This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Applied Science Research Center Applied Science Private University Amman 11931 Jordan

Artificial Intelligence and Sensing Technologies Research Center University of Tabuk Tabuk 71491 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 Pulau Pinang 11800 Malaysia

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

University Centre for Research and Development Chandigarh University Mohali 140413 India

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Holland J.H., Reitman J.S. Cognitive systems based on adaptive algorithms. ACM SIGART Bull. 1977;(63) doi: 10.1145/1045343.1045373. 49–49. DOI

Tsai C.-F., Eberle W., Chu C.-Y. Genetic algorithms in feature and instance selection. Knowl. Base Syst. 2013;39:240–247. doi: 10.1016/j.knosys.2012.11.005. DOI

Lin M.-H., Tsai J.-F., Yu C.-S. A review of deterministic optimization methods in engineering and management. Math. Probl Eng. 2012;2012:1–15. doi: 10.1155/2012/756023. DOI

Shmoys D.B., Swamy C. Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science. 2004. Stochastic optimization is (almost) as easy as deterministic optimization; pp. 228–237. 2004. DOI

Dorigo M., Birattari M., Stutzle T. Ant colony optimization. IEEE Comput. Intell. Mag. 2006;1:28–39.

Kennedy J. Encyclopedia of Machine Learning. EDN. Springer; 2011. Particle swarm optimization; pp. 760–766.

Storn R., Price K. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 1997;11(4):341–359. doi: 10.1023/A:1008202821328. 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;1 doi: 10.1109/TIE.2023.3321997. –10. 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. Transport. Syst. 2023;24(8):7974–7986. doi: 10.1109/TITS.2023.3268324. DOI

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

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

Cao B., Li Z., Liu X., Lv Z., He H. Mobility-aware multiobjective task offloading for vehicular edge computing in digital twin environment. IEEE J. Sel. Area. Commun. 2023;41(10):3046–3055. doi: 10.1109/JSAC.2023.3310100. 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 Network. 2020;34(5):78–83. doi: 10.1109/MNET.011.1900536. DOI

BoussäıD I., Lepagnot J., Siarry P. A survey on optimization metaheuristics. Inf. Sci. 2013;237:82–117. doi: 10.1016/j.ins.2013.02.041. DOI

Helbig M., Engelbrecht A.P. Performance measures for dynamic multi-objective optimisation algorithms. Inf. Sci. 2013;250:61–81. doi: 10.1016/j.ins.2013.06.051. DOI

Beyer H.-G., Sendhoff B. Robust optimization–a comprehensive survey. Comput. Methods Appl. Mech. Eng. 2007;196(33–34):3190–3218. doi: 10.1016/j.cma.2007.03.003. DOI

Coello Coello C.A.C. A comprehensive survey of evolutionarybased multiobjective optimization techniques. Knowl. Inf. Syst. 1999;1(3):269–308. doi: 10.1007/BF03325101. DOI

Deb K. vol. 16. Wiley; 2001. (Multi-objective Optimization Using Evolutionary Algorithms).

von Lucken C., Bar, an B., Brizuela C. A survey on multi-” objective evolutionary algorithms for many-objective problems. Comput. Optim. Appl. 2014;58:707–756.

Nguyen T.T., Yang S., Branke J. Evolutionary dynamic optimization: a survey of the state of the art. Swarm Evol. Comput. 2012;6:1–24. doi: 10.1016/j.swevo.2012.05.001. DOI

Padhye N., Mittal P., Deb K. Feasibility preserving constraint-handling strategies for real parameter evolutionary optimization. Comput. Optim. Appl. 2015;62(3):851–890. doi: 10.1007/s10589-015-9752-6. DOI

Kaidi W., Khishe M., Mohammadi M. Dynamic levy flight chimp optimization. Knowl. Base Syst. 2022;235 doi: 10.1016/j.knosys.2021.107625. DOI

Khishe M., Nezhadshahbodaghi M., Mosavi M.R., Martín D. A weighted chimp optimization algorithm. IEEE Access. 2021;9:158508–158539. doi: 10.1109/ACCESS.2021.3130933. DOI

Khishe M., Orouji N., Mosavi M.R. Multi-objective chimp optimizer: an innovative algorithm for multi-objective problems. Expert Syst. Appl. 2023;211 doi: 10.1016/j.eswa.2022.118734. DOI

Khishe M., Mosavi M.R. Chimp optimization algorithm. Expert Syst. Appl. 2020;149 doi: 10.1016/j.eswa.2020.113338. PubMed DOI PMC

Bo Q., Cheng W., Khishe M. Evolving chimp optimization algorithm by weighted opposition-based technique and greedy search for multimodal engineering problems. Appl. Soft Comput. 2023;132 doi: 10.1016/j.asoc.2022.109869. DOI

Khishe M. Greedy opposition-based learning for chimp optimization algorithm. Artif. Intell. Rev. 2023;56(8):7633–7663. doi: 10.1007/s10462-022-10343-w. DOI

Asrari A., Lotfifard S., Payam M.S. Pareto dominancebased multiobjective optimization method for distribution network reconfiguration. IEEE Trans. Smart Grid. 2016;7(3):1401–1410. doi: 10.1109/TSG.2015.2468683. DOI

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. 2011;1(1):32–49. doi: 10.1016/j.swevo.2011.03.001. 3// DOI

Deb K. Search Methodologies. 449. Springer; 2014. Multi-objective optimization; p. 403. EDN.

Padhye N., Deb K. Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation. 2010. Evolutionary multi-objective optimization and decision making for selective laser sintering; pp. 1259–1266. DOI

Gharehchopogh F.S., Abdollahzadeh B., Barshandeh S., Arasteh B. A multi-objective mutation-based dynamic Harris Hawks optimization for botnet detection in IoT. Int. Things. 2023;24 doi: 10.1016/j.iot.2023.100952. DOI

Gharehchopogh F.S., Ibrikci T. An improved African vultures optimization algorithm using different fitness functions for multi-level thresholding image segmentation. Multimed. Tool. Appl. 2023:1–47. doi: 10.1007/s11042-023-16300-1. DOI

Gharehchopogh F.S. An improved Harris Hawks optimization algorithm with multi-strategy for community detection in social networks. JBE. 2023;20(3):1175–1197. doi: 10.1007/s42235-022-00303-z. DOI

Gharehchopogh F.S., Ucan A., Ibrikci T., Arasteh B., Isik G. Slime mould algorithm: a comprehensive survey of its variants and applications. Arch. Comput. Methods Eng.: State of the Art Reviews. 2023;30(4):2683–2723. doi: 10.1007/s11831-023-09883-3. PubMed DOI PMC

Piri J., Mohapatra P., Acharya B., Gharehchopogh F.S., Gerogiannis V.C., Kanavos A., Manika S. Feature selection using artificial gorilla troop optimization for biomedical data: a case analysis with COVID-19 data. Mathematics. 2022;10(15):2742. doi: 10.3390/math10152742. DOI

Xiao Z., Shu J., Jiang H., Lui J.C.S., Min G., Liu J., Dustdar S. Multi-objective parallel task offloading and content caching in D2D-aided MEC networks. IEEE Trans. Mobile Comput. 2022:1–16. doi: 10.1109/TMC.2022.3199876. DOI

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 doi: 10.1016/j.swevo.2019.100626. 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 and Networks. 2023;34 doi: 10.1016/j.segan.2023.101004. DOI

Deb K., Pratap A., Agarwal S., Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002;6(2):182–197. doi: 10.1109/4235.996017. DOI

Coello Coello C.A., Lechuga M.S. Proceedings of the 2002 Congress on Evolutionary Computation. 2002. MOPSO: a proposal for multiple objective particle swarm optimization; pp. 1051–1056. 2002. CEC. DOI

Alaya I., Solnon C., Ghedira K. Ant colony optimization for multi-objective optimization problems. ICTAI. 2007;1:450–457. doi: 10.1109/ICTAI.2007.108. DOI

Xue F., Sanderson A.C., Graves R.J. The 2003 Congress on Evolutionary Computation. 2003. Pareto-based multiobjective differential evolution; pp. 862–869. 2003. CEC’03.

Knowles J.D., Corne D.W. Approximating the nondominated front using the Pareto archived evolution strategy. Evol. Comput. 2000;8(2):149–172. doi: 10.1162/106365600568167. PubMed DOI

Wolpert D. No free lunch theorem for optimization. IEEE Trans. Evol. Comput. 1997:467–482.

Jin Y., Olhofer M., Sendhoff B. Dynamic weighted aggregation for evolutionary multi-objective optimization. Why does it work and how? 2001

Branke J., Deb K., Dierolf H., Osswald M. International Conference on Parallel Problem Solving from Nature. 2004. Finding knees in multi-objective optimization; pp. 722–731.

Kollat J.B., Reed P. A framework for visually interactive decision-making and design using evolutionary multiobjective optimization [Video] Environ. Model. Software. 2007;22(12):1691–1704. doi: 10.1016/j.envsoft.2007.02.001. 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 H.H., Mirjalili S., Kumar B.S. Multi-objective equilibrium optimizer: framework and development for solving multi-objective optimization problems. J. Comput. Design and Eng. 2021;9(1):24–50. doi: 10.1093/jcde/qwab065. DOI

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. 2020;9:3229–3248. doi: 10.1109/ACCESS.2020.3047936. DOI

Premkumar M., Jangir P., Santhosh Kumar B., Sowmya R., Haes Alhelou H., Abualigah L., Yildiz A.R., Mirjalili S. A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimiza- tion problems: diversity analysis and validations. IEEE Access. 2021;9:84263–84295.

Buch H., Trivedi I.N. A new non-dominated sorting ions motion algorithm: development and applications, Deci- SionSci. Letture. 2020;9(1):59–76.

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

Deb K., Pratap A., Agarwal S., Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002;6(2):182–197. doi: 10.1109/4235.996017. DOI

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. Base 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. Base Syst. 2021;218 doi: 10.1016/j.knosys.2021.106856. DOI

Kumar S., Jangir P., Tejani G.G., Premkumar M., Alhelou H.H. 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 A.A., Chen H. Elitist non-dominated sorting Harris hawks optimization: framework and developments for multi-objective problems. Expert Syst. Appl. 2021;186 doi: 10.1016/j.eswa.2021.115747. DOI

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

Kumar S., Jangir P., Tejani G.G., Premkumar M. A decomposition based multi-objective heat transfer search algorithm for structure optimization. Knowl. Base Syst. 2022;253 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 S.B., Visumathi J., Mahdal M., Mahanta T.K., 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.

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

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

Binh T.T., Korn U. MOBES: a multiobjective evolution strategy for constrained optimization problems. Third Int. Conf. Genetic Algorithms. 1997;Mendel 97:27.

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

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 Evol. Comput. 2022;69 doi: 10.1016/j.swevo.2021.100987. DOI

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

Zouache D., Abdelaziz F.B. Guided manta ray foraging optimization using epsilon dominance for multi-objective optimization in engineering design. Expert Syst. Appl. 2022;189 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. JBE. 2022:1–28.

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

Houssein E.H., Oliva D., Samee N.A., Mahmoud N.F., Emam M.M. Liver Cancer Algorithm: a novel bio-inspired optimizer. Comput. Biol. Med. 2023;165 doi: 10.1016/j.compbiomed.2023.107389. ISSN 0010-4825. PubMed DOI