The exponential distribution optimizer (EDO) represents a heuristic approach, capitalizing on exponential distribution theory to identify global solutions for complex optimization challenges. This study extends the EDO's applicability by introducing its multi-objective version, the multi-objective EDO (MOEDO), enhanced with elite non-dominated sorting and crowding distance mechanisms. An information feedback mechanism (IFM) is integrated into MOEDO, aiming to balance exploration and exploitation, thus improving convergence and mitigating the stagnation in local optima, a notable limitation in traditional approaches. Our research demonstrates MOEDO's superiority over renowned algorithms such as MOMPA, NSGA-II, MOAOA, MOEA/D and MOGNDO. This is evident in 72.58% of test scenarios, utilizing performance metrics like GD, IGD, HV, SP, SD and RT across benchmark test collections (DTLZ, ZDT and various constraint problems) and five real-world engineering design challenges. The Wilcoxon Rank Sum Test (WRST) further confirms MOEDO as a competitive multi-objective optimization algorithm, particularly in scenarios where existing methods struggle with balancing diversity and convergence efficiency. MOEDO's robust performance, even in complex real-world applications, underscores its potential as an innovative solution in the optimization domain. The MOEDO source code is available at: https://github.com/kanak02/MOEDO .

Artificial Intelligence and Sensing Technologies Research Center University of Tabuk 71491 Tabuk Saudi Arabia

Computer Science Department Al al Bayt University Mafraq 25113 Jordan

Department of Biosciences Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai 602 105 India

Department of Computer Science and Engineering Koneru Lakshmaiah Education Foundation Vaddeswaram Guntur 522502 India

Department of Electrical and Computer Engineering Lebanese American University Byblos 13 5053 Lebanon

Department of Electrical Engineering Shri K J Polytechnic Bharuch 392 001 India

Department of Machining Assembly and Engineering Metrology Faculty of Mechanical Engineering VSB Technical University of Ostrava 70800 Ostrava Czech Republic

Department of Mechanical Engineering Vel Tech Rangarajan Dr Sagunthala R and D Institute of Science and Technology Avadi 600 062 India

Hourani Center for Applied Scientific Research Al Ahliyya Amman University Amman 19328 Jordan

MEU Research Unit Middle East University Amman 11831 Jordan

School of Computer Sciences Universiti Sains Malaysia 11800 Pulau Pinang Malaysia

School of Engineering and Technology Sunway University Malaysia 27500 Petaling Jaya Malaysia

University Centre for Research and Development Chandigarh University Mohali 140413 India

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Shi M, Lv L, Xu L. A multi-fidelity surrogate model based on extreme support vector regression: Fusing different fidelity data for engineering design. Eng. Comput. 2023;40(2):473–493. doi: 10.1108/EC-10-2021-0583. DOI

Zhou S, Zhang W, Jiang J, Zhong W, Gu J, Zhu W. On the convergence of stochastic multi-objective gradient manipulation and beyond. Adv. Neural. Inf. Process. Syst. 2022;35:38103–38115.

Cao B, Zhao J, Gu Y, Ling Y, Ma X. Applying graph-based differential grouping for multiobjective large-scale optimization. Swarm Evol. Comput. 2020;53:100626. doi: 10.1016/j.swevo.2019.100626. DOI

Zhu B, Sun Y, Zhao J, Han J, Zhang P, Fan T. A critical scenario search method for intelligent vehicle testing based on the social cognitive optimization algorithm. IEEE Trans. Intell. Transp. Syst. 2023;24(8):7974–7986. doi: 10.1109/TITS.2023.3268324. DOI

Cao B, Wang X, Zhang W, Song H, Lv Z. A many-objective optimization model of industrial Internet of things based on private blockchain. IEEE Netw. 2020;34(5):78–83. doi: 10.1109/MNET.011.1900536. DOI

Zhang C, Zhou L, Li Y. Pareto optimal reconfiguration planning and distributed parallel motion control of mobile modular robots. IEEE Trans. Ind. Electron. 2023 doi: 10.1109/TIE.2023.3321997. DOI

Li S, Chen H, Chen Y, Xiong Y, Song Z. Hybrid method with parallel-factor theory, a support vector machine, and particle filter optimization for intelligent machinery failure identification. Machines. 2023;11(8):837. doi: 10.3390/machines11080837. DOI

Zhang L, Sun C, Cai G, Koh LH. Charging and discharging optimization strategy for electric vehicles considering elasticity demand response. eTransportation. 2023;18:100262. doi: 10.1016/j.etran.2023.100262. DOI

Cao B, Zhao J, Yang P, Gu Y, Muhammad K, Rodrigues JJPC, de Albuquerque VHC. Multiobjective 3-D topology optimization of next-generation wireless data center network. IEEE Trans. Ind. Inform. 2020;16(5):3597–3605. doi: 10.1109/TII.2019.2952565. DOI

Duan Y, Zhao Y, Hu J. An initialization-free distributed algorithm for dynamic economic dispatch problems in microgrid: Modeling, optimization and analysis. Sustain. Energy Grids Netw.orks. 2023;34:101004. doi: 10.1016/j.segan.2023.101004. DOI

Almufti SM. Historical survey on metaheuristics algorithms. Int. J. Sci. World. 2019;7(1):1. doi: 10.14419/ijsw.v7i1.29497. DOI

Alorf A. A survey of recently developed metaheuristics and their comparative analysis. Eng. Appl. Artif. Intell. 2023;117:105622. doi: 10.1016/j.engappai.2022.105622. DOI

Dokeroglu T, Sevinc E, Kucukyilmaz T, Cosar A. A survey on new generation metaheuristic algorithms. Comput. Ind. Eng. 2019;137:106040. doi: 10.1016/j.cie.2019.106040. DOI

Zhou A, Qu B-Y, Li H, Zhao S-Z, Suganthan PN, Zhang Q. Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm Evol. Comput. 2011;1(1):32–49. doi: 10.1016/j.swevo.2011.03.001. DOI

Hu, X., & Eberhart, R. Multiobjective optimization using dynamic neighborhood particle swarm optimization. In Proceedings of the 2002 Congress on Evolutionary Computation, 2 (pp. 1677–1681). CEC'02. IEEE Publications (Cat. No. 02TH8600) (2002).

Gunantara N. A review of multi-objective optimization: Methods and its applications. Cogent Eng. 2018;5(1):1502242. doi: 10.1080/23311916.2018.1502242. DOI

Sharma S, Kumar V. A comprehensive review on multi-objective optimization techniques: Past, present and future. Arch. Comput. Methods Eng. 2022;29(7):5605–5633. doi: 10.1007/s11831-022-09778-9. DOI

Pereira JLJ, Oliver GA, Francisco MB, Cunha SS, Gomes GF. A review of multi-objective optimization: Methods and algorithms in mechanical engineering problems. Arch. Comput. Methods Eng. 2021;20:1–24.

Huy THB, Nallagownden P, Truong KH, Kannan R, Vo DN, Ho N. Multi-objective search group algorithm for engineering design problems. Appl. Soft Comput. 2022;126:109287. doi: 10.1016/j.asoc.2022.109287. DOI

Li Y-J, Li H-N. Interactive evolutionary multi-objective optimization and decision-making on life-cycle seismic design of bridge. Adv. Struct. Eng. 2018;21(15):2227–2240. doi: 10.1177/1369433218770819. DOI

Zhang, J., & Xing, L. A survey of multiobjective evolutionary algorithms. In IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing, Vol. 1, 93–100 (IEEE Publications, 2017). 10.1109/CSE-EUC.2017.27.

Guliashki V, Toshev H, Korsemov C. Survey of evolutionary algorithms used in multiobjective optimization. Probl. Eng. Cybern. Robot. 2009;60(1):42–54.

Wang J, Su Y, Lin Q, Ma L, Gong D, Li J, Ming Z. A survey of decomposition approaches in multiobjective evolutionary algorithms. Neurocomputing. 2020;408:308–330. doi: 10.1016/j.neucom.2020.01.114. DOI

Mashwani WK. Hybrid multiobjective evolutionary algorithms: A survey of the state-of-the-art. Int. J. Comput. Sci. Issues. 2011;8(6):374.

Xu, Q., Xu, Z., & Ma, T. (2019). A short survey and challenges for multiobjective evolutionary algorithms based on decomposition. In International Conference on Computer, Information and Telecommunication Systems, CITS, IEEE, 1–5 (2019). 10.1109/CITS.2019.8862046.

Igel C. Theory and Principled Methods for the Design of Metaheuristics. Springer; 2014. No free lunch theorems: Limitations and perspectives of metaheuristics; pp. 1–23.

Chopard B, Tomassini M. An Introduction to Metaheuristics for Optimization. Springer; 2018. Performance and limitations of metaheuristics; pp. 191–203.

Dorigo M, Stützle T. Handbook of Metaheuristics. Springer; 2003. The ant colony optimization metaheuristic: Algorithms, applications and advances; pp. 250–285.

Marca, Y., Aguirre, H., Zapotecas, S., Liefooghe, A., Derbel, B., Verel, S., & Tanaka, K. Pareto dominance-based MOEAs on problems with difficult pareto set topologies. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, 189–190 (2018). 10.1145/3205651.3205746.

Zhang Q, Li H, MOEA/D MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 2007;11(6):712–731. doi: 10.1109/TEVC.2007.892759. DOI

Khodadadi N, Talatahari S, DadrasEslamlou A. MOTEO: A novel multi-objective thermal exchange optimization algorithm for engineering problems. Soft Comput. 2022;26(14):6659–6684. doi: 10.1007/s00500-022-07050-7. DOI

Houssein EH, Çelik E, Mahdy MA, Ghoniem RM. Self-adaptive equilibrium optimizer for solving global, combinatorial, engineering and multi-objective problems. Expert Syst. Appl. 2022;195:116552. doi: 10.1016/j.eswa.2022.116552. DOI

Lin A, Yu P, Cheng S, Xing L. One-to-one ensemble mechanism for decomposition-based multi-objective optimization. Swarm Evolut. Comput. 2022;68:101007. doi: 10.1016/j.swevo.2021.101007. DOI

Zheng J, Zhang Z, Zou J, Yang S, Ou J, Hu Y. A dynamic multiobjective particle swarm optimization algorithm based on adversarial decomposition and neighborhood evolution. Swarm Evolut. Comput. 2022;69:100987. doi: 10.1016/j.swevo.2021.100987. DOI

Ben-Said A, Moukrim A, Guibadj RN, Verny J. Using decompositionbased multi-objective algorithm to solve selective pickup and delivery problems with time windows. Comput. Oper. Res. 2022;145:105867. doi: 10.1016/j.cor.2022.105867. DOI

Zouache D, Abdelaziz FB. Guided manta ray foraging optimization using epsilon dominance for multi-objective optimization in engineering design. Expert Syst. Appl. 2022;189:116126. doi: 10.1016/j.eswa.2021.116126. DOI

Yin S, Luo Q, Zhou Y. IBMSMA: An indicator-based multi-swarm slime mould algorithm for multi-objective truss optimization problems. J. Bionic Eng. 2022 doi: 10.1007/s42235-022-00307-9. DOI

Zitzler E, Künzli S. PPSN. Springer; 2004. Indicator-based selection in multiobjective search; pp. 832–842.

Abdi Y, Feizi-Derakhshi M-R. Hybrid multi-objective evolutionary algorithm based on search manager framework for big data optimization problems. Appl. Soft Comput. 2020;87:105991. doi: 10.1016/j.asoc.2019.105991. DOI

Dutta S, Mallipeddi R, Das KN. Hybrid selection based multi/manyobjective evolutionary algorithm. Sci. Rep. 2022;12(1):6861. doi: 10.1038/s41598-022-10997-0. PubMed DOI PMC

Kalita K, Pal S, Haldar S, Chakraborty S. A hybrid TOPSIS-PR-GWO approach for multi-objective process parameter optimization. Process Integrat. Optim. Sustain. 2022;6(4):1011–1026. doi: 10.1007/s41660-022-00256-0. DOI

Chennuru VK, Timmappareddy SR. Simulated annealing based undersampling (SAUS): A hybrid multi-objective optimization method to tackle class imbalance. Appl. Intell. 2022;52(2):2092–2110. doi: 10.1007/s10489-021-02369-4. DOI

Mirjalili S, Jangir P, Saremi S. Multi-objective ant lion optimizer: A multi-objective optimization algorithm for solving engineering problems. Appl. Intell. 2017;46(1):79–95. doi: 10.1007/s10489-016-0825-8. DOI

Premkumar M, Jangir P, Sowmya R, Alhelou HH, Mirjalili S, Kumar BS. Multi-objective equilibrium optimizer: Framework and development for solving multi-objective optimization problems. J. Comput. Design Eng. 2021;9(1):24–50. doi: 10.1093/jcde/qwab065. DOI

Premkumar M, Jangir P, Sowmya R, Alhelou HH, Heidari AA, Chen H. MOSMA: Multi-objective slime mould algorithm based on elitist non-dominated sorting. IEEE Access. 2020;9:3229–3248. doi: 10.1109/ACCESS.2020.3047936. DOI

Premkumar M, Jangir P, Santhosh Kumar B, Sowmya R, HaesAlhelou H, Abualigah L, Yildiz AR, Mirjalili S. A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimization problems: Diversity analysis and validations. IEEE Access. 2021;9:84263–84295. doi: 10.1109/ACCESS.2021.3085529. DOI

Buch H, Trivedi IN. A new non-dominated sorting ions motion algorithm: Development and applications. Decis. Sci. Lett. 2020;9(1):59–76. doi: 10.5267/j.dsl.2019.8.001. DOI

Jangir P, Buch H, Mirjalili S, Manoharan P. MOMPA: Multi-objective marine predator algorithm for solving multi-objective optimization problems. Evolut. Intell. 2021 doi: 10.1007/s12065-021-00649-z. DOI

Mirjalili S, Jangir P, Mirjalili SZ, Saremi S, Trivedi IN. Optimization of problems with multiple objectives using the multi-verse optimization algorithm. Knowl. Based Syst. 2017;134:50–71. doi: 10.1016/j.knosys.2017.07.018. DOI

Jangir P, Jangir N. A new non-dominated sorting grey wolf optimizer (NS-GWO) algorithm: Development and application to solve engineering designs and economic constrained emission dispatch problem with integration of wind power. Eng. Appl. Artif. Intell. 2018;72:449–467. doi: 10.1016/j.engappai.2018.04.018. DOI

Premkumar M, Jangir P, Sowmya R. MOGBO: A new multiobjective gradient-based optimizer for real-world structural optimization problems. Knowl. Based Syst. 2021;218:106856. doi: 10.1016/j.knosys.2021.106856. DOI

Kumar S, Jangir P, Tejani GG, Premkumar M, Alhelou HH. MOPGO: A new physics-based multi-objective plasma generation optimizer for solving structural optimization problems. IEEE Access. 2021;9:84982–85016. doi: 10.1109/ACCESS.2021.3087739. DOI

Jangir P, Heidari AA, Chen H. Elitist non-dominated sorting Harris hawks optimization: Framework and developments for multi-objective problems. Expert Syst. Appl. 2021;186:115747. doi: 10.1016/j.eswa.2021.115747. DOI

Kumar S, Jangir P, Tejani GG, Premkumar M. MOTEO: A novel physics-based multiobjective thermal exchange optimization algorithm to design truss structures. Knowl. Based Syst. 2022;242:108422. doi: 10.1016/j.knosys.2022.108422. DOI

Kumar S, Jangir P, Tejani GG, Premkumar M. A decomposition based multi-objective heat transfer search algorithm for structure optimization. Knowl. Based Syst. 2022;253:109591. doi: 10.1016/j.knosys.2022.109591. DOI

Ganesh N, Shankar R, Kalita K, Jangir P, Oliva D, Pérez-Cisneros M. A novel decomposition-based multi-objective symbiotic organism search optimization algorithm. Mathematics. 2023;11(8):1898. doi: 10.3390/math11081898. DOI

Pandya SB, Visumathi J, Mahdal M, Mahanta TK, Jangir P. A novel MOGNDO algorithm for security-constrained optimal power flow problems. Electronics. 2022;11(22):3825. doi: 10.3390/electronics11223825. DOI

Jangir P. Non-dominated sorting moth flame optimizer: A novel multi-objective optimization algorithm for solving engineering design problems. Eng. Technol. Open Access J. 2018;2(1):17–31. doi: 10.19080/ETOAJ.2018.02.555579. DOI

Jangir P, Jangir N. Non-dominated sorting whale optimization algorithm. Glob. J. Res. Eng. 2017;17(4):15–42.

Jangir P. ‘MONSDA:-A novel multi-objective non-dominated sorting dragonfly algorithm’. glob. J. Res. Eng. F Electr. Electron. Eng. 2020;20:28–52.

Jiao K, Chen J, Xin B, Li L. A reference vector based multiobjective evolutionary algorithm with Q-learning for operator adaptation. Swarm Evolut. Comput. 2023;76:101225. doi: 10.1016/j.swevo.2022.101225. DOI

Li, C., Deng, L., Gong, W., & Qiao, L. A many-objective evolutionary algorithm based on hybrid dynamic decomposition IEEE Congress on Evolutionary Computation (CEC), 2023, 1–8 (IEEE Publications, 2023). 10.1109/CEC53210.2023.10254128.

Pang LM, Ishibuchi H, Shang K. Use of two penalty values in multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Cybern. 2023;53(11):7174–7186. doi: 10.1109/TCYB.2022.3182167. PubMed DOI

Abdel-Basset M, El-Shahat D, Jameel M, Abouhawwash M. Exponential distribution optimizer (EDO): A novel math-inspired algorithm for global optimization and engineering problems. Artif. Intell. Rev. 2023;20:1–72. doi: 10.1016/j.knosys.2022.110248. DOI

Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput. 2000;8(2):173–195. doi: 10.1162/106365600568202. PubMed DOI

Deb K, Thiele L, Laumanns M, Zitzler E. Evolutionary Multiobjective Optimization. Springer; 2005. Scalable test problems for evolutionary multiobjective optimization; pp. 105–145.

Binh, T. T., & Korn, U. MOBES: A multiobjective evolution strategy for constrained optimization problems. In The Third International Conference on Genetic Algorithms (Mendel 97), 27 (1997).

Osyczka A, Kundu S. A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct. Optim. 1995;10(2):94–99. doi: 10.1007/BF01743536. DOI

Branke J, Kaußler T, Schmeck H. Guidance in evolutionary multi-objective optimization. Adv. Eng. Softw. 2001;32(6):499–507. doi: 10.1016/S0965-9978(00)00110-1. DOI

De la Hoz E, de la Hoz E, Ortiz A, Ortega J, Martínez-Álvarez A. Feature selection by multi-objective optimisation: Application to network anomaly detection by hierarchical self-organising maps. Knowl. Based Syst. 2014;71:322–338. doi: 10.1016/j.knosys.2014.08.013. DOI

Martínez-Álvarez A, Cuenca-Asensi S, Ortiz A, Calvo-Zaragoza J, VivasTejuelo LAV. Tuning compilations by multi-objective optimization: Application to apache web server. Appl. Soft Comput. 2015;29:461–470. doi: 10.1016/j.asoc.2015.01.029. DOI

Wang GG, Tan Y. Improving metaheuristic algorithms with information feedback models. IEEE Trans. Cybern. 2019;49(2):542–555. doi: 10.1109/TCYB.2017.2780274. PubMed DOI