - Export Date: 11 July 2022 CODEN: CMMEC Correspondence Address: Wang, L.; School of Water Conservancy and Hydropower, Hebei, China; email: [email protected] Funding details: SLRC2019022 Funding details: National Natural Science Foundation of China, NSFC, 11972144, 12072098 Funding text 1: This work was supported in part by National Natural Science Foundation of China ( 11972144 and 12072098 ), and One Hundred Outstanding Innovative Scholars of Colleges and Universities in Hebei Province of China ( SLRC2019022 ). References: Shefaei, A., Vahid-Pakdel, M.J., Mohammadi-Ivatloo, B., Application of a hybrid evolutionary algorithm on reactive power compensation problem of distribution network (2018) Comput. Electr. Eng., 72, pp. 125-136; Eberhart, R., Kennedy, J., A new optimizer using particle swarm theory (1995) Proceedings of the Sixth International Symposium on Micro Machine and Human Science, MHS’95, pp. 39-43. , Ieee; Dorigo, M., Di Caro, G., Ant colony optimization: a new meta-heuristic (1999) Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), Vol. 2, pp. 1470-1477. , IEEE; Karaboga, D., Akay, B., A comparative study of artificial bee colony algorithm (2009) Appl. Math. Comput., 214 (1), pp. 108-132; Yang, X.S., Deb, S., Cuckoo search via Lévy flights (2009) 2009 World Congress on Nature & Biologically Inspired Computing, Vol. 21, NaBIC, pp. 0-214. , Ieee; Mirjalili, S., Lewis, A., The whale optimization algorithm (2016) Adv. Eng. Softw., 95, pp. 51-67; Arora, S., Singh, S., Butterfly optimization algorithm: a novel approach for global optimization (2019) Soft Comput., 23 (3), pp. 715-734; Rao, R.V., Savsani, V.J., Vakharia, D.P., Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems (2012) Inform. Sci., 183 (1), pp. 1-15; Li, S., Chen, H., Wang, M., Heidari, A.A., Mirjalili, S., Slime mould algorithm: A new method for stochastic optimization (2020) Future Gener. Comput. Syst., 111, pp. 300-323; 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 (2017) Adv. Eng. Softw., 114, pp. 163-191; Zhao, W., Zhang, Z., Wang, L., Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications (2020) Eng. Appl. Artif. Intell., 87; Faramarzi, A., Heidarinejad, M., Stephens, B., Mirjalili, S., Equilibrium optimizer: A novel optimization algorithm (2020) Knowl.-Based Syst., 191; Wang, Z., Luo, Q., Zhou, Y., Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems (2021) Eng. Comput., 37 (4), pp. 3665-3698; Yin, S., Luo, Q., Zhou, Y., EOSMA: An equilibrium optimizer slime mould algorithm for engineering design problems (2022) Arab. J. Sci. Eng., pp. 1-32; Hu, G., Li, M., Wang, X., Wei, G., Chang, C.T., An enhanced manta ray foraging optimization algorithm for shape optimization of complex CCG-ball curves (2022) Knowl.-Based Syst.; Tang, C., Zhou, Y., Tang, Z., Luo, Q., Teaching-learning-based pathfinder algorithm for function and engineering optimization problems (2021) Appl. Intell., 51 (7), pp. 5040-5066; Yapici, H., Cetinkaya, N., A new meta-heuristic optimizer: Pathfinder algorithm (2019) Appl. Soft Comput., 78, pp. 545-568; Coello, C.A.C., A comprehensive survey of evolutionary- based multi-objective optimization techniques (1999) Knowl. Inf. Syst., 1 (3), pp. 269-308; Fonseca, C.M., Fleming, P.J., An overview of evolutionary algorithms in multi-objective optimization (1995) Evol. Comput., 3 (1), pp. 1-1622; Marler, R.T., Arora, J.S., Survey of multi-objective optimization methods for engineering (2004) Struct. Multidiscip. Optim., 26, pp. 369-395; Aragón, A.M., Wayer, J.K., Geubelle, P.H., Goldberg, D.E., White, S.R., Design of microvascular flow networks using multi-objective genetic algorithms (2008) Comput. Methods Appl. Mech. Engrg., 197 (49-50), pp. 4399-4410; Wang, C., Yu, T., Shao, G., Bui, T.Q., Multi-objective isogeometric integrated optimization for shape control of piezoelectric functionally graded plates (2021) Comput. Methods Appl. Mech. Engrg., 377; Naranjani, Y., Sardahi, Y., Chen, Y., Sun, J.Q., Multi-objective optimization of distributed-order fractional damping (2015) Commun. Nonlinear Sci. Numer. Simul., 24 (1-3), pp. 159-168; Amani, M., Amani, P., Mahian, O., Estellé, P., Multi-objective optimization of thermophysical properties of eco-friendly organic nanofluids (2017) J. Cleaner Prod., 166, pp. 350-359; Yang, S., Gu, X., Liu, Y., Hao, R., Li, S., A general multi-objective optimized wavelet filter and its applications in fault diagnosis of wheelset bearings (2020) Mech. Syst. Signal Process., 145; Liu, X., Li, T., Zhou, Z., Hu, L., An efficient multi-objective reliability-based design optimization method for structure based on probability and interval hybrid model (2022) Comput. Methods Appl. Mech. Engrg., 392; Mirjalili, S., Jangir, P., Mirjalili, S.Z., Saremi, S., Trivedi, I.N., Optimization of problems with multiple objectives using the multi-verse optimization algorithm (2017) Knowl.-Based Syst., 134, pp. 50-71; Zamani, H., Nadimi-Shahraki, M.H., Gandomi, A.H., Starling murmuration optimizer: A novel bio-inspired algorithm for global and engineering optimization (2022) Comput. Methods Appl. Mech. Engrg., 392; Zhao, W., Wang, L., Zhang, Z., Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm (2020) Neural Comput. Appl., 32 (13), pp. 9383-9425; Ab Wahab, M.N., Nefti-Meziani, S., Atyabi, A., A comprehensive review of swarm optimization algorithms (2015) PLoS One, 10 (5); Zhao, W., Wang, L., Zhang, Z., Atom search optimization and its application to solve a hydrogeologic parameter estimation problem (2019) Knowl.-Based Syst., 163, pp. 283-304; Messac, A., Mattson, C.A., Generating well-distributed sets of Pareto points for engineering design using physical programming (2002) Optim. Eng., 3, pp. 431-450; Nicholson, E., Possingham, H.P., Objectives for multiple-species conservation planning (2006) Conserv. Biol., 20 (3), pp. 871-881; Branke, J., Deb, K., Dierolf, H., Osswald, M., Finding Knees in multi-objective optimization (2004) Parallel Problem Solving from Nature - PPSN VIII. PPSN 2004, Lecture Notes in Computer Science, 3242. , Yao X. Springer Berlin, Heidelberg; Chou, J.S., Truong, D.N., Multiobjective optimization inspired by behavior of jellyfish for solving structural design problems (2020) Chaos Solitons Fractals, 135; Cui, Y., Geng, Z., Zhu, Q., Han, Y., Review: Multi-objective optimization methods and application in energy saving (2017) Energy, 125, pp. 681-704; Schaffer, D.J., Multiple Objective Optimization with Vector Evaluated Genetic Algorithms (1985), Proceedings of the 1st International Conference on Genetic Algorithms, Pittsburgh, PA, USA; Srinivas, N., Deb, K., Multi-objective function optimizadon using non-dominated sorting genetic algorithms (1995) Evol. Comput., 2 (3), pp. 221-248; Bagchi, T.P., The nondominated sorting genetic algorithm: NSGA (1999) Multiobjective Scheduling By Genetic Algorithms, pp. 171-202. , Springer Boston, MA; Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II (2002) IEEE Trans. Evol. Comput., 6, pp. 182-197; Wang, X.D., Hirsch, C., Kang, S., Lacor, C., Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model (2011) Comput. Methods Appl. Mech. Engrg., 200 (9-12), pp. 883-895; Xu, J., Tang, H., Wang, X., Qin, G., Jin, X., Li, D., NSGA-II algorithm-based LQG controller design for nuclear reactor power control (2022) Ann. Nucl. Energy, 169; Chen, H., Deng, T., Du, T., Chen, B., Skibniewski, M.J., Zhang, L., An RF and LSSVM–NSGA-II method for the multi-objective optimization of high-performance concrete durability (2022) Cem. Concr. Compos.; Deng, Q., Gong, G., Gong, X., Zhang, L., Liu, W., Ren, Q., A Bee evolutionary guiding nondominated sorting genetic algorithm II for multiobjective flexible job-shop scheduling (2017) Comput. Intell. Neurosci., 2017; Zitzler, E., Evolutionary algorithms for multiobjective optimization: Methods and applications, vol. 63 (1999); Zitzler, E., Laumanns, M., Thiele, L., SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization (2002) Evolutionary Methods for Design, Optimisation and Control with Applica- Tion to Industrial Problems, pp. 95-100. , Giannakoglou K. EUROGEN 2001 International Center for Numerical MethodsinEngineering(CIMNE; Gharari, R., Poursalehi, N., Abbasi, M., Aghaie, M., Implementation of strength pareto evolutionary algorithm ii in the multiobjective burnable poison placement optimization of kwu pressurized water reactor (2016) Nucl. Eng. Technol., 48 (5), pp. 1126-1139; Corne, D., Knowles, J.D., Oates, M.J., The Pareto envelope-based selection algorithm for multi-objective optimisation (2000) Proceedings of the 6th International Conference on Parallel Problem Solving from Nature PPSN VI, Paris, Prance, 18–20 2000, pp. 839-848. , Springer Berlin/Heidelberg, Germany; Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J., PESA-II: Region-based Selection in Evolutionary Multiobjective Optimization (2001), pp. 7-11. , Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, San Francisco, CA, USA; Zhang, Q., Li, H., MOEA/D: a multi-objective evolutionary algorithm based on decomposition (2007) IEEE Trans. Evol. Comput., 11 (6), pp. 712-731; Qi, Y., Ma, X., Liu, F., Jiao, L., Sun, J., Wu, J., MOEA/D with adaptive weight adjustment (2014) Evol. Comput., 22 (2), pp. 231-264; Liang, S., Fang, Z., Li, G., Zhao, Y., Liu, X., Sun, G., An improved multiobjective evolutionary algorithm based on decomposition approach and its application in antenna array beam pattern synthesis (2022) Int. J. Numer. Modelling, Electron. Netw. Devices Fields, 35 (1); Tan, K.C., Yang, Y.J., Goh, C.K., A distributed cooperative coevolutionary algorithm for multiobjective optimization (2006) IEEE Trans. Evol. Comput., 10 (5), pp. 527-549; Soliman, O., Bui, L.T., Abbass, H., A memetic coevolutionary multi-objective differential evolution algorithm (2009) Multi-Objective Memetic Algorithms, pp. 369-388. , Springer Berlin, Heidelberg; Zhang, Q., Zhou, A., Jin, Y., RM-MEDA: A regularity model-based multiobjective estimation of distribution algorithm (2008) IEEE Trans. Evol. Comput., 12 (1), pp. 41-63; BenMansour, I., Alaya, I., Tagina, M., Indicator weighted based multi-objective approach using self-adaptive neighborhood operator (2021) Procedia Comput. Sci., 192, pp. 338-347; Potter, M.A., Jong, K.A.D., A cooperative coevolutionary approach to function optimization (1994) International Conference on Parallel Problem Solving from Nature, pp. 249-257. , Springer Berlin, Heidelberg; Keerativuttitumrong, N., Chaiyaratana, N., Varavithya, V., Multi-objective co-operative co-evolutionary genetic algorithm (2002) International Conference on Parallel Problem Solving from Nature, pp. 288-297. , Springer Berlin, Heidelberg; Okuda, T., Hiroyasu, T., Miki, M., Watanabe, S., DCMOGA: Distributed cooperation model of multi-objective genetic algorithm (2002) Advances in Nature-Inspired Computation: The PPSN VII Workshops, pp. 25-26; Coello, C.A.C., Pulido, G.T., Lechuga, M.S., Handling multiple objectives with particle swarm optimization (2004) IEEE Trans. Evol. Comput., 8 (3), pp. 256-279; Kennedy, J., Eberhart, R., Particle swarm optimization (1995), 194, pp. 2-8. , Proceedings of the 1995 IEEE International Conference on Neural Networks; Wang, C., Koh, J.M., Yu, T., Xie, N.G., Cheong, K.H., Material and shape optimization of bi-directional functionally graded plates by GIGA and an improved multi-objective particle swarm optimization algorithm (2020) Comput. Methods Appl. Mech. Engrg., 366; Zheng, Y., Chen, J., A modified multi-objective particle swarm optimization approach and its application to the design of a deepwater composite riser (2018) Acta Mech. Sinica, 34 (2), pp. 275-284; Mirjalili, S., Mirjalili, S.M., Lewis, A., Grey wolf optimizer (2014) Adv. Eng. Softw., 69, pp. 46-61; Mirjalili, S., Saremi, S., Mirjalili, S.M., Coelho, L.D.S., Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization (2016) Expert Syst. Appl., 47, pp. 106-119; 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 (2017) Adv. Eng. Softw., 114, pp. 163-191; Mirjalili, S., Jangir, P., Saremi, S., Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems (2017) Appl. Intell., 46 (1), pp. 79-95; Mukherjee, A., Barma, P.S., Dutta, J., Panigrahi, G., Kar, S., Maiti, M., A multi-objective antlion optimizer for the ring tree problem with secondary sub-depots (2021) Oper. Res., pp. 1-39; Premkumar, M., Jangir, P., Sowmya, R., Alhelou, H.H., Mirjalili, S., Kumar, B.S., Multi-objective equilibrium optimizer: framework and development for solving multi-objective optimization problems (2022) J. Comput. Des. Eng., 9 (1), pp. 24-50; Pereira, J.L.J., Oliver, G.A., Francisco, M.B., Cunha, S.S., Jr., Gomes, G.F., Multi-objective lichtenberg algorithm: A hybrid physics-based meta-heuristic for solving engineering problems (2022) Expert Syst. Appl., 187; Houssein, E.H., Mahdy, M.A., Shebl, D., Manzoor, A., Sarkar, R., Mohamed, W.M., An efficient slime mould algorithm for solving multi-objective optimization problems (2022) Expert Syst. Appl., 187; 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 (2020) IEEE Access, 9, pp. 3229-3248; Lai, X., Li, C., Zhang, N., Zhou, J., A multi-objective artificial sheep algorithm (2019) Neural Comput. Appl., 31 (8), pp. 4049-4083; Acharya, S., Ganesan, S., Kumar, D.V., Subramanian, S., A multi-objective multi-verse optimization algorithm for dynamic load dispatch problems (2021) Knowl.-Based Syst., 231; Got, A., Zouache, D., Moussaoui, A., MOMRFO: Multi-objective manta ray foraging optimizer for handling engineering design problems (2022) Knowl.-Based Syst., 237; Zouache, D., Abdelaziz, F.B., Guided Manta ray foraging optimization using epsilon dominance for multi-objective optimization in engineering design (2022) Expert Syst. Appl., 189; Yüzgeç, U., Kusoglu, M., Multi-objective harris hawks optimizer for multiobjective optimization problems (2020) BSEU J. Eng. Res. Technol., 1 (1), pp. 31-41; Piri, J., Mohapatra, P., An analytical study of modified multi-objective harris hawk optimizer towards medical data feature selection (2021) Comput. Biol. Med., 135; Mirjalili, S.Z., Mirjalili, S., Saremi, S., Faris, H., Aljarah, I., Grasshopper optimization algorithm for multi-objective optimization problems (2018) Appl. Intell., 48 (4), pp. 805-820; Akbari, R., Hedayatzadeh, R., Ziarati, K., Hassanizadeh, B., A multi-objective arti?cial bee colony algorithm (2012) Swarm Evol. Comput., 2, pp. 39-52; García-Martínez, C., Cordón, O., Herrera, F., A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP (2007) Eur. J. Oper. Res., 180, pp. 116-148; Yang, X.-S., Multiobjective firefly algorithm for continuous optimization (2013) Eng. Comput., 29, pp. 175-184; Jangir, P., Non-dominatedsortingmothflameoptimizer:A novel multi-objective optimization algorithm for solving en- gineeringdesignproblems (2018) Eng. Technol. Open Access J., 2 (1), pp. 17-31; Nanda, S.J., Multi-objective moth flame optimization (2016) Communications and Informatics, ICACCI, 2016 International conference on Advances in computing, pp. 2470-2476. , IEEE; Jangir, P., Jangir, N., Non-dominated sorting whale optimization algorithm (2017) Global J. Res. Eng., 17 (4), pp. 15-42; Premkumar, M., Jangir, P., Santhosh Kumar, B., Sowmya, R., Haes Alhelou, H., Abualigah, L., Riza Yildiz, A., Mirjalili, S., A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimiza- tion problems: Diversity analysis and validations (2021) IEEE Ac-Cess, 9, pp. 84263-84295; Buch, H., Trivedi, I.N., A new non-dominated sorting ions motion algorithm: Development and applications (2020) Deci- SionSci. Lett., 9 (1), pp. 59-76; Zhong, K., Zhou, G., Deng, W., Zhou, Y., Luo, Q., MOMPA: Multi-objective marine predator algorithm (2021) Comput. Methods Appl. Mech. Engrg., 385; Jangir, P., Buch, H., Mirjalili, S., Manoharan, P., MOMPA: Multi-objective marine predator algorithm for solving multi-objective optimization problems (2021) Evol. Intell., pp. 1-27; Hassanzadeh, H.R., Rouhani, M., A multi-objective gravitational search algorithm (2010) 2010 2nd International Conference on Computational Intelligence, communication systems and networks, pp. 7-12. , IEEE; Modiri-Delshad, M., Abd Rahim, N., Multi-objective backtracking search algorithm for economic emission dispatch problem (2016) Appl. Soft Comput., 40, pp. 479-494; Di Barba, P., Multi-objective wind-driven optimisation and magnet design (2016) Electron. Lett., 52 (14), pp. 1216-1218; Kumar, S., Tejani, G.G., Pholdee, N., Bureerat, S., Multi-objective passing vehicle search algorithm for structure optimization (2021) Expert Syst. Appl., 169; Li, M., Zheng, J., Spread assessment for evolutionary multi-objective optimization (2009) International Conference on Evolutionary Multi-Criterion Optimization, , 216–230 Berlin, Heidelberg; Wolpert, D.H., Macready, W.G., No free lunch theorems for optimization (1997) IEEE Trans. Evol. Comput., 1 (1), pp. 67-82; Zhao, W., Wang, L., Mirjalili, S., Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications (2022) Comput. Methods Appl. Mech. Engrg., 388; Ramadan, A., Kamel, S., Hassan, M.H., Ahmed, E.M., Hasanien, H.M., Accurate photovoltaic models based on an adaptive opposition artificial hummingbird algorithm (2022) Electronics, 11 (3), p. 318; Zitzler, E., Deb, K., Thiele, L., Comparison of multiob- jective evolutionary algorithms: Empirical results (2000) Evol.- AryComput., 8 (2), pp. 173-195; Ngatchou, P., Zarei, A., El-Sharkawi, M., Pareto multi objec- tive optimization (2005), pp. 84-91. , Proceedings of the 13th International Con- Ference on Intelligent Systems Application to Power Systems 2005; Knowles, J.D., Corne, D.W., Approximating the nondominated front using the Pareto archived evolution strategy (2000) Evol. Comput., 8, pp. 149-172; Britto, A., Pozo, A., Using archiving methods to control convergence and diversity for many-objective problems in particle swarm optimization (2012) 2012 IEEE Congress on Evolutionary Computation, pp. 1-8. , IEEE; Laumanns, M., Thiele, L., Deb, K., Zitzler, E., Combining convergence and diversity in evolutionary multiobjective optimization (2002) Evol. Comput., 10 (3), pp. 263-282; Liu, J., Chen, X., An improved NSGA-II algorithm based on crowding distance elimination strategy (2019) Int. J. Comput. Intell. Syst., 12 (2), pp. 513-518; Luo, B., Zheng, J., Xie, J., Wu, J., Dynamic crowding distance? A new diversity maintenance strategy for MOEAs (2008) 2008 Fourth International Conference on Natural Computation, Vol. 1, pp. 580-585. , IEEE; Patil, M.B., Using external archive for improved performance in multi-objective optimization (2018), arXiv preprint; Cheng, S., Chen, M.Y., Fleming, P.J., Improved multi-objective particle swarm optimization with preference strategy for optimal DG integration into the distribution system (2015) Neurocomputing, 148, pp. 23-29; Zeng, G.Q., Chen, J., Li, L.M., Chen, M.R., Wu, L., Dai, Y.X., Zheng, C.W., An improved multi-objective population-based extremal optimization algorithm with polynomial mutation (2016) Inform. Sci., 330, pp. 49-73; Chow, C.K., Yuen, S.Y., A multiobjective evolutionary algorithm that diversifies population by its density (2011) IEEE Trans. Evol. Comput., 16 (2), pp. 149-172; Bui, L.T., Liu, J., Bender, A., Barlow, M., Wesolkowski, S., Abbass, H.A., Dmea: a direction-based multiobjective evolutionary algorithm (2011) Memetic Comput., 3 (4), pp. 271-285; Deb, K., Thiele, L., Laumanns, M., Zitzler, E., Scalable test problems for evolutionary multiobjective optimization (2005) Evolutionary Multiobjective Optimization, pp. 105-145. , Springer London; Zhang, Q., Zhou, A., Zhao, S., Suganthan, P.N., Liu, W., Tiwari, S., Multiobjective optimization test instances for the CEC 2009 special session and competition (2008) Special Session on Performance Assessment of Multi-Objective Optimization Algorithms: technical report, pp. 1-30. , University of Essex, Colchester, UK and Nanyang technological University Singapore; Van Veldhuizen, D.A., Lamont, G.B., Multiobjective Evolutionary Algorithm Research: A History and Analysis: Technical Report TR-98-03 (1998), pp. 1-88. , Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology Wright-Patterson AFB, Ohio; Schott, J.R., Fault Tolerant Design using Single and Multicriteria Genetic Algorithm Optimization: DTIC Document (1995), Massachusetts Institute of Technology, Department of Aeronautics and Astronautics; Zitzler, E., Thiele, L., Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach (1999) IEEE Trans. Evol. Comput., 3 (4), pp. 257-271; Chi, K.C., Yuen, S.Y., A multiobjective evolutionary algorithm that diversifies population by its density (2012) Ieee T. Evolut. Comput., 16, pp. 149-172; Derrac, J., García, S., Molina, D., Herrera, F., A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms (2011) Swarm Evol. Comput., 1 (1), pp. 3-18; Friedman, M., The use of ranks to avoid the assumption of normality implicit in the analysis of variance (1937) J. Amer. Statist. Assoc., 32, pp. 674-701; Coello, C.A.C., Pulido, G.T., Multiobjective structural optimization using a micro genetic algorithm (2005) Struct. Multidiscip. Optim., 30 (5), pp. 388-390; Ray, T., Liew, K.M., A swarm metaphor for multiobjective design optimization (2002) Eng. Optim., 34, pp. 141-150; Yang, X.S., Deb, S., Multiobjective cuckoo search for design optimization (2013) Comput. Oper. Res., 40 (6), pp. 1616-1624; Deb, K., Pratap, A., Moitra, S., Mechanical component design for multiple objectives using elitist non-dominated sorting GA (2000) Parall. Probl. Solv. Nat. PPSN VI, 1917, pp. 859-868; Sadollah, A., Eskandar, H., Bahreininejad, A., Kim, J.H., Water cycle algorithm for solving multi-objective optimization problems (2015) Soft Comput., 19 (9), pp. 2587-2603; Lavangnananda, K., Wangsom, P., Multi-objective shipment allocation using extreme nondominated sorting genetic algorithm-III (e-NSGA-III) (2019) 2019 18th IEEE International Conference on Machine Learning and Applications, ICMLA, pp. 1500-1505. , IEEE

PY - 2022

Y1 - 2022

N2 - Artificial hummingbird algorithm (AHA) is a recently developed bio-based metaheuristic and it shows superior performance in handling single-objective optimization problems. Despite the merit, this algorithm can only solve problems with one objective. To solve complex multi-objective optimization problems, including engineering design problems, a multi-objective AHA (MOAHA) is developed in this study. In MOAHA, an external archive is employed to save Pareto optimal solutions, and a dynamic elimination-based crowding distance (DECD) method is developed to maintain this archive to effectively preserve the population diversity. In addition, a non-dominated sorting strategy is merged with MOAHA to construct a solution update mechanism, which effectively refines Pareto optimal solutions for improving the convergence of the algorithm. The superior results over 7 competitors on 28 benchmark functions in terms of convergence, diversity and solution distribution are demonstrated with a suite of comprehensive tests. The MOAHA algorithm is also applied to 5 real-world engineering design problems with multiple objectives, demonstrating its superiority in handling challenging real-world multi-objective problems with unknown true Pareto optimal solutions and fronts. The source code of MOAHA is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/113535-moaha-multi-objective-artificial-hummingbird-algorithm and https://seyedalimirjalili.com/aha. © 2022 Elsevier B.V.

AB - Artificial hummingbird algorithm (AHA) is a recently developed bio-based metaheuristic and it shows superior performance in handling single-objective optimization problems. Despite the merit, this algorithm can only solve problems with one objective. To solve complex multi-objective optimization problems, including engineering design problems, a multi-objective AHA (MOAHA) is developed in this study. In MOAHA, an external archive is employed to save Pareto optimal solutions, and a dynamic elimination-based crowding distance (DECD) method is developed to maintain this archive to effectively preserve the population diversity. In addition, a non-dominated sorting strategy is merged with MOAHA to construct a solution update mechanism, which effectively refines Pareto optimal solutions for improving the convergence of the algorithm. The superior results over 7 competitors on 28 benchmark functions in terms of convergence, diversity and solution distribution are demonstrated with a suite of comprehensive tests. The MOAHA algorithm is also applied to 5 real-world engineering design problems with multiple objectives, demonstrating its superiority in handling challenging real-world multi-objective problems with unknown true Pareto optimal solutions and fronts. The source code of MOAHA is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/113535-moaha-multi-objective-artificial-hummingbird-algorithm and https://seyedalimirjalili.com/aha. © 2022 Elsevier B.V.

KW - Artificial hummingbird algorithm

KW - Convergence and diversity

KW - Dynamic elimination-based crowding distance

KW - Engineering design problems

KW - Multi-objective optimization

KW - Non-dominated sorting

KW - HTTP

KW - Optimal systems

KW - Pareto principle

KW - Crowding distance

KW - Multi objective

KW - Multi-objectives optimization

KW - Non-dominated Sorting

KW - Pareto optimal solutions

KW - Real-world

KW - Multiobjective optimization

U2 - 10.1016/j.cma.2022.115223

DO - 10.1016/j.cma.2022.115223

M3 - Article

SN - 0045-7825

VL - 398

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -