MOMPA: multi-objective marine predator algorithm. (English) Zbl 07415675

Summary: In this paper, a multi-objective version of the recently proposed marine predator algorithm (MPA) is presented, which is called the multi-objective marine predator algorithm (MOMPA). In this algorithm, an external archive component is introduced to store the non dominated Pareto optimal solutions found so far. Based on the elite selection method, a top predator selection mechanism is proposed, which selects the effective solutions from the archive as the top predators to simulate the predator’s foraging behavior. The CEC2019 multi-modal multi-objective benchmark functions are utilized to evaluate the performance of the proposed algorithm and compared with nine state-of-the-art multi-objective meta-heuristics algorithms. In addition, seven multi-objective engineering design problems (car side impact problem, gear train design problem, welded beam design problem, disk brake design problem, two bar truss design problem, spring design problem and cantilever beam design problem) are used to further verify the effectiveness of the proposed algorithm. The results demonstrate that the proposed MOMPA algorithm not only provides very competitive results but also outperforms other algorithms.


90-XX Operations research, mathematical programming
74-XX Mechanics of deformable solids
Full Text: DOI


[1] S. Tiwari, G. Fadel, P. Koch, K. Deb, Performance assessment of the hybrid Archive-based Micro Genetic Algorithm (AMGA) on the CEC09 test problems, in: 2009 IEEE Congress on Evolutionary Computation, Trondheim, Norway, 2009, pp. 1935-1942.
[2] Zhou, A.; Qu, B.-Y.; Li, H.; Zhao, S.-Z.; Suganthan, P. N.; Zhang, Q., Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm Evol. Comput., 1, 1, 32-49 (2011)
[3] Jin, Y.; Olhofer, M.; Sendhoff, B., Dynamic weighted aggregation for evolutionary multi-objective optimization: Why does it work and how?, (Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, GECCO’01 (2001), Morgan Kaufmann Publishers Inc.: Morgan Kaufmann Publishers Inc. San Francisco, CA, USA), 1042-1049
[4] Branke, J.; Deb, K.; Dierolf, H.; Osswald, M., Finding knees in multi-objective optimization, (8th International Conference on Parallel Problem Solving from Nature, vol. 3242 (2004), Springer), 722-731
[5] Kollat, J. B.; Reed, P., A framework for visually interactive decision-making and design using evolutionary multi-objective optimization (video), Environ. Model. Softw., 22, 12, 1691-1704 (2007)
[6] Manoharan, P.; Jangir, P.; Ravichandran, S., MOGBO: A new multiobjective gradient-based optimizer for real-world structural optimization problems, Knowl.-Based Syst., 218, Article 106856 pp. (2021)
[7] Coello, C. A.C.; Lamont, G. B.; Veldhuizen, D. A.V., (Evolutionary Algorithms for Solving Multi-Objective Problems. Evolutionary Algorithms for Solving Multi-Objective Problems, Genetic and Evolutionary Computation (2006), Springer-Verlag: Springer-Verlag Berlin, Heidelberg) · Zbl 1142.90029
[8] Abdel-Basset, M.; Mohamed, R.; Abouhawwash, M., Balanced multi-objective optimization algorithm using improvement based reference points approach, Swarm Evol. Comput., 60, Article 100791 pp. (2021)
[9] Madavan, N. K., Multiobjective optimization using a Pareto differential evolution approach, (Proceedings of the 2002 Congress on Evolutionary Computation, Vol. 2 (2002), IEEE), 1145-1150
[10] Coello, C. A.C., Evolutionary multi-objective optimization: A historical view of the field, IEEE Comput. Intell. Mag., 1, 1, 28-36 (2006)
[11] Liu, H.; Li, Y.; Duan, Z.; Chen, C., A review on multi-objective optimization framework in wind energy forecasting techniques and applications, Energ. Convers. Manage., 224, Article 113324 pp. (2020)
[12] Gholami, M.; Fathi, A.; Baghestani, A. M., Multi-objective optimal structural design of composite superstructure using a novel MONMPSO algorithm, Int. J. Mech. Sci., 193, Article 106149 pp. (2021)
[13] Kiouche, A. E.; Bessedik, M.; Tayeb, B. S.; Keddar, M. R., An efficient hybrid multi-objective memetic algorithm for the frequency assignment problem, Eng. Appl. Artif. Intell., 87, Article 103265 pp. (2020)
[14] Weiszer, M.; Burke, E. K.; Chen, J., Multi-objective routing and scheduling for airport ground movement, Transp. Res. C, 119, Article 102734 pp. (2020)
[15] Chen, H.; Li, X.-Y.; Lu, X.-R.; Sheng, N.; Zhou, W.; Geng, H.-P.; Yu, S., A multi-objective optimization approach for the selection of overseas oil projects, Comput. Ind. Eng., 151, Article 106977 pp. (2021)
[16] 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, Comput. Methods Appl. Mech. Engrg., 197, 49-50, 4399-4410 (2008) · Zbl 1194.74196
[17] Wang, X. D.; Hirsch, C.; Kang, S.; Lacor, C., Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model, Comput. Methods Appl. Mech. Engrg., 200, 9-12, 883-895 (2011) · Zbl 1225.76255
[18] Markou, G.; Papadrakakis, M., An efficient generation method of embedded reinforcement in hexahedral elements for reinforced concrete simulations, Adv. Eng. Softw., 45, 1, 175-187 (2012)
[19] Mourlas, C.; Markou, G.; Papadrakakis, M., Accurate and computationally efficient nonlinear static and dynamic analysis of reinforced concrete structures considering damage factors, Eng. Struct., 178, 258-285 (2019)
[20] Babaei, M.; Mollayi, M., Multi-objective optimization of reinforced concrete frames using NSGA-II algorithm, Eng. Struct. Technol., 8, 4, 157-164 (2016)
[21] Liu, G. P.; Han, X.; Jiang, C., A novel multi-objective optimization method based on an approximation model management technique, Comput. Methods Appl. Mech. Engrg., 197, 33-40, 2719-2731 (2008) · Zbl 1194.74253
[22] Mirjalili, S.; Lewis, A.; Mirjalili, S. A.M., Multi-objective optimisation of marine propellers, Procedia Comput. Sci., 51, 2247-2256 (2015)
[23] Herath, M. T.; Natarajan, S.; Prusty, B. G.; John, N. S., Isogeometric analysis and genetic algorithm for shape-adaptive composite marine propellers, Comput. Methods Appl. Mech. Engrg., 284, 835-860 (2015) · Zbl 1423.74271
[24] Poloni, C.; Giurgevich, A.; Onesti, L.; Pediroda, V., Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics, Comput. Methods Appl. Mech. Engrg., 186, 2-4, 403-420 (2000) · Zbl 0956.76023
[25] Ronco, C. C.D.; Ponza, R.; Benini, E., Aerodynamic shape optimization of aircraft components using an advanced multi-objective evolutionary approach, Comput. Methods Appl. Mech. Engrg., 285, 255-290 (2015) · Zbl 1423.76175
[26] 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, Comput. Methods Appl. Mech. Engrg., 366, Article 113017 pp. (2020) · Zbl 1442.74161
[27] Savage, D. J.; Feng, Z.; Knezevic, M., Identification of crystal plasticity model parameters by multi-objective optimization integrating microstructural evolution and mechanical data, Comput. Methods Appl. Mech. Engrg., 379, Article 113747 pp. (2021) · Zbl 07340354
[28] Papadrakakis, M.; Lagaros, N. D.; Plevris, V., Multi-objective optimum design of 3D structures under static and seismic loading conditions, (4th GRACM Congress on Computational Mechanics (2002), Greek Association of Computational Mechanics: Greek Association of Computational Mechanics Patras)
[29] Coverstone-Carroll, V.; Hartmann, J. W.; Mason, W. J., Optimal multi-objective low-thrust spacecraft trajectories, Comput. Methods Appl. Mech. Engrg., 186, 2-4, 387-402 (2000) · Zbl 0956.70020
[30] Faramarzi, A.; Heidarinejad, M.; Mirjalili, S.; Gandomi, A. H., Marine predators algorithm: A nature-inspired metaheuristic, Expert Syst. Appl., 152, Article 113377 pp. (2020)
[31] Wolpert, D. H.; Macready, W. G., No free lunch theorems for optimization, IEEE Trans. Evol. Comput., 1, 1, 67-82 (1997)
[32] Wang, G.-G.; Tan, Y., Improving metaheuristic algorithms with information feedback models, IEEE Trans. Cybern., 49, 2, 542-555 (2017)
[33] Abualigah, L.; Diabat, A., Advances in sine cosine algorithm: A comprehensive survey, Artif. Intell. Rev., 54, 2567-2608 (2021)
[34] Gao, D.; Wang, G. G.; Pedrycz, W., Solving fuzzy job-shop scheduling problem using de algorithm improved by a selection mechanism, IEEE Trans. Fuzzy Syst., 28, 12, 3265-3275 (2020) · Zbl 1440.74042
[35] Wang, G.-G.; Guo, L.; Gandomi, A. H.; Hao, G. S.; Wang, H., Chaotic krill herd algorithm, Inform. Sci., 274, 17-34 (2014)
[36] Holland, J. H., Adaptation in Natural and Artificial Systems (1992), MIT Press: MIT Press Cambridge
[37] Rechenberg, I., Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen evolution (1973), Frommann-Holzboog Verlag: Frommann-Holzboog Verlag Stuttgart
[38] Storn, R.; Price, K., Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., 11, 4, 341-359 (1997) · Zbl 0888.90135
[39] Kennedy, J.; Eberhart, R., Particle swarm optimization, (Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4 (1995), IEEE), 1942-1948
[40] Mirjalili, S., Ant colony optimisation, (Evolutionary Algorithms and Neural Networks. Evolutionary Algorithms and Neural Networks, Studies in Computational Intelligence, vol. 780 (2019), Springer: Springer Cham)
[41] Akay, B.; Karaboga, D.; Gorkemli, B.; Kaya, E., A survey on the artificial bee colony algorithm variants for binary, integer and mixed integer programming problems, Appl. Soft Comput., 106, 3, Article 107351 pp. (2021)
[42] Abualigah, L.; Yousri, D.; Elaziz, M. A.; Ewees, A. A.; Al-qaness, M. A.A.; Gandomi, A. H., Aquila optimizer: A novel meta-heuristic optimization algorithm, Comput. Ind. Eng., 157, Article 107250 pp. (2021)
[43] Braik, M. S., Chameleon swarm algorithm: A bio-inspired optimizer for solving engineering design problems, Expert Syst. Appl., 174, 1, Article 114685 pp. (2021)
[44] Jain, M.; Singh, V.; Rani, A., A novel nature-inspired algorithm for optimization: Squirrel search algorithm, Swarm Evol. Comput., 44, 148-175 (2019)
[45] Sulaiman, M. H.; Mustaffa, Z.; Saari, M. M.; Daniyal, H., Barnacles mating optimizer: A new bio-inspired algorithm for solving engineering optimization problems, Eng. Appl. Artif. Intell., 87, Article 103330 pp. (2020)
[46] Fathollahi-Fard, A. M.; Hajiaghaei-Keshteli, M.; Tavakkoli-Moghaddam, R., Red deer algorithm (RDA): A new nature-inspired meta-heuristic, Soft Comput., 24, 14637-14665 (2020)
[47] Amaran, S.; Sahinidis, N. V.; Sharda, B.; Bury, S. J., Simulation optimization: A review of algorithms and applications, 4OR, 12, 4, 301-333 (2014) · Zbl 1317.90002
[48] Shareef, H.; Ibrahim, A. A.; Mutlag, A. H., Lightning search algorithm, Appl. Soft Comput., 36, 315-333 (2015)
[49] 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)
[50] Anita A. Yadav, S., AEFA: Artificial electric field algorithm for global optimization, Swarm Evol. Comput., 48, 93-108 (2019)
[51] Faramarzi, A.; Heidarinejad, M.; Stephens, B. E.; Mirjalili, S., Equilibrium optimizer: A novel optimization algorithm, Knowl.-Based Syst., 191, Article 105190 pp. (2020)
[52] Hashim, F. A.; Houssein, E. H.; Mai, S. M.; Al-Atabany, W.; Mirjalili, S., Henry gas solubility optimization: A novel physics-based algorithm, Future Gener. Comput. Syst., 101, 646-667 (2019)
[53] Y. Shi, Brain storm optimization algorithm, in: Proceedings of International Conference on Swarm Intelligence, 2011, pp. 303-309.
[54] Rao, R. V.; Savsani, V. J.; Vakharia, D. P., Teaching-learning-based optimization: An optimization method for continuous non-linear large scale problems, Inform. Sci., 183, 1, 1-15 (2012)
[55] Moghdani, R.; Salimifard, K., Volleyball premier league algorithm, Appl. Soft Comput., 64, 161-185 (2018)
[56] Kaur, S.; Awasthi, L. K.; Sangal, A. L., A brief review on multi-objective software refactoring and a new method for its recommendation, Arch. Comput. Methods Eng., 28, 1-25 (2020)
[57] P. Ngatchou, A. Zarei, A. El-Sharkawi, Pareto multi objective optimization, in: Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems, Arlington, VA, USA, 2005, pp. 84-91.
[58] Raimundo, M. M.; Drumond, T. F.; Marques, A.; Lyra, C.; Zuben, F., Exploring multiobjective training in multiclass classification, Neurocomputing, 435, 307-320 (2021)
[59] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 2, 182-197 (2002)
[60] Srinivas, N.; Deb, K., Multi objective optimization using nondominated sorting in genetic algorithms, Evol. Comput., 2, 3, 221-248 (1995)
[61] Coello, C. A.C.; Pulido, G. T.; Lechuga, M. S., Handling multiple objectives with particle swarm optimization, IEEE Trans. Evol. Comput., 8, 3, 256-279 (2004)
[62] Zhang, Q.; Li, H., MOEA/D: A multiobjective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput., 11, 6, 712-731 (2008)
[63] Angus, D.; Woodward, C., Multiple objective ant colony optimization, Swarm Intell., 3, 1, 69-85 (2009)
[64] Zitzler, E.; Thiele, L., Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evol. Comput., 3, 4, 257-271 (1999)
[65] Mirjalili, S.; Saremi, S.; Mirjalili, S. M.; Coelho, L. D.S., Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization, Expert Syst. Appl., 47, 106-119 (2015)
[66] Mirjalili, S., SCA: A sine cosine algorithm for solving optimization problems, Knowl.-Based Syst., 96, 120-133 (2016)
[67] Tawhid, M. A.; Savsani, V., Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems, Neural Comput. Appl., 31, 915-929 (2019)
[68] Mirjalili, S.; Jangir, P.; Saremi, S., Multi-objective ant lion optimizer: A multi-objective optimization algorithm for solving engineering problems, Appl. Intell., 46, 79-95 (2017)
[69] Pradhan, P. M.; Panda, G., Solving multiobjective problems using cat swarm optimization, Expert Syst. Appl., 39, 3, 2956-2964 (2012)
[70] E. Hancer, B. Xue, M. Zhang, D. Karaboga, B. Akay, A multi-objective artificial bee colony approach to feature selection using fuzzy mutual information, in: 2015 IEEE Congress on Evolutionary Computation, CEC, Sendai, Japan, 2015, pp. 2420-2427.
[71] Wu, D.; Gao, H., Multi-objective bird swarm algorithm, (Lu, H., Cognitive Internet of Things: Frameworks, Tools and Applications (2020), Springer: Springer Cham), 109-119
[72] Zhong, W.; Liu, J.; Xue, M.; Jiao, L., A multiagent genetic algorithm for global numerical optimization, IEEE Trans. Syst. Man Cybern. B, 34, 2, 1128-1141 (2004)
[73] 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)
[74] Mirjalili, S.; Jangir, P.; Mirjalili, S. Z.; Saremi, S.; Trivedi, I. N., Optimization of problems with multiple objectives using the multi-verse optimization algorithm, Knowl.-Based Syst., 134, 50-71 (2017)
[75] Mirjalili, S., Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems, Neural Comput. Appl., 27, 4, 1053-1073 (2016)
[76] Corne, D. W.; Jerram, N. R.; Knowles, J. D.; Oates, M. J., PESA-II: Region-based selection in evolutionary multiobjective optimization, (Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, GECCO’01 (2001), Morgan Kaufmann Publishers: Morgan Kaufmann Publishers San Francisco), 283-290
[77] Mohammadi-Balani, A.; Nayeri, M. D.; Azar, A.; Taghizadeh-Yazdi, M., Golden eagle optimizer: A nature-inspired metaheuristic algorithm, Comput. Ind. Eng., 152, Article 107050 pp. (2021)
[78] Mirjalili, S. Z.; Mirjalili, S.; Saremi, S.; Faris, H.; Aljarah, I., Grasshopper optimization algorithm for multi-objective optimization problems, Appl. Intell., 48, 805-820 (2018)
[79] Elaziz, M. A.; Shehabeldeen, T. A.; Elsheikh, A. H.; Zhou, J.; Ewees, A. A.; Al-qaness, M. A.A., Utilization of random vector functional link integrated with marine predators algorithm for tensile behavior prediction of dissimilar friction stir welded aluminum alloy joints, J. Mater. Res. Technol., 9, 5, 11370-11381 (2020)
[80] Soliman, M. A.; Hasanien, H. M.; Alkuhayli, A., Marine predators algorithm for parameters identification of triple-diode photovoltaic models, IEEE Access, 8, Article 155832-155842 (2020)
[81] Al-qaness, M. A.A.; Ewees, A. A.; Fan, H.; Abualigah, L.; Elaziz, M. A., Marine predators algorithm for forecasting confirmed cases of COVID-19 in Italy, USA, Iran and Korea, Int. J. Environ. Res. Public Health, 17, 10, 3520 (2020)
[82] Yousri, D.; Hasanien, H. M.; Fathy, A., Parameters identification of solid oxide fuel cell for static and dynamic simulation using comprehensive learning dynamic multi-swarm marine predators algorithm, Energy Convers. Manage., 228, Article 113692 pp. (2021)
[83] Abdel-Basset, M.; Mohamed, R.; Chakrabortty, R. K.; Ryan, M.; Mirjalili, S., New binary marine predators optimization algorithms for 0-1 knapsack problems, Comput. Ind. Eng., 151, Article 106949 pp. (2021)
[84] Eid, A.; Kamel, S.; Abualigah, L., Marine predators algorithm for optimal allocation of active and reactive power resources in distribution networks, Neural Comput. Appl., 3, 1-29 (2021)
[85] Abdel-Basset, M.; Mohamed, R.; Mirjalili, S.; Chakrabortty, R. K.; Ryan, M., An efficient marine predators algorithm for solving multi-objective optimization problems: Analysis and validations, IEEE Access, 9, 42817-42844 (2021)
[86] Elsayed, A. M.; Shaheen, A. M.; Alharthi, M. M.; Ghoneim, S. S.M.; El-Sehiemy, R. A., Adequate operation of hybrid AC/MT-HVDC power systems using an improved multi- objective marine predators optimizer, IEEE Access, 9, 51065-51087 (2021)
[87] Yue, C.; Qu, B.; Liang, J., A multi-objective particle swarm optimizer using ring topology for solving multimodal multi-objective problems, IEEE Trans. Evol. Comput., 22, 5, 805-817 (2018)
[88] Yan, Z.; Tan, Y.; Zheng, W.; Meng, L.; Zhang, H., Leader recommend operators selection strategy for a multiobjective evolutionary algorithm based on decomposition, Inform. Sci., 550, 166-188 (2020)
[89] Zhou, A.; Zhang, Q.; Jin, Y., Approximating the set of Pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm, IEEE Trans. Evol. Comput., 13, 5, 1167-1189 (2009)
[90] Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C. M.; da Fonseca, V. G., Performance assessment of multiobjective optimizers: An analysis and review, IEEE Trans. Evol. Comput., 7, 2, 117-132 (2003)
[91] Das, A. K.; Nikum, A. K.; Krishnan, S. V.; Pratihar, D. K., Multi-objective bonobo optimizer (MOBO): An intelligent heuristic for multi-criteria optimization, Knowl. Inf. Syst., 62, 4407-4444 (2020)
[92] Zimmerman, D. W.; Zumbo, B. D., Relative power of the wilcoxon test, the Friedman test, and repeated-measures anova on ranks, J. Exp. Educ., 62, 1, 75-86 (1993)
[93] Fang, J.; Sun, G.; Qiu, N.; Kim, N. H.; Li, Q., On design optimization for structural crashworthiness and its state of the art, Struct. Multidiscip. Optim., 55, 3, 1091-1119 (2017)
[94] Audet, C.; Bigeon, J.; Cartier, D.; Digabel, S. L.; Salomon, L., Performance indicators in multiobjective optimization, European J. Oper. Res., 292, 2, 397-422 (2021) · Zbl 1487.90580
[95] Deb, K.; Pratap, A.; Moitra, S., Mechanical component design for multiple ojectives using elitist non-dominated sorting GA, (Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, PPSN VI (2000), Springer-Verlag: Springer-Verlag Berlin, Heidelberg), 859-868
[96] Gupta, S.; Deep, K., A hybrid self-adaptive sine cosine algorithm with opposition based learning, Expert Syst. Appl., 119, 210-230 (2019)
[97] Sadollah, A.; Eskandar, H.; Kim, J. H., Water cycle algorithm for solving constrained multi-objective optimization problems, Appl. Soft Comput., 27, 279-298 (2015)
[98] Tawhid, M. A.; Savsani, V., Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems, Neural Comput. Appl., 31, 915-929 (2019)
[99] Abualigah, L.; Diabat, A.; Mirjalili, S.; Elaziz, M. A.; Gandomi, A. H., The arithmetic optimization algorithm, Comput. Methods Appl. Mech. Engrg., 376, Article 113609 pp. (2021) · Zbl 07340412
[100] Gong, W.; Cai, Z.; Zhu, L., An efficient multiobjective differential evolution algorithm for engineering design, Struct. Multidiscipl. Optim., 38, 137-157 (2009)
[101] Nuh, J. A.; Koh, T. W.; Baharom, S.; Osman, M. H.; Si, N. K., Performance evaluation metrics for multi-objective evolutionary algorithms in search-based software engineering: Systematic literature review, Appl. Sci., 11, 7, 3117 (2021)
[102] Zeng, N.; Song, D.; Li, H.; You, Y.; Alsaadi, F. E., A competitive mechanism integrated multi-objective whale optimization algorithm with differential evolution, Neurocomputing, 432, 12, 170-182 (2021)
[103] Hinojosa, S.; Oliva, D.; Cuevas, E.; Pajares, G.; Avalos, O.; Gálvez, J., Improving multi-criterion optimization with chaos: A novel multi-objective chaotic crow search algorithm, Neural Comput. Appl., 29, 319-335 (2018)
[104] Rizk-Allah, R. M.; Hassanien, A. E.; Slowik, A., Multi-objective orthogonal opposition-based crow search algorithm for large-scale multi-objective optimization, Neural Comput. Appl., 32, 17, 13715-13746 (2020)
[105] Diaz, P. M.; Palanikumar, K.; Kumar, P. R., Multi objective design optimization of two bar truss using NSGA II and TOPSIS, Adv. Mater. Res., 984-985, 419-424 (2014)
[106] Deb, K.; Pratap, A.; Moitr, S., Mechanical component design for multiple objectives using elitist non-dominated sorting GA, (Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, PPSN VI (2000), Springer-Verlag: Springer-Verlag Berlin, Heidelberg), 859-868
[107] Deb, K., GeneAS: A robust optimal design technique for mechanical component design, (Dasgupta, D.; Michalewicz, Z., Evolutionary Algorithms in Engineering Applications (1997), Springer: Springer Berlin, Heidelberg)
[108] Kannan, B. K.; Kramer, S. N., An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design, Trans. ASME, J. Mech. Des., 116, 2, 405-411 (1994)
[109] Sapre, S.; Mini, S., Emulous mechanism based multi-objective moth flame optimization algorithm, J. Parallel Distrib. Comput., 150, 15-33 (2021)
[110] Kiani, E.; Doagou-Mojarrad, H.; Razmi, H., Multi-objective optimal power flow considering voltage stability index and emergency demand response program, Electr. Eng., 102, 2493-2508 (2020)
[111] Gupta, S.; Deep, K.; Moayedi, H.; Foong, L. K.; Assad, A., Sine cosine grey wolf optimizer to solve engineering design problems, Eng. Comput., 2, 1-27 (2020)
[112] Xu, G.; Ding, H.; Feng, Z., Optimal design of hydraulic excavator shovel attachment based on multiobjective evolutionary algorithm, IEEE/ASME Trans. Mechatronics, 24, 2, 808-819 (2019)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.