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Prediction in Nature-Inspired Dynamic Optimization

  • Almuth MeierEmail author
  • Oliver KramerEmail author
Chapter
  • 18 Downloads
Part of the Springer Tracts in Nature-Inspired Computing book series (STNIC)

Abstract

In dynamic black-box optimization, time-varying objective functions are optimized. Nature-inspired optimization algorithms like evolution strategies and swarm optimization algorithms are common choices for solving dynamic optimization problems. In real-world scenarios, objective functions often change in the course of the optimization process. Frequently, their change is not random, but certain time-depending characteristics and relationships exist. Algorithms exploiting such information are often superior to naive variants based on random restarts. Predicting the moving optimum based on previous information and incorporating the predictions into the optimization process are a strategy that has attained attention in the recent past. In this chapter, we introduce the foundations of prediction-based dynamic optimization with nature-inspired methods. We present benchmark sets and quality measures and give insight into mechanisms to employ predictions into evolution strategy and particle swarm optimization-based search. Further, we show how predictive uncertainty information allows the optimizer to explore regions with higher predictive uncertainty more extensively.

Keywords

Dynamic optimization Prediction Evolution strategies Particle swarm optimization Predictive uncertainty 

References

  1. 1.
    Bai S, Kolter JZ, Koltun V (2018) An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. CoRR abs/1803.01271Google Scholar
  2. 2.
    Ben-Romdhane H, Alba E, Krichen S (2013) Best practices in measuring algorithm performance for dynamic optimization problems. Soft Comput 17(6):1005–1017CrossRefGoogle Scholar
  3. 3.
    Beyer H-G, Schwefel H-P (2002) Evolution strategies—a comprehensive introduction. Nat Comput 1(1):3–52MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bishop CM (2007) Pattern recognition and machine learning. Information science and statistics. Springer, BerlinGoogle Scholar
  5. 5.
    Bosman PAN (2005). Learning, anticipation and time-deception in evolutionary online dynamic optimization. In: Genetic and Evolutionary Computation (GECCO) Workshop Proceedings, pp 39–47Google Scholar
  6. 6.
    Bosman PAN, La Poutré H (2007) Learning and anticipation in online dynamic optimization with evolutionary algorithms: the stochastic case. In: Genetic and evolutionary computation (GECCO), pp 1165–1172Google Scholar
  7. 7.
    Branke J (1999) Memory enhanced evolutionary algorithms for changing optimization problems. In: Congress on evolutionary computation (CEC), pp 1875–1882Google Scholar
  8. 8.
    Bu C, Luo W, Zhu T, Yue L (2017) Solving online dynamic time-linkage problems under unreliable prediction. Appl Soft Comput 56:702–716CrossRefGoogle Scholar
  9. 9.
    Cheng H, Yang S (2013) Genetic algorithms for dynamic routing problems in mobile ad hoc networks. Springer, Berlin, pp 343–375Google Scholar
  10. 10.
    Cruz C, González JR, Pelta DA (2011) Optimization in dynamic environments: a survey on problems, methods and measures. Soft Comput 15(7):1427–1448CrossRefGoogle Scholar
  11. 11.
    Fu X, Sun J (2017) A new learning based dynamic multi-objective optimisation evolutionary algorithm. In: Congress on evolutionary computation (CEC), pp 341–348Google Scholar
  12. 12.
    Gal Y (2016) Uncertainty in Deep Learning. PhD thesis, University of CambridgeGoogle Scholar
  13. 13.
    Grefenstette JJ (1992) Genetic algorithms for changing environments. In: Parallel problem solving from nature (PPSN), pp 139–146Google Scholar
  14. 14.
    Gupta N, Khosravy M, Patel N, Sethi IK (2018) Evolutionary optimization based on biological evolution in plants. Proc Comput Sci 126:146–155CrossRefGoogle Scholar
  15. 15.
    Gupta N, Patel N, Tiwari B, Khosravy M (2018) Genetic algorithm based on enhanced selection and log-scaled mutation technique. In: Proceedings of the future technologies conference. Springer, Berlin, pp 1942–1948Google Scholar
  16. 16.
    Hastie T, Tibshirani R, Friedman JH (2009) The elements of statistical learning: data mining, inference, and prediction. Springer, BerlinCrossRefGoogle Scholar
  17. 17.
    Hatzakis I, Wallace D (2006) Dynamic multi-objective optimization with evolutionary algorithms: a forward-looking approach. In: Genetic and evolutionary computation conference (GECCO), pp 1201–1208Google Scholar
  18. 18.
    Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780CrossRefGoogle Scholar
  19. 19.
    Hu X, Eberhart RC (2002) Adaptive particle swarm optimization: detection and response to dynamic systems. In: Congress on evolutionary computation (CEC), pp 1666–1670Google Scholar
  20. 20.
    Hyndman RJ, Athanasopoulos G (2013) Forecasting: principles and practice. OTexts: Melbourne, Australia, 2013. Accessed on 03 June 2019Google Scholar
  21. 21.
    James G, Witten D, Hastie T, Tibshirani R (2013) An introduction to statistical learning with applications in R. Springer, BerlinCrossRefGoogle Scholar
  22. 22.
    Jin Y, Yang C, Ding J, Chai T (2016) Reference point based prediction for evolutionary dynamic multiobjective optimization. In: Congress on evolutionary computation (CEC), pp 3769–3776Google Scholar
  23. 23.
    Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82(1):35–45MathSciNetCrossRefGoogle Scholar
  24. 24.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: International conference on neural networks (ICNN), pp 1942–1948Google Scholar
  25. 25.
    Kramer O (2016) Machine learning for evolution strategies. Springer, BerlinCrossRefGoogle Scholar
  26. 26.
    Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In: Advances in neural information processing systems (NeurIPS), pp 1106–1114Google Scholar
  27. 27.
    Li C, Mavrovouniotis M, Yang S, Yao X (2013) Benchmark generator for the IEEE WCCI-2014 competition on evolutionary computation for dynamic optimization problems: dynamic rotation peak benchmark generator (DRPBG) and dynamic composition benchmark generator (DCBG). Technical report, De Montfort UniversityGoogle Scholar
  28. 28.
    Li C, Nguyen TT, Zeng S, Yang M, Wu M (2018) An open framework for constructing continuous optimization problems. IEEE Trans Cybern pp 1–15Google Scholar
  29. 29.
    Li C, Yang S, Nguyen TT, Yu E, Yao X, Jin Y, Beyer H-G, Suganthan PN (2008) Benchmark generator for CEC 2009 competition on dynamic optimization. Technical report, University of LeicesterGoogle Scholar
  30. 30.
    Li C, Yang S, Pelta DA (2011) Benchmark generator for the IEEE WCCI-2012 competition on evolutionary computation for dynamic optimization problems. Technical report, Brunel UniversityGoogle Scholar
  31. 31.
    Meier A, Kramer O (2018) Prediction with recurrent neural networks in evolutionary dynamic optimization. In: Applications of evolutionary computation (EvoAPPS), pp 848–863Google Scholar
  32. 32.
    Meier A, Kramer O (2018) Recurrent neural network-predictions for PSO in dynamic optimization. In: Genetic and evolutionary computation conference (GECCO), pp 29–36Google Scholar
  33. 33.
    Meier A, Kramer O (2019) Predictive uncertainty estimation with temporal convolutional networks for dynamic evolutionary optimization. In: International conference on neural networks (ICANN). Springer, pp 409–421Google Scholar
  34. 34.
    Morrison RW, De Jong KA (1999) A test problem generator for non-stationary environments. In: Congress on evolutionary computation (CEC), pp 2047–2053Google Scholar
  35. 35.
    Moser I, Chiong R (2013) Dynamic function optimization: the moving peaks benchmark. In: Metaheuristics for dynamic optimization. Springer, Berlin, pp 35–59Google Scholar
  36. 36.
    Muruganantham A, Tan KC, Vadakkepat P (2016) Evolutionary dynamic multiobjective optimization via Kalman filter prediction. Trans Cybern 46(12):2862–2873CrossRefGoogle Scholar
  37. 37.
    Neumaier A, Schneider T (2001) Estimation of parameters and eigenmodes of multivariate autoregressive models. Trans Math Software (TOMS) 27(1):27–57CrossRefGoogle Scholar
  38. 38.
    Nguyen TT (2011) Continuous dynamic optimization using evolutionary algorithms. PhD thesis, University of BirminghamGoogle Scholar
  39. 39.
    Nguyen TT, Yang S, Branke J (2012) Evolutionary dynamic optimization: a survey of the state of the art. Swarm Evol Comput 6:1–24CrossRefGoogle Scholar
  40. 40.
    Nguyen TT, Yao X (2009) Benchmarking and solving dynamic constrained problems. In: Congress on evolutionary computation (CEC), pp 690–697Google Scholar
  41. 41.
    Nguyen TT, Yao X (2009) Dynamic time-linkage problems revisited. In: Applications of evolutionary computing. Springer, Berlin, pp 735–744Google Scholar
  42. 42.
    Rechenberg I (1973) Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzbog, StuttgartGoogle Scholar
  43. 43.
    Rojas R (1996) Neural networks: a systematic introduction. Springer, BerlinCrossRefGoogle Scholar
  44. 44.
    Rong M, Gong D, Zhang Y, Jin Y, Pedrycz W (2018) Multidirectional prediction approach for dynamic multiobjective optimization problems. IEEE Trans Cybern pp 1–13Google Scholar
  45. 45.
    Rossi C, Abderrahim M, Díaz JC (2008) Tracking moving optima using Kalman-based predictions. Evol Comput 16(1):1–30CrossRefGoogle Scholar
  46. 46.
    Simões A, Costa E (2008) Evolutionary algorithms for dynamic environments: prediction using linear regression and Markov chains. In: Parallel problem solving from nature (PPSN), pp 306–315Google Scholar
  47. 47.
    Simões A, Costa E (2009) Improving prediction in evolutionary algorithms for dynamic environments. In: Genetic and evolutionary computation conference (GECCO), pp 875–882Google Scholar
  48. 48.
    Simões A, Costa E (2014) Prediction in evolutionary algorithms for dynamic environments. Soft Comput 18(8):1471–1497CrossRefGoogle Scholar
  49. 49.
    Trojanowski K, Michalewicz Z (1999) Searching for optima in non-stationary environments. In: Congress on evolutionary computation (CEC), pp 1843–1850Google Scholar
  50. 50.
    Wu Y, Jin Y, Liu X (2015) A directed search strategy for evolutionary dynamic multiobjective optimization. Soft Comput 19(11):3221–3235CrossRefGoogle Scholar
  51. 51.
    Yang S, Yao X (2003) Dual population-based incremental learning for problem optimization in dynamic environments. In: Asia pacific symposium on intelligent and evolutionary systems (IES), pp 49–56Google Scholar
  52. 52.
    Yazdani D, Omidvar MN, Branke J, Nguyen TT, Yao X (2019) Scaling up dynamic optimization problems: a divide-and-conquer approach. Trans Evol ComputGoogle Scholar
  53. 53.
    Zhou A, Jin Y, Zhang Q, Sendhoff B, Tsang E (2007) Prediction-based population re-initialization for evolutionary dynamic multi-objective optimization. In: Evolutionary multi-criterion optimization (EMO), pp 832–846Google Scholar
  54. 54.
    Zhou J, Zou J, Yang S, Ruan G, Ou J, Zheng J (2018) An evolutionary dynamic multi-objective optimization algorithm based on center-point prediction and sub-population autonomous guidance. In: Symposium series on computational intelligence (SSCI), pp 2148–2154Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Computational Intelligence Group, Department of Computer ScienceUniversity of OldenburgOldenburgGermany

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