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Multi-objective Bonobo Optimizer (MOBO): an intelligent heuristic for multi-criteria optimization

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Abstract

Non-traditional optimization tools have proved their potential in solving various types of optimization problems. These problems deal with either single objective or multiple/many objectives. Bonobo Optimizer (BO) is an intelligent and adaptive metaheuristic optimization algorithm inspired from the social behavior and reproductive strategies of bonobos. There is no study in the literature to extend this BO to solve multi-objective optimization problems. This paper presents a Multi-objective Bonobo Optimizer (MOBO) to solve different optimization problems. Three different versions of MOBO are proposed in this paper, each using a different method, such as non-dominated sorting with adaptation of grid approach; a ranking scheme for sorting of population with crowding distance approach; decomposition technique, wherein the solutions are obtained by dividing a multi-objective problem into a number of single-objective problems. The performances of all three different versions of the proposed MOBO had been tested on a set of thirty diversified benchmark test functions, and the results were compared with that of four other well-known multi-objective optimization techniques available in the literature. The obtained results showed that the first two versions of the proposed algorithms either outperformed or performed competitively in terms of convergence and diversity compared to the others. However, the third version of the proposed techniques was found to have the poor performance.

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References

  1. Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395. https://doi.org/10.1007/s00158-003-0368-6

    Article  MathSciNet  MATH  Google Scholar 

  2. Ghiassi M, Devor RE, Dessouky MI, Kijowski BA (1984) An application of multiple criteria decision making principles for planning machining operations. IIE Trans 16(2):106–114. https://doi.org/10.1080/07408178408974675

    Article  Google Scholar 

  3. Fox AD, Corne DW, Mayorga Adame CG, Polton JA, Henry L-A, Roberts JM (2019) An efficient multi-objective optimization method for use in the design of marine protected area networks. Front Mar Sci. https://doi.org/10.3389/fmars.2019.00017

    Article  Google Scholar 

  4. Acharya PS (2019) Intelligent algorithmic multi-objective optimization for renewable energy system generation and integration problems: a review. Int J Renew Energy Res 9(1):271–280

    Google Scholar 

  5. Gopakumar AM, Balachandran PV, Xue D, Gubernatis JE, Lookman T (2018) Multi-objective optimization for materials discovery via adaptive design. Sci Rep 8(1):3738

    Article  Google Scholar 

  6. Franken T, Duggan A, Matrisciano A, Lehtiniemi H, Borg A, Mauss F (2019) Multi-objective optimization of fuel consumption and NOx emissions with reliability analysis using a stochastic reactor model. SAE technical paper, 2019-01-1173. https://doi.org/10.4271/2019-01-1173

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Coello CAC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceedings of the congress on evolutionary computation (CEC’02), pp 1051–1056. https://doi.org/10.1109/cec.2002.1004388

  10. Mirjalili S, Saremi S, Mirjalili SM, Coelho LdS (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47:106–119. https://doi.org/10.1016/j.eswa.2015.10.039

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Golberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Longman Publishing Co, Reading

    Google Scholar 

  13. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science (MHS’95). IEEE, pp 39–43

  14. Shabani A, Asgarian B, Gharebaghi SA, Salido MA, Giret A (2019) A new optimization algorithm based on search and rescue operations. Math Probl Eng. https://doi.org/10.1155/2019/2482543

    Article  Google Scholar 

  15. Harifi S, Khalilian M, Mohammadzadeh J, Ebrahimnejad S (2019) Emperor Penguins Colony: a new metaheuristic algorithm for optimization. Evol Intel 12(2):211–226. https://doi.org/10.1007/s12065-019-00212-x

    Article  Google Scholar 

  16. Hayyolalam V, Pourhaji Kazem AA (2020) Black Widow Optimization Algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intell 87:103249. https://doi.org/10.1016/j.engappai.2019.103249

    Article  Google Scholar 

  17. Zervoudakis K, Tsafarakis S (2020) A mayfly optimization algorithm. Comput Ind Eng 145:106559. https://doi.org/10.1016/j.cie.2020.106559

    Article  Google Scholar 

  18. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2020) Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft Comput. https://doi.org/10.1007/s00500-020-04812-z

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Wong W, Ming CI (2019) A review on metaheuristic algorithms: recent trends, benchmarking and applications. In: 2019 7th international conference on smart computing and communications (ICSCC), 28–30 June 2019, pp 1–5. https://doi.org/10.1109/icscc.2019.8843624

  21. Das AK, Pratihar DK (2019) A new Bonobo Optimizer (BO) for real-parameter optimization. In: IEEE region 10 symposium (TENSYMP 2019) Kolkata, India, pp 108–113. https://doi.org/10.1109/tensymp46218.2019.8971108

  22. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  23. Deb K (2012) Advances in evolutionary multi-objective optimization. In: Fraser G, Teixeira de Souza J (eds) Search based software engineering (SSBSE), 2012. Lecture notes in computer science. Springer, Berlin, pp 1–26. https://doi.org/10.1007/978-3-642-33119-0_1

    Chapter  Google Scholar 

  24. Zadeh L (1963) Optimality and non-scalar-valued performance criteria. IEEE Trans Autom Control 8(1):59–60. https://doi.org/10.1109/TAC.1963.1105511

    Article  Google Scholar 

  25. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271. https://doi.org/10.1109/4235.797969

    Article  Google Scholar 

  26. Bhargava S (2013) A note on evolutionary algorithms and its applications. Adults Learn Math 8(1):31–45

    Google Scholar 

  27. Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput 8(2):149–172. https://doi.org/10.1162/106365600568167

    Article  Google Scholar 

  28. Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248. https://doi.org/10.1162/evco.1994.2.3.221

    Article  Google Scholar 

  29. Xiangui S, Dekui K (2015) A multi-objective ant colony optimization algorithm based on elitist selection strategy. Metall Min Ind 7(6):333–338

    Google Scholar 

  30. Jiang S, Yang S (2017) A strength Pareto evolutionary algorithm based on reference direction for multiobjective and many-objective optimization. IEEE Trans Evol Comput 21(3):329–346. https://doi.org/10.1109/TEVC.2016.2592479

    Article  Google Scholar 

  31. Zeng J, Dou L, Xin B (2018) Multi-objective cooperative salvo attack against group target. J Syst Sci Complex 31(1):244–261. https://doi.org/10.1007/s11424-018-7437-9

    Article  MATH  Google Scholar 

  32. Zapotecas-Martínez S, López-Jaimes A, García-Nájera A (2019) LIBEA: a Lebesgue indicator-based evolutionary algorithm for multi-objective optimization. Swarm Evol Comput 44:404–419. https://doi.org/10.1016/j.swevo.2018.05.004

    Article  Google Scholar 

  33. Foroughi Nematollahi A, Rahiminejad A, Vahidi B (2019) A novel multi-objective optimization algorithm based on lightning attachment procedure optimization algorithm. Appl Soft Comput 75:404–427. https://doi.org/10.1016/j.asoc.2018.11.032

    Article  Google Scholar 

  34. Liu C, Du Y, Li A, Lei J (2020) Evolutionary multi-objective membrane algorithm. IEEE Access 8:6020–6031. https://doi.org/10.1109/ACCESS.2019.2939217

    Article  Google Scholar 

  35. RamuNaidu Y, Ojha AK, SusheelaDevi V (2020) Multi-objective Jaya Algorithm for solving constrained multi-objective optimization problems. In: Kim JH, Geem ZW, Jung D, Yoo DG, Yadav A (eds) Advances in Harmony search, soft computing and applications. Springer, Cham, pp 89–98

    Chapter  Google Scholar 

  36. Han X, Liu J (2020) Micro multi-objective genetic algorithm. In: Han X, Liu J (eds) Numerical simulation-based design: theory and methods. Springer, Singapore, pp 153–178. https://doi.org/10.1007/978-981-10-3090-1_9

    Chapter  Google Scholar 

  37. Wu D, Gao H (2020) Multi-objective bird swarm algorithm. In: Lu H (ed) Cognitive internet of things: frameworks, tools and applications. Springer, Cham, pp 109–119. https://doi.org/10.1007/978-3-030-04946-1_12

    Chapter  Google Scholar 

  38. Gunantara N (2018) A review of multi-objective optimization: methods and its applications. Cogent Eng 5(1):1502242. https://doi.org/10.1080/23311916.2018.1502242

    Article  Google Scholar 

  39. Emmerich MTM, Deutz AH (2018) A tutorial on multiobjective optimization: fundamentals and evolutionary methods. Nat Comput 17(3):585–609. https://doi.org/10.1007/s11047-018-9685-y

    Article  MathSciNet  Google Scholar 

  40. Huang W, Zhang Y, Li L (2019) Survey on multi-objective evolutionary algorithms. J Phys: Conf Ser 1288:012057. https://doi.org/10.1088/1742-6596/1288/1/012057

    Article  Google Scholar 

  41. Ojstersek R, Brezocnik M, Buchmeister B (2020) Multi-objective optimization of production scheduling with evolutionary computation: a review. Int J Ind Eng Comput 11(3):359–376

    Google Scholar 

  42. Social Organization. http://luna.cas.usf.edu/~rtykot/ANT3101/primates/organization.html. Accessed 23/10/2019

  43. Holland JH (1992) Adaptation in natural and artificial systems. An introductory analysis with application to biology, control, and artificial intelligence. MIT Press, Cambridge

    Google Scholar 

  44. Miettinen K (2012) Nonlinear multiobjective optimization, vol 12. Springer, New York. https://doi.org/10.1007/978-1-4615-5563-6

    Book  MATH  Google Scholar 

  45. Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Eiben AE, Bäck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature—PPSN V. Lecture notes in computer science. Springer, Berlin, pp 292–301. https://doi.org/10.1007/bfb0056872

    Chapter  Google Scholar 

  46. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester

    MATH  Google Scholar 

  47. Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. Master thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Boston

  48. Kursawe F (1991) A variant of evolution strategies for vector optimization. In: Schwefel HP, Männer R (eds) International conference on parallel problem solving from nature (PPSN). Lecture notes in computer science. Springer, Berlin, pp 193–197. https://doi.org/10.1007/bfb0029752

    Chapter  Google Scholar 

  49. http://delta.cs.cinvestav.mx/~ccoello/EMOO/testfuncs/. Accessed on 23/09/2019

  50. http://jmetal.sourceforge.net/problems.html. Accessed on 23/09/2019

  51. Deb K (1999) Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput 7(3):205–230. https://doi.org/10.1162/evco.1999.7.3.205

    Article  Google Scholar 

  52. Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization. Advanced information and knowledge processing. Springer, London, pp 105–145. https://doi.org/10.1007/1-84628-137-7_6

    Chapter  MATH  Google Scholar 

  53. Gong W, Duan Q, Li J, Wang C, Di Z, Ye A, Miao C, Dai Y (2016) Multiobjective adaptive surrogate modeling-based optimization for parameter estimation of large, complex geophysical models. Water Resour Res 52(3):1984–2008

    Article  Google Scholar 

  54. Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multiobjective optimization test instances for the CEC 2009 special session and competition. University of Essex, Colchester, UK and Nanyang Technological University, Singapore. Special session on performance assessment of multi-objective optimization algorithms, technical report 264

  55. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google Scholar 

  56. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the first international conference on genetic algorithms and their applications. Lawrence Erlbaum Associates Inc., Publishers

  57. Fonseca CM, Fleming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation. IEEE Trans Syst Man Cybern Part A Syst Hum 28(1):26–37

    Article  Google Scholar 

  58. Poloni C, Giurgevich A, Onesti L, Pediroda V (2000) 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 Eng 186(2–4):403–420

    Article  Google Scholar 

  59. Viennet R, Fonteix C, Marc I (1996) Multicriteria optimization using a genetic algorithm for determining a Pareto set. Int J Syst Sci 27(2):255–260. https://doi.org/10.1080/00207729608929211

    Article  MATH  Google Scholar 

  60. Pratihar DK (2013) Soft computing: fundamentals and applications. Alpha Science International Ltd, Oxford

    Google Scholar 

  61. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617

    Article  Google Scholar 

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Das, A.K., Nikum, A.K., Krishnan, S.V. et al. Multi-objective Bonobo Optimizer (MOBO): an intelligent heuristic for multi-criteria optimization. Knowl Inf Syst 62, 4407–4444 (2020). https://doi.org/10.1007/s10115-020-01503-x

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