Soft Computing

, Volume 22, Issue 7, pp 2139–2158 | Cite as

Adaptive racing ranking-based immune optimization approach solving multi-objective expected value programming

Methodologies and Application
  • 176 Downloads

Abstract

This work investigates a bio-inspired adaptive sampling immune optimization approach to solve a general kind of nonlinear multi-objective expected value programming without any prior noise distribution. A useful lower bound estimate is first developed to restrict the sample sizes of random variables. Second, an adaptive racing ranking scheme is designed to identify those valuable individuals in the current population, by which high-quality individuals in the process of solution search can acquire large sample sizes and high importance levels. Thereafter, an immune-inspired optimization approach is constructed to seek \(\varepsilon \)-Pareto optimal solutions, depending on a novel polymerization degree model. Comparative experiments have validated that the proposed approach with high efficiency is a competitive optimizer.

Keywords

Immune optimization Multi-objective expected value programming Sample bound estimate Adaptive racing ranking Computational complexity 

Notes

Acknowledgements

This work is supported by National Natural Science Foundation NSFC (61563009).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Aickelin U, Dasgupta D, Gu F (2014) Artificial immune systems. Search Methodologies. Springer US, pp 187–211Google Scholar
  2. Aydin I, Karakose M, Akin E (2011) A multi-objective artificial immune approach for parameter optimization in support vector machine. Appl Soft Comput 11:120–129CrossRefGoogle Scholar
  3. Batista LS, Campelo F, Guimarães FG et al (2011) Pareto cone \(\varepsilon \)-dominance: improving convergence and diversity in multiobjective evolutionary approaches. In: Evolutionary multi-criterion optimization, Springer, Berlin, pp 76–90Google Scholar
  4. Bui LT et al (2005) Fitness inheritance for noisy evolutionary multi-objective optimization. In: The 7th annual conference on genetic and evolutionary computation, ACM, pp 779–785Google Scholar
  5. Cantú-Paz E (2004) Adaptive sampling for noisy problems. In: Genetic and evolutionary computation conference, GECCO2004, pp 947–958Google Scholar
  6. Chen CH (2003) Efficient sampling for simulation-based optimization under uncertainty. In: Fourth International symposium on uncertainty modeling and analysis, ISUMA’03, pp 386–391Google Scholar
  7. Coello CAC, Cortés NC (2005) Solving multi-objective optimization problems using an artificial immune system. Genet Program Evol Mach 6:163–190CrossRefGoogle Scholar
  8. Corne DW, Jerram NR, Knowles JD et al (2001) PESA-II: region-based selection in evolutionary multiobjective optimization. In: Genetic and evolutionary computation conference, GECCO’2001, pp 283–290Google Scholar
  9. Deb K et al (2002) A fast and elitist multi-objective genetic approach: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  10. Drugan MM, Nowe A (2013) Designing multi-objective multi-armed bandits approaches: a study. In: International joint conference on neural networks, IJCNN, pp 1–8Google Scholar
  11. El-Wahed WFA, Lee SM (2006) Interactive fuzzy goal programming for multi-objective transportation problems. Omega 34(2):158–166CrossRefGoogle Scholar
  12. Eskandari H, Geiger CD (2009) Evolutionary multi-objective optimization in noisy problem environments. J Heuristics 15:559–595CrossRefMATHGoogle Scholar
  13. Even-Dar E, Mannor S, Mansour Y (2006) Action elimination and stopping conditions for the multi-armed bandit and reinforcement learning problems. J Mach Learn Res 7:1079–1105MathSciNetMATHGoogle Scholar
  14. Gong MG, Jiao LC, Du HF, Bo LF (2008) Multi-objective immune approach with nondominated neighbor-based selection. Evol Comput 16:225–255CrossRefGoogle Scholar
  15. Gong MG et al (2013) Identification of multi-resolution network structures with multi-objective immune approach. Appl Soft Comput 13:1705–1717CrossRefGoogle Scholar
  16. Gutjahr WJ, Pichler A (2016) Stochastic multi-objective optimization: a survey on non-scalarizing methods. Ann Oper Res 236:475–499MathSciNetCrossRefMATHGoogle Scholar
  17. Higle JL, Zhao L (2004) Adaptive and nonadaptive samples in solving stochastic linear programs: a computational investigation. The University of Arizona, TucsonMATHGoogle Scholar
  18. Hoeffding W (1963) Probability inequalities for sums of bounded random variables. J Am Stat Assoc 58(301):13–30MathSciNetCrossRefMATHGoogle Scholar
  19. Hu ZH (2010) A multiobjective immune approach based on a multiple-affinity model. Eur J Oper Res 202:60–72CrossRefMATHGoogle Scholar
  20. Hughes EJ (2001) Constraint handling with uncertain and noisy multi-objective evolution. In: Congress on evolutionary computation 2001, CEC’2001, pp 963–970Google Scholar
  21. Jin Y, Branke J (2005) Evolutionary optimization in uncertain environments: a survey. IEEE Trans Evol Comput 9:303–317CrossRefGoogle Scholar
  22. Lee LH et al (2010) Finding the nondominated Pareto set for multi-objective simulation models. IIE Trans 42:656–674CrossRefGoogle Scholar
  23. Lee LH, Pujowidianto NA, Li LW et al (2012) Approximate simulation budget allocation for selecting the best design in the presence of stochastic constraints. IEEE Trans Autom Control 57:2940–2945MathSciNetCrossRefMATHGoogle Scholar
  24. Lin Q, Chen J (2013) A novel micro-population immune multi-objective optimization approach. Comput Oper Res 40:1590–1601MathSciNetCrossRefMATHGoogle Scholar
  25. Liu B (2009) Theory and practice of uncertain programming. Physica, HeidelbergCrossRefMATHGoogle Scholar
  26. Marler RT, Arora JS (2010) The weighted sum method for multi-objective optimization: new insights. Struct Multidiscip Optim 41(6):853–862MathSciNetCrossRefMATHGoogle Scholar
  27. Owen J, Punt J, Stranford S (2013) Kuby immunology, 7th edn. Freeman, New YorkGoogle Scholar
  28. Park T, Ryu KR (2011) Accumulative sampling for noisy evolutionary multi-objective optimization. In: the 13th annual conference on Genetic and evolutionary computation, ACM, pp 793–800Google Scholar
  29. Phan DH, Suzuki J (2012) A non-parametric statistical dominance operator for noisy multi-objective optimization. In: Simulated evolution and learning, SEAL’12, pp 42–51Google Scholar
  30. Qi Y, Liu F, Liu M et al (2012) Multi-objective immune approach with Baldwinian learning. Appl Soft Comput 12:2654–2674CrossRefGoogle Scholar
  31. Qi Y, Hou Z, Yin M et al (2015) An immune multi-objective optimization approach with differential evolution inspired recombination. Appl Soft Comput 29:395–410CrossRefGoogle Scholar
  32. Robert C, Casella G (2013) Monte Carlo statistical methods. Springer, BerlinMATHGoogle Scholar
  33. Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on stochastic programming: modeling and theory. SIAM-MPS PhiladelphiaGoogle Scholar
  34. Tan KC, Lee TH, Khor EF (2001) Evolutionary approaches with dynamic population size and local exploration for multiobjective optimization. IEEE Trans Evol Comput 5:565–588CrossRefGoogle Scholar
  35. Tan KC, Goh CK, Mamun AA et al (2008) An evolutionary artificial immune system for multi-objective optimization. Eur J Oper Res 187:371–392MathSciNetCrossRefMATHGoogle Scholar
  36. Trautmann H, Mehnen J, Naujoks B (2009) Pareto-dominance in noisy environments. In IEEE congress on evolutionary computation(CEC’09), pp 3119–3126Google Scholar
  37. Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph. D. Thesis, OH: Air force Institute of Technology, Technical Report No. AFIT/DS/ENG/99-01, DaytonGoogle Scholar
  38. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731CrossRefGoogle Scholar
  39. Zhang ZH, Tu X (2007a) Immune approach with adaptive sampling in noisy environments and its application to stochastic optimization problems. IEEE Comput Intell Mag 2:29–40CrossRefGoogle Scholar
  40. Zhang ZH, Tu X (2007b) Probabilistic dominance-based multi-objective immune optimization approach in noisy environments. J Comput Theor Nanosci 4:1380–1387CrossRefGoogle Scholar
  41. Zhang ZH, Wang L, Liao M (2013a) Adaptive sampling immune approach solving joint chance-constrained programming. J Control Theory Appl 11:237–246MathSciNetCrossRefMATHGoogle Scholar
  42. Zhang ZH, Wang L, Long F (2013b) Immune optimization approach solving multi-objective chance constrained programming. Evol Syst 6:41–53CrossRefGoogle Scholar
  43. Zhang W, Xu W, Liu G, et al (2015) An effective hybrid evolutionary approach for stochastic multiobjective assembly line balancing problem. J Intell Manuf 1–8. doi: 10.1007/s10845-015-1037-5
  44. Zheng JH et al (2004) A multi-objective genetic approach based on quick sort. Advances in Artificial Intelligence. Springer, BerlinGoogle Scholar
  45. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary approaches: empirical results. Evol Comput 8:173–195CrossRefGoogle Scholar
  46. Zitzler E, Thiele L (1999) Multi-objective evolutionary approaches: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3:257–271CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Computer Science & TechnologyGuizhou UniversityGuiyangChina
  2. 2.Department of Big Data Science and Engineering, College of Big Data and Information EngineeringGuizhou UniversityGuiyangChina

Personalised recommendations