Soft Computing

, Volume 21, Issue 5, pp 1109–1128 | Cite as

Many-objective optimization based on information separation and neighbor punishment selection

Methodologies and Application

Abstract

Many-objective optimization refers to optimizing a multi-objective optimization problem (MOP) where the number of objectives is more than 3. Most classical evolutionary multi-objective optimization (EMO) algorithms use the Pareto dominance relation to guide the search, which usually perform poorly in the many-objective optimization scenario. This paper proposes an EMO algorithm based on information separation and neighbor punishment selection (ISNPS) to deal with many-objective optimization problems. ISNPS separates individual’s behavior in the population into convergence information and distribution information by rotating the original coordinates in the objective space. Specifically, the proposed algorithm employs one coordinate to reflect individual’s convergence and the remaining \(m-1\) coordinates to reflect individual’s distribution, where m is the number of objectives in a given MOP. In addition, a neighborhood punishment strategy is developed to prevent individuals from being crowded. From a series of experiments on 42 test instances with 3–10 objectives, ISNPS has been found to be very competitive against six representative algorithms in the EMO area.

Keywords

Evolutionary multi-objective optimization Many-objective optimization Information separation Neighbor punishment selection 

References

  1. Adra SF, Fleming PJ (2009) A diversity management operator for evolutionary many-objective optimisation. In: Evolutionary multi-criterion optimization, pp. 81–94. Springer, Nantes, France. doi:10.1007/978-3-642-01020-0_11
  2. Aguirre HE, Tanaka K (2007) Working principles, behavior, and performance of MOEAs on MNK-landscapes. Eur J Oper Res 181(3):1670–1690. doi:10.1016/j.ejor.2006.08.004 CrossRefMATHGoogle Scholar
  3. Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76. doi:10.1162/EVCO_a_00009
  4. Bentley PJ, Wakefield JP (1997) Finding acceptable Pareto-optimal solutions using multiobjective genetic algorithms. Soft Comput Eng Des Manuf 5:231–240Google Scholar
  5. Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181(3):1653–1669. doi:10.1016/j.ejor.2006.08.008 CrossRefMATHGoogle Scholar
  6. Bosman PA, Thierens D (2003) The balance between proximity and diversity in multi-objective evolutionary algorithms. IEEE Trans Evol Comput 7(2):174–188. doi:10.1109/TEVC.2003.810761 CrossRefGoogle Scholar
  7. Cheney W, Kincaid DR (2010) Linear algebra: theory and applications, 2nd edn. Jones & Bartlett Publishers. ISBN 1449613527, 9781449613525Google Scholar
  8. Coello CA, Lamont GB (2004) Applications of multi-objective evolutionary algorithms. World Scientific Publisher, SingaporeCrossRefMATHGoogle Scholar
  9. Corne DW, Knowles JD (2007) Techniques for highly multiobjective optimisation: some nondominated points are better than others. In: Genetic and evolutionary computation conference, pp. 773–780. London, England, UK. doi:10.1145/1276958.1277115
  10. 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(3):631–657. doi:10.1137/S1052623496307510 MathSciNetCrossRefMATHGoogle Scholar
  11. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley-interscience series in systems and optimization, 1st edn. Wiley, Chichester, New YorkGoogle Scholar
  12. Deb K, Agrawal RB (1994) Simulated binary crossover for continuous search space. Complex Syst 9(2):115–148MathSciNetMATHGoogle Scholar
  13. Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inform 26(4):30–45Google Scholar
  14. Deb K, Jain H (2004) An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601. doi:10.1109/TEVC.2013.2281535 CrossRefGoogle Scholar
  15. Deb K, Jain S (2002) Running performance metrics for evolutionary multi-objective optimization. Tech. Rep. Kangal Report No. 2002004, Indian Institute of TechnologyGoogle Scholar
  16. Deb K, Kumar A (1995) Real-coded genetic algorithms with simulated binary crossover: studies on multimodal and multiobjective problems. Complex Syst 9(6):431–454Google Scholar
  17. 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. doi:10.1109/4235.996017 CrossRefGoogle Scholar
  18. Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multi-objective optimization. In: Evolutionary multiobjective optimization, advanced information and knowledge processing, pp. 105–145. Springer, Berlin. doi:10.1007/1-84628-137-7_6
  19. Drechsler N, Drechsler R, Becker B (2001) Multi-objective optimisation based on relation favour. In: Evolutionary multi-criterion optimization, pp. 154–166. Springer, Berlin. doi:10.1007/3-540-44719-9_11
  20. Durillo JJ, Nebro AJ (2011) jMetal: a java framework for multi-objective optimization. Adv Eng Softw 42:760–771. doi:10.1016/j.advengsoft.2011.05.014 CrossRefGoogle Scholar
  21. Durillo JJ, Nebro AJ, Alba E (2010) The jMetal framework for multi-objective optimization: design and architecture. In: IEEE congress on evolutionary computation, pp. 4138–4325. Barcelona, Spain. doi:10.1109/CEC.2010.5586354
  22. Farina M, Amato P (2002) On the optimal solution definition for many-criteria optimization problems. In: Proceedings of the NAFIPS-FLINT international conference, pp. 233–238. IEEE Serv Center. doi:10.1109/NAFIPS.2002.1018061
  23. Farina M, Amato P (2004) A fuzzy definition of “optimality” for many-criteria optimization problems. IEEE Trans Syst Man Cybern Part A: Syst Hum 34(3):315–326. doi:10.1109/TSMCA.2004.824873 CrossRefGoogle Scholar
  24. Glaser RE (1983) Levene’s robust test of homogeneity of variances. Encycl Stat Sci 4:608–610Google Scholar
  25. Gómez RH, Coello CA (2013) MOMBI: a new metaheuristic for many-objective optimization based on the R2 indicator. In: IEEE congress on evolutionary computation, pp. 2488–2495. Cancun. doi:10.1109/CEC.2013.6557868
  26. 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(5):477–506. doi:10.1109/TEVC.2005.861417 CrossRefMATHGoogle Scholar
  27. Hughes EJ (2003) Multiple single objective Pareto sampling. In: IEEE congress on evolutionary computation, vol. 4, pp. 2678–2684. IEEE, Canberra, Australia. doi:10.1109/CEC.2003.1299427
  28. Hughes EJ (2005) Evolutionary many-objective optimisation: many once or one many? In: IEEE congress on evolutionary computation, vol. 1, pp. 222–227. IEEE Press. doi:10.1109/CEC.2005.1554688
  29. Ikeda K, Kita H (2001) Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? IEEE Congr Evol Comput 2:957–962. doi:10.1109/CEC.2001.934293 Google Scholar
  30. Inselberg A (1985) The plane with parallel coordinates. Vis Comput 1(4):69–91. doi:10.1007/BF01898350 MathSciNetCrossRefMATHGoogle Scholar
  31. Inselberg A, Dimsdale B (1990) Parallel coordinates: a tool for visualizing multi-dimensional geometry. In: IEEE conference on visualization, pp. 361–378. IEEE Computer Society Press. doi:10.1109/VISUAL.1990.146402
  32. Ishibuchi H, Sakane Y, Tsukamoto N, Nojima Y (2009) Evolutionary many-objective optimization by NSGA-II and MOEA/D with large populations. In: IEEE International Conference on Systems, Man, and Cybernetics, pp. 1820–1825. San Antonio, USA. doi:10.1109/ICSMC.2009.5346628
  33. Ishibuchi H, Tsukamoto N, Hitotsuyanagi Y, Nojima Y (2008) Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems. In: Annual conference on genetic and evolutionary computation, pp. 649–656. ACM, New York, USA. doi:10.1145/1389095.1389225
  34. Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: A short review. In: IEEE congress on evolutionary computation, pp. 2424–2431. doi:10.1109/CEC.2008.4631121
  35. Jaimes AL, Quintero LVS, Coello CA (2009) Ranking methods in many-objective evolutionary algorithms. In: Nature-inspired algorithms for optimisation, pp. 413–434. Springer, BerlinGoogle Scholar
  36. Knowles JD, Corne DW (2007) Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In: Evolutionary multi-criterion optimization, pp. 757–771. Springer, Berlin. doi:10.1007/978-3-540-70928-2_57
  37. Köppen M, Yoshida K (2007) Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Evolutionary multi-criterion optimization, pp. 727–741. doi:10.1007/978-3-540-70928-2_55
  38. Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multi-objective optimization. Evol Comput 10(3):263–282. doi:10.1162/106365602760234108 CrossRefGoogle Scholar
  39. Li M, Yang S, Liu X (2014) Diversity comparison of Pareto front approximations in many-objective optimization. IEEE Trans Cybern 44(12):2568–2584. doi:10.1109/TCYB.2014.2310651
  40. 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. doi:10.1109/TEVC.2013.2262178 CrossRefGoogle Scholar
  41. Li M, Yang S, Liu X, Shen R (2013) A comparative study on evolutionary algorithms for many-objective optimization. In: Evolutionary multi-criterion optimization, lecture notes in computer science, pp. 261–275. Sheffield, UK. doi:10.1007/978-3-642-37140-0_22
  42. Li M, Zheng J, Li K, Yuan Q, Shen R (2010) Enhancing diversity for average ranking method in evolutionary many-objective optimization. In: Parallel problem solving from nature, pp. 647–656. Springer, Berlin. doi:10.1007/978-3-642-15844-5_65
  43. Li M, Zheng J, Shen R, Li K, Yuan Q (2010) A grid-based fitness strategy for evolutionary many-objective optimization. In: Genetic and evolutionary computation conference, pp. 463–470. ACM. doi:10.1145/1830483.1830570
  44. Miller BL, Goldberg DE (1995) Genetic algorithms, tournament selection, and the effects of noise. Complex Syst 9:193–212MathSciNetGoogle Scholar
  45. Miller RGJ (1981) Simultaneous statistical inference, 2nd edn. Springer, New YorkCrossRefMATHGoogle Scholar
  46. Mostaghim S, Schmeck H (2008) Distance based ranking in many-objective particle swarm optimization.In: Parallel problem solving from nature, pp. 753–762. Springer, Berlin. doi:10.1007/978-3-540-87700-4_75
  47. Phan DH, Suzuki J (2013) R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization. In: IEEE congress on evolutionary computation, pp. 1836–1845. IEEE, Cancun, Mexico. doi:10.1109/CEC.2013.6557783
  48. Phan DH, Suzuki J, Hayashi I (2011) BIBEA: boosted indicator based evolutionary algorithm for multiobjective optimization. In: Asia pacific symposium of intelligent and evolutionary systems. Yokosuka, JapanGoogle Scholar
  49. di Pierro F (2006) Many-objective evolutionary algorithms and applications to water resources engineering. Ph.d. thesis, school of engineering, computer science and mathematics, University of Exeter, UKGoogle Scholar
  50. di Pierro F, Khu ST, Savić DA (2007) An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput 11(1):17–45. doi:10.1109/TEVC.2006.876362 CrossRefGoogle Scholar
  51. Purshouse RC, Fleming PJ (2003) Evolutionary many-objective optimization: an exploratory analysis. IEEE Congr Evol Comput 3:2066–2073. doi:10.1109/CEC.2003.1299927
  52. Purshouse RC, Fleming PJ (2007) On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput 11(6):770–784. doi:10.1109/TEVC.2007.910138 CrossRefGoogle Scholar
  53. Rice J (1995) Mathematical statistics and data analysis. Duxbury PressGoogle Scholar
  54. Rudolph G, Trautmann H, Sengupta S, Schütze O (2013) Evenly spaced Pareto front approximations for tricriteria problems based on triangulation. In: Evolutionary multi-criterion optimization, pp. 443–458. Springer, Sheffield, UK. doi:10.1007/978-3-642-37140-0_34
  55. Sato H, Aguirre HE, Tanaka K (2007) Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Evolutionary multi-criterion optimization, pp. 5–20. Springer, Berlin. doi:10.1007/978-3-540-70928-2_5
  56. Tamhane AC (1977) Multiple comparisons in model I one-way ANOVA with unequal variances. Commun Stat 6(1):15–32. doi:10.1080/03610927708827466
  57. Veldhuizen DAV, Lamont GB (1998) Evolutionary computation and convergence to a Pareto front. In: Late breaking papers at the genetic programming 1998 conference, pp. 221–228. Stanford University Bookstore, University of Wisconsin, Madison, Wisconsin, USAGoogle Scholar
  58. Wagner T, Beume N, Naujoks B (2007) Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Evolutionary multi-criterion optimization, pp. 742–756. Springer, Berlin. doi:10.1007/978-3-540-70928-2_56
  59. Wegman EJ (1990) Hyperdimensional data analysis using parallel coordinates. J Am Stat Assoc 85:664–675CrossRefGoogle Scholar
  60. Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721–736. doi:10.1109/TEVC.2012.2227145 CrossRefGoogle Scholar
  61. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731. doi:10.1109/TEVC.2007.892759 MathSciNetCrossRefGoogle Scholar
  62. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.d. thesis, Eidgenössische Technische Hochschule Zürich. Swiss Federal Institute of TechnologyGoogle Scholar
  63. Zitzler E, Künzli S (2004 Indicator-based selection in multiobjective search. In: Parallel problem solving from nature, pp. 832–842. Springer, Berlin. doi:10.1007/978-3-540-30217-9_84
  64. Zitzler E, Laumanns M, Thiele L (2002) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. Evolutionary methods for design., optimisation, and controlCIMNE, Barcelona, Spain, pp 95–100Google Scholar
  65. Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Parallel problem solving from nature, pp. 292–301. Springer, Berlin. doi:10.1007/BFb0056872
  66. 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. doi:10.1109/4235.797969 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ruimin Shen
    • 1
  • Jinhua  Zheng
    • 2
    • 3
  • Miqing Li
    • 2
    • 4
  • Juan Zou
    • 2
  1. 1.School of Mathematics and Computational ScienceXiangtan UniversityXiangtanChina
  2. 2.Department of Xiangtan UniversityInstitute of Information EngineeringXiangtanChina
  3. 3.Key Laboratory of Intelligent Computing and Information Processing(Xiangtan University) Ministry of EducationXiangtanChina
  4. 4.Department of Information Systems and ComputingBrunel UniversityUxbridgeUnited Kingdom

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