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Evolutionary Many-Objective Algorithms for Combinatorial Optimization Problems: A Comparative Study

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Abstract

Many optimization problems encountered in the real-world have more than two objectives. To address such optimization problems, a number of evolutionary many-objective optimization algorithms were developed recently. In this paper, we tested 18 evolutionary many-objective algorithms against well-known combinatorial optimization problems, including knapsack problem (MOKP), traveling salesman problem (MOTSP), and quadratic assignment problem (mQAP), all up to 10 objectives. Results show that some of the dominance and reference-based algorithms such as non-dominated sort genetic algorithm (NSGA-III), strength Pareto-based evolutionary algorithm based on reference direction (SPEA/R), and Grid-based evolutionary algorithm (GrEA) are promising algorithms to tackle MOKP and MOTSP with 5 and 10 while increasing the number of objectives. Also, the dominance-based algorithms such as MaOEA-DDFC as well as the indicator-based algorithms such as HypE are promising to solve mQAP with 5 and 10 objectives. In contrast, decomposition based algorithms present the best on almost problems at saving time. For example, t-DEA displayed superior performance on MOTSP for up to 10 objectives.

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References

  1. Tian Y et al (2018) An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evol Comput 22(4):609–622

    Google Scholar 

  2. He C et al (2017) A radial space division based evolutionary algorithm for many-objective optimization. Appl Soft Comput 61:603–621

    Google Scholar 

  3. Li T, Li J (2018) Using modified determinantal point process sampling to update population. In: 2018 IEEE congress on evolutionary computation (CEC). IEEE

  4. Deb K (2014) Multi-objective optimization. Search methodologies. Springer, Berlin, pp 403–449

    Google Scholar 

  5. Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscipl Optim 26(6):369–395

    MathSciNet  MATH  Google Scholar 

  6. Caramia M, Dell’Olmo P (2008) Multi-objective optimization. Springer, Berlin

    MATH  Google Scholar 

  7. Coello CAC, Lamont GB, Van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems, vol 5. Springer, Berlin

    MATH  Google Scholar 

  8. Deb K (2001) Multi objective optimization using evolutionary algorithms. Wiley, New York

    MATH  Google Scholar 

  9. 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

    Google Scholar 

  10. Gul S et al (2011) Bi-criteria scheduling of surgical services for an outpatient procedure center. Prod Oper Manag 20(3):406–417

    Google Scholar 

  11. Minella G, Ruiz R, Ciavotta M (2008) A review and evaluation of multiobjective algorithms for the flowshop scheduling problem. INFORMS J Comput 20(3):451–471

    MathSciNet  MATH  Google Scholar 

  12. Wang H (2012) Zigzag search for continuous multiobjective optimization. INFORMS J Comput 25(4):654–665

    MathSciNet  Google Scholar 

  13. Loganathan G, Sherali HD (1987) A convergent interactive cutting-plane algorithm for multiobjective optimization. Oper Res 35(3):365–377

    MathSciNet  MATH  Google Scholar 

  14. Erlebach T, Kellerer H, Pferschy U (2002) Approximating multiobjective knapsack problems. Manag Sci 48(12):1603–1612

    MATH  Google Scholar 

  15. Sourd F, Spanjaard O (2008) A multiobjective branch-and-bound framework: application to the biobjective spanning tree problem. INFORMS J Comput 20(3):472–484

    MathSciNet  MATH  Google Scholar 

  16. Stidsen T, Andersen KA, Dammann B (2014) A branch and bound algorithm for a class of biobjective mixed integer programs. Manag Sci 60(4):1009–1032

    Google Scholar 

  17. Jozefowiez N, Laporte G, Semet F (2012) A generic branch-and-cut algorithm for multiobjective optimization problems: application to the multilabel traveling salesman problem. INFORMS J Comput 24(4):554–564

    MathSciNet  MATH  Google Scholar 

  18. Köksalan M, Phelps S (2007) An evolutionary metaheuristic for approximating preference-nondominated solutions. INFORMS J Comput 19(2):291–301

    MathSciNet  MATH  Google Scholar 

  19. Müller J (2017) SOCEMO: surrogate optimization of computationally expensive multiobjective problems. INFORMS J Comput 29(4):581–596

    MathSciNet  MATH  Google Scholar 

  20. Mete HO, Zabinsky ZB (2014) Multiobjective interacting particle algorithm for global optimization. INFORMS J Comput 26(3):500–513

    MathSciNet  MATH  Google Scholar 

  21. Phelps S, Köksalan M (2003) An interactive evolutionary metaheuristic for multiobjective combinatorial optimization. Manag Sci 49(12):1726–1738

    MATH  Google Scholar 

  22. Rauner MS et al (2010) Dynamic policy modeling for chronic diseases: metaheuristic-based identification of pareto-optimal screening strategies. Oper Res 58(5):1269–1286

    MathSciNet  MATH  Google Scholar 

  23. Dentcheva D, Wolfhagen E (2016) Two-stage optimization problems with multivariate stochastic order constraints. Math Oper Res 41(1):1–22

    MathSciNet  MATH  Google Scholar 

  24. Masin M, Bukchin Y (2008) Diversity maximization approach for multiobjective optimization. Oper Res 56(2):411–424

    MathSciNet  MATH  Google Scholar 

  25. Herrmann JW, Lee CY, Hinchman J (1995) Global job shop scheduling with a genetic algorithm. Prod Oper Manag 4(1):30–45

    Google Scholar 

  26. Halim AH, Ismail I (2019) Combinatorial optimization: comparison of heuristic algorithms in travelling salesman problem. Arch Comput Methods Eng 26(2):367–380

    MathSciNet  Google Scholar 

  27. Tang Z, Hu X, Périaux J (2019) Multi-level hybridized optimization methods coupling local search deterministic and global search evolutionary algorithms. Arch Comput Methods Eng 2019:1–37

    Google Scholar 

  28. Zabinsky ZB (2013) Stochastic adaptive search for global optimization, vol 72. Springer, Berlin

    MATH  Google Scholar 

  29. Zabinsky ZB (2010) Random search algorithms. Wiley Encyclopedia of Operations Research and Management Science, New York

    Google Scholar 

  30. Liu L et al (2018) A new multi-objective evolutionary algorithm for inter-cloud service composition. KSII Trans Internet Inf Syst 12(1):1–20

    Google Scholar 

  31. Yuan S et al (2017) Multi-objective evolutionary algorithm based on decomposition for energy-aware scheduling in heterogeneous computing systems. J Univers Comput Sci 23(7):636–651

    Google Scholar 

  32. Mohammadi S, Monfared M, Bashiri M (2017) An improved evolutionary algorithm for handling many-objective optimization problems. Appl Soft Comput 52:1239–1252

    Google Scholar 

  33. Ishibuchi H, Akedo N, Nojima Y (2015) Behavior of multiobjective evolutionary algorithms on many-objective knapsack problems. IEEE Trans Evol Comput 19(2):264–283

    Google Scholar 

  34. Lust T, Teghem J (2010) The multiobjective traveling salesman problem: a survey and a new approach. In: Advances in multi-objective nature inspired computing. Springer, pp 119–141

  35. Knowles J, Corne D (2003) Instance generators and test suites for the multiobjective quadratic assignment problem. In: International conference on evolutionary multi-criterion optimization. Springer

  36. Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76

    Google Scholar 

  37. Wang R, Purshouse RC, Fleming PJ (2013) Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Trans Evol Comput 17(4):474–494

    Google Scholar 

  38. Yang S et al (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721–736

    Google Scholar 

  39. Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Google Scholar 

  40. Jain H, Deb K (2014) An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18(4):602–622

    Google Scholar 

  41. Li M, Yang S, Liu X (2014) Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18(3):348–365

    Google Scholar 

  42. Li M, Yang S, Liu X (2015) Bi-goal evolution for many-objective optimization problems. Artif Intell 228:45–65

    MathSciNet  MATH  Google Scholar 

  43. Yuan Y et al (2016) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20(2):180–198

    Google Scholar 

  44. Asafuddoula M, Ray T, Sarker R (2015) A decomposition-based evolutionary algorithm for many objective optimization. IEEE Trans Evol Comput 19(3):445–460

    Google Scholar 

  45. Zhang X, Tian Y, Jin Y (2015) A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 19(6):761–776

    Google Scholar 

  46. Cheng J, Yen GG, Zhang G (2015) A many-objective evolutionary algorithm with enhanced mating and environmental selections. IEEE Trans Evol Comput 19(4):592–605

    Google Scholar 

  47. Li K et al (2014) Combining dominance and decomposition in evolutionary many-objective optimization. IEEE Trans Evol Comput 99:1–23

    Google Scholar 

  48. Hernández Gómez R, Coello Coello CA (2015) Improved metaheuristic based on the R2 indicator for many-objective optimization. In: Proceedings of the 2015 annual conference on genetic and evolutionary computation. ACM

  49. He Z, Yen GG (2016) Many-objective evolutionary algorithm: objective space reduction and diversity improvement. IEEE Trans Evol Comput 20(1):145–160

    Google Scholar 

  50. Cheng R et al (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20(5):773–791

    Google Scholar 

  51. 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

    Google Scholar 

  52. Yuan Y et al (2016) A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20(1):16–37

    Google Scholar 

  53. Liu H-L, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455

    Google Scholar 

  54. Tanabe R, Ishibuchi H, Oyama AJIA (2017) Benchmarking multi-and many-objective evolutionary algorithms under two optimization scenarios. IEEE Access 5:19597–19619

    Google Scholar 

  55. Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Google Scholar 

  56. Tian Y et al (2017) PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag 12(4):73–87

    Google Scholar 

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Acknowledgements

Authors would like to thank Prof. Jürgen Branke (Warwick Business School) for his valuable comments and helps.

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Authors and Affiliations

  1. Department of Accounting, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

    Reza Behmanesh

  2. Young Researchers and Elite Club, Islamic Azad University, Isfahan, Iran

    Iman Rahimi

  3. Faculty of Engineering & Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia

    Amir H. Gandomi

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  1. Reza Behmanesh
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  2. Iman Rahimi
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  3. Amir H. Gandomi
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Correspondence to Amir H. Gandomi.

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Behmanesh, R., Rahimi, I. & Gandomi, A.H. Evolutionary Many-Objective Algorithms for Combinatorial Optimization Problems: A Comparative Study. Arch Computat Methods Eng 28, 673–688 (2021). https://doi.org/10.1007/s11831-020-09415-3

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