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A niche-elimination operation based NSGA-III algorithm for many-objective optimization

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Abstract

Decomposition-based multi-objective evolutionary algorithms have been found to be very promising for many-objective optimization. The recently presented non-dominated sorting genetic algorithm III (NSGA-III) employs the decomposition idea to efficiently promote the population diversity. However, due to the low selection pressure of the Pareto-dominance relation the convergence of NSGA-III could still be improved. For this purpose, an improved NSGA-III algorithm based on niche-elimination operation (we call it NSGA-III-NE) is proposed. In the proposed algorithm, an adaptive penalty distance (APD) function is presented to consider the importance of convergence and diversity in the different stages of the evolutionary process. Moreover, the niche-elimination operation is designed by exploiting the niching technique and the worse-elimination strategy. The niching technique identifies the most crowded subregion, and the worse-elimination strategy finds and further eliminates the worst individual. The proposed NSGA-III-NE is tested on a number of well-known benchmark problems with up to fifteen objectives and shows the competitive performance compared with five state-of-the-art decomposition-based algorithms. Additionally, a vector angle based selection strategy is also proposed for handling irregular Pareto fronts.

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Notes

  1. The code of MOEA/DD is downloaded from http://www.cs.bham.ac.uk/~likw/code/MOEADD.zip.

  2. The code of 𝜃-DEA is downloaded from http://learn.tsinghua.edu.cn:8080/2012310563/ManyEAs.rar

  3. The code of NSGA-III is downloaded from http://learn.tsinghua.edu.cn:8080/2012310563/ManyEAs.rar

  4. The code of MOEA/D-DU is from http://www.cs.bham.ac.uk/~xin/journal/~papers.html http://www.cs.bham.ac.uk/xin/journal/papers.html.

  5. The code of MOEA/D-PBI is from http://dces.essex.ac.uk/staff/zhang/webofmoead.htm

References

  1. Adra SF, Fleming PJ (2011) diversity management in evolutionary many-objective optimization evolutionary computation. IEEE Trans 15:183–195. doi:10.1109/TEVC.2010.2058117

    Google Scholar 

  2. Agrawal RB, Deb K (1994) Simulated binary crossover for continuous search space complex systems, pp 115–148

  3. Asafuddoula M, Ray T, Sarker R (2013) A decomposition based evolutionary algorithm for many objective optimization with systematic sampling and adaptive epsilon control. In: Purshouse R, Fleming P, Fonseca C, Greco S, Shaw J (eds) Evolutionary multi-criterion optimization, vol 7811. Lecture notes in computer science. Springer Berlin Heidelberg. doi:10.1007/978-3-642-37140-032, pp 413–427

    Google Scholar 

  4. Asafuddoula M, Ray T, Sarker R (2015) A decomposition-based evolutionary algorithm for many objective optimization evolutionary computation. IEEE Trans 19:445–460. doi:10.1109/TEVC.2014.2339823

    Google Scholar 

  5. Bader J, Zitzler E (2011) HypE: An algorithm for fast hypervolume-based many-objective. Optim Evol Comput 19:45–76. doi:10.1162/EVCOa00009

    Article  Google Scholar 

  6. Carreno Jara E (2014) Multi-objective optimization by using evolutionary algorithms: The p-optimality criteria . IEEE Trans Evol Comput 18:167–179. doi:10.1109/TEVC.2013.2243455

    Article  Google Scholar 

  7. Cheng J, Yen GG, Zhang G (2015) A many-objective evolutionary algorithm with enhanced mating and environmental selections. IEEE Trans Evol Comput 19:592–605. doi:10.1109/TEVC.2015.2424921

    Article  Google Scholar 

  8. Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput PP:1–1. doi:10.1109/TEVC.2016.2519378

    Google Scholar 

  9. Conover WJ (1999) Practical nonparametric statistics

  10. Corne DW, Jerram NR, Knowles JD, Oates MJ, Martin J (2001) Pesa-Ii: Region-based selection in evolutionary multiobjective optimization. In: Proceedings of the genetic and evolutionary computation conference GECCO’2001

  11. Das I, Dennis JE (1998) Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8:631–657

    Article  MathSciNet  MATH  Google Scholar 

  12. Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inf 26:30–45

    Google Scholar 

  13. Deb K, Gupta S, Daum D, Branke J, Mall AK, Padmanabhan D (2009) Reliability-based optimization using evolutionary algorithms. IEEE Trans Evol Comput 13:1054–1074. doi:10.1109/TEVC.2009.2014361

    Article  Google Scholar 

  14. 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 18:577–601. doi:10.1109/TEVC.2013.2281535

    Article  Google Scholar 

  15. Deb K, Mohan M, Mishra S (2005) Evaluating the ϵ-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-Optimal Solutions. Evol Comput 13:501–525. doi:10.1162/106365605774666895

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. 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. doi:10.1007/1-84628-137-76. Springer, London, pp 105–145

    Chapter  Google Scholar 

  18. Farina M, Amato P (2004) A fuzzy definition of “optiMality” for many-criteria optimization problems. IEEE Trans Syst Man, Cybern - Part A: Syst Humans 34:315–326. doi:10.1109/TSMCA.2004.824873

    Article  Google Scholar 

  19. Fu G, Kapelan Z, Kasprzyk JR, Reed P (2013) Optimal design of water distribution systems using many-objective visual analytics. J Water Resour Plann Manag 139:624–633

    Article  Google Scholar 

  20. Garza-Fabre M, Pulido G, Coello CC (2009) Ranking methods for many-objective optimization. In: Aguirre A, Borja R, Garciá C (eds) MICAI 2009: advances in artificial intelligence, vol 5845. Lecture notes in computer science. doi:10.1007/978-3-642-05258-356. Springer, Berlin Heidelberg, pp 633–645

    Google Scholar 

  21. Hai-lin L, Fangqing G, Qingfu Z (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18:450–455. doi:10.1109/TEVC.2013.2281533

    Article  Google Scholar 

  22. He Z, Yen GG, Zhang J (2014) Fuzzy-based pareto optimality for many-objective evolutionary algorithms. IEEE Trans Evol Comput 18:269–285. doi:10.1109/TEVC.2013.2258025

    Article  Google Scholar 

  23. Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10:477–506. doi:10.1109/TEVC.2005.861417

    Article  MATH  Google Scholar 

  24. Ikeda K, Kita H, Kobayashi S (2001) Failure of Pareto-based MOEAs: Does non-dominated really mean near to optimal? 2001. Proceedings of the 2001 congress on evolutionary computation. doi:10.1109/CEC.2001.934293, vol 952, pp 957–962

  25. Ishibuchi H, Setoguchi Y, Masuda H, Nojima Y (2016) Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans Evol Comput PP:1–1. doi:10.1109/TEVC.2016.2587749

    Google Scholar 

  26. 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 18:602–622. doi:10.1109/TEVC.2013.2281534

    Article  Google Scholar 

  27. Li B, Li J, Tang K, Yao X (2015) Many-objective evolutionary algorithms: A survey. ACM Comput Surv 48:1–35. doi:10.1145/2792984

    Article  Google Scholar 

  28. Li K, Deb K, Zhang Q, Kwong S (2015) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19:694–716. doi:10.1109/TEVC.2014.2373386

    Article  Google Scholar 

  29. Li M, Yang S, Liu X (2014) Shift-based density estimation for pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18:348–365. doi:10.1109/TEVC.2013.2262178

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  31. Lygoe R, Cary M, Fleming P (2013) A real-world application of a many-objective optimisation complexity reduction process. In: Purshouse R, Fleming P, Fonseca C, Greco S, Shaw J (eds) Evolutionary multi-criterion optimization, vol 7811. Lecture notes in computer science. doi:10.1007/978-3-642-37140-048. Springer, Berlin Heidelberg, pp 641–655

    Google Scholar 

  32. Mezura-Montes E, Coello Coello CA (2011) Constraint-handling in nature-inspired numerical optimization: Past, present and future. Swarm Evol Comput 1:173–194. doi:10.1016/j.swevo.2011.10.001

    Article  Google Scholar 

  33. Mohammadi A, Omidvar MN, Li X, Deb K (2015) Sensitivity analysis of penalty-based boundary intersection on aggregation-based EMO algorithms 2015 IEEE Congress on Evolutionary Computation (CEC). doi:10.1109/CEC.2015.7257248, pp 2891–2898

    Chapter  Google Scholar 

  34. Pierro Fd, Khu ST, Savic DA (2007) An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput 11:17–45. doi:10.1109/TEVC.2006.876362

    Article  Google Scholar 

  35. Sato H, Aguirre H, Tanaka K (2007) Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T (eds) Evolutionary multi-criterion optimization, vol 4403. Lecture notes in computer science. doi:10.1007/978-3-540-70928-25. Springer, Berlin Heidelberg, pp 5–20

    Google Scholar 

  36. Trivedi A, Srinivasan D, Sanyal K, Ghosh A (2016) A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans Evol Comput PP:1–1. doi:10.1109/TEVC.2016.2608507

    Article  Google Scholar 

  37. Von Lücken C, Barán B, Brizuela C (2014) A survey on multi-objective evolutionary algorithms for many-objective problems. Comput Optim Appl 58:707–756. doi:10.1007/s10589-014-9644-1

    MathSciNet  MATH  Google Scholar 

  38. While L, Bradstreet L, Barone L (2012) A fast way of calculating exact hypervolumes. IEEE Trans Evol Comput 16:86–95. doi:10.1109/TEVC.2010.2077298

    Article  Google Scholar 

  39. Wickramasinghe UK, Carrese R, Li X (2010) Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm IEEE congress on evolutionary computation. doi:10.1109/CEC.2010.5586221, pp 1–8

    Google Scholar 

  40. Xiang Y, Yang Z, Li M, Chen Z (2016) A vector angle based evolutionary algorithm for unconstrained many-objective optimization. IEEE Trans Evol Comput PP:1–1. doi:10.1109/TEVC.2016.2587808

    Google Scholar 

  41. Yang S, Jiang S, Jiang Y (2016) Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes Soft Comput 1–15. doi:10.1007/s00500-016-2076-3

  42. Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17:721–736. doi:10.1109/TEVC.2012.2227145

    Article  Google Scholar 

  43. Yuan Y, Xu H, Wang B, Yao X (2016) A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20:16–37. doi:10.1109/TEVC.2015.2420112

    Article  Google Scholar 

  44. Yuan Y, Xu H, Wang B, Zhang B, Yao X (2016) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20:180–198. doi:10.1109/TEVC.2015.2443001

    Article  Google Scholar 

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

    Article  Google Scholar 

  46. Zhang X, Tian Y, Cheng R, Jin Y (2015) An efficient approach to nondominated sorting for evolutionary multiobjective optimization. IEEE Trans Evol Comput 19:201–213. doi:10.1109/TEVC.2014.2308305

    Article  Google Scholar 

  47. Zhang X, Tian Y, Jin Y (2015) A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 19:761–776. doi:10.1109/TEVC.2014.2378512

    Article  Google Scholar 

  48. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: Improving the strength pareto evolutionary algorithm tik, Swiss federal institute of technology ETH

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

    Article  Google Scholar 

  50. Zitzler E, Thiele L, Laumanns M, Fonseca CM, Da Fonseca VG (2003) Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans Evol Comput 7:117–132. doi:10.1109/TEVC.2003.810758

    Article  Google Scholar 

  51. Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst, Man, Cybern, Part B Cybern 38:1402–1412. doi:10.1109/TSMCB.2008.926329

    Article  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 61175126) and the International S&T Cooperation Program of China (Grant No. 2015DFG12150). The authors declare that they have no conflict of interest. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study.

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  1. College of Information and Communication Engineering, Harbin Engineering University, Harbin, 150000, People’s Republic of China

    Xiaojun Bi & Chao Wang

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Correspondence to Chao Wang.

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Bi, X., Wang, C. A niche-elimination operation based NSGA-III algorithm for many-objective optimization. Appl Intell 48, 118–141 (2018). https://doi.org/10.1007/s10489-017-0958-4

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