Soft Computing

, Volume 19, Issue 11, pp 3083–3107 | Cite as

An orthogonal predictive model-based dynamic multi-objective optimization algorithm

  • Ruochen Liu
  • Xu Niu
  • Jing Fan
  • Caihong Mu
  • Licheng Jiao
Methodologies and Application


In this paper, a new dynamic multi-objective optimization evolutionary algorithm is proposed for tracking the Pareto-optimal set of time-changing multi-objective optimization problems effectively. In the proposed algorithm, to select individuals which are best suited for a new time from the historical optimal sets, an orthogonal predictive model is presented to predict the new individuals after the environment change is detected. Also, to converge to optimal front more quickly, an modified multi-objective optimization evolutionary algorithm based on decomposition is adopted. The proposed method has been extensively compared with other three dynamic multi-objective evolutionary algorithms over several benchmark dynamic multi-objective optimization problems. The experimental results indicate that the proposed algorithm achieves competitive results.


Dynamic environment Multi-objective optimization Decomposition Forecasting model 



The authors would like to thank the editor and the reviewers for helpful comments that greatly improved the paper. This work was supported by the National Natural Science Foundation of China (Nos. 61373111, 61272279, 61003199 and 61203303), the Fundamental Research Funds for the Central University (Nos. K50511020014, K5051302084, K50510020011, K5051302049, and K5051302023); the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048), the Program for Century Excellent Talents in University (No. NCET-12-0920), and the Provincial Natural Science Foundation of Shaanxi of China (no. 2014JM8321).


  1. Connolly JF, Granger E, Sabourin R (2013) Dynamic multi-objective evolution of classifier ensembles for video face recognition. Appl Soft Comput 13:3149–3166CrossRefGoogle Scholar
  2. Deb K, Jain S (2002) Running performance metrics for evolutionary multiobjective optimization. Technical Report 2002004, KanGAL, Indian Institute of Technology, Kanpur 208016, IndiaGoogle Scholar
  3. Deb K, Bhaskara UN, Karthik S (2007) Dynamic multi-objective optimization and decision-making using modified NSGA-II: a case study on hydro-thermal power scheduling. In: Obayashi S et al (ed) Proceedings of EMO 2007. LNCS, vol 4403. Springer, Berlin, pp 803–817Google Scholar
  4. Farina M, Amato P, Deb K (2004) Dynamic multi-objective optimization problems: test cases, approximations and applications. IEEE Trans Evol Comput 8:425–442CrossRefGoogle Scholar
  5. García S, Molina D, Lozano M et al (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15:617–644CrossRefMATHGoogle Scholar
  6. Goh CK, Tan KC (2009) A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans Evol Comput 13:103–127CrossRefGoogle Scholar
  7. Hatzakis I, Wallace D (2006) Dynamic multi-objective optimization with evolutionary algorithms: a forward-looking approach. In: Proceedings of genetic and evolutionary computation conference (GECCO 2006), Seattle, Washington, USA, pp 1201–1208Google Scholar
  8. Helbig M, Engelbrecht AP (2013) Analysing the performance of dynamic multi-objective optimization algorithms. In: 2013 IEEE congress on evolutionary computation, Cancún, México, pp 1531–1539Google Scholar
  9. Knowles J, Zitzler E, Thiele L et al (2006) A tutorial on the performance assessment of stochastic multiobjective optimizers. In: Third international conference on evolutionary multi-criterion optimization, vol 216, pp 13Google Scholar
  10. Koo WT, Goh CK, Tan KC (2010) A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment. Memet Comput 2:87–110CrossRefGoogle Scholar
  11. Leung YW, Zhang Q (1997) Evolutionary algorithms + experimental design methods: a hybrid approach for hard optimization and search problems. Research Grant Proposal, Hong Kong Baptist UniversityGoogle Scholar
  12. Liu M, Zeng WH (2013) Memory enhanced dynamic multi-objective evolutionary algorithm based on decomposition. J Softw 24(7):1571–1588 (in Chinese).
  13. Liu RC, Chen YY et al (2013) A novel cooperative coevolutionary dynamic multi-objective optimization algorithm using a new predictive model. Soft Comput 18:743–756Google Scholar
  14. Schott JR (1995) Fault tolerant design using single and multictiteria genetic algorithm optimization. Master thesis, Massachusetts Institute of TechnologyGoogle Scholar
  15. Shang RH, Jiao LC, Gong MG (2005) Clonal selection algorithm for dynamic multiobjective optimization. In: Hao Y et al (ed) CIS 2005, Part I. LNCS (LNAI), vol 3801. Springer, Heidelberg, pp 846–851Google Scholar
  16. Shang RH, Jiao LC, Ren YP et al (2014) Quantum immune clonal coevolutionary algorithm for dynamic multiobjective optimization. Soft Comput 18:743–756CrossRefGoogle Scholar
  17. Van V, David A (1999) Multi-objective evolutionary algorithms: classification, analyzes, and new innovations. PhD thesis, Air Force Institute of Technology, Wright-Patterson AFBGoogle Scholar
  18. Wang YP, Dang CY (2008) An evolutionary algorithm for dynamic multi-objective optimization. Appl Math Comput 205:6–18MathSciNetCrossRefMATHGoogle Scholar
  19. Wei JX, Wang YP (2012) Hyper rectangle search based particle swarm algorithm for dynamic constrained multi-objective optimization problems. In: IEEE World Congress on Computational Intelligence (WCCI 2012), pp 1–8Google Scholar
  20. Wei JX, Jia LP (2013) A novel particle swarm optimization algorithm with local search for dynamic constrained multi-objective optimization problems. In: 2013 IEEE congress on evolutionary computation, Cancún, México, pp 2436–2443Google Scholar
  21. Wu Q (1998) On the optimality of orthogonal experimental design. Acta Math Appl Sin 1:283–299Google Scholar
  22. Zeng SY, Yao SZ, Kang LS et al (2005) An efficient multi-objective evolutionary algorithm: OMOEA-II. Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. Lecture notes in computer science, vol 3410. Springer, Berlin, pp 108–119Google Scholar
  23. Zeng SY, Chen G, Zheng L et al (2006) A dynamic multi-objective evolutionary algorithm based on an orthogonal design. In: IEEE congress on evolutionary computation, pp 573–580Google Scholar
  24. Zeng SY, Kang LS, Ding LX (2006) An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints. Evol Comput 12:77–98Google Scholar
  25. Zhan ZH, Zhang J, Li Y et al (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evol Comput 15:832–847Google Scholar
  26. Zhang QF, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731CrossRefGoogle Scholar
  27. Zhang ZH (2008) Multiobjective optimization immune algorithm in dynamic environments and its application to greenhouse control. Appl Soft Comput 8:959–971CrossRefGoogle Scholar
  28. Zhang ZH, Qian SQ (2009) Multi-objective immune optimization in dynamic environments and its application to signal simulation. In: 2009 international conference on measuring technology and mechatronics automation, vol 3, Hunan, China, pp 246–250Google Scholar
  29. Zhang ZH, Qian SQ (2011) Artificial immune system in dynamic environments solving time-varying non-linear constrained multi-objective problems. Soft Comput 15:1333–1349CrossRefGoogle Scholar
  30. Zheng BJ (2007) A new dynamic multi-objective optimization evolutionary algorithm. In: Third international conference on natural computation (ICNC 2007), pp 565–570Google Scholar
  31. Zhou AM, Jin YC, Zhang QF et al (2007) Prediction-based population re-initialization for evolutionary dynamic multi-objective optimization. In: Obayashi S et al (ed) EMO 2007. LNCS, vol 4403. Springer, Heidelberg, pp 832–846Google Scholar
  32. Zitzler E, Thiele L (1999) Multi-objective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271Google Scholar
  33. Zitzler E, Thiele L et al (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Eiben AE, Bäck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature-PPSN V, vol 1498. Springer, Berlin 292–301Google Scholar
  34. Zitzler E, Thiele L et al (2003) Performance assessment of multi-objective optimizers: an analysis and review. IEEE Trans Evol Comput 7:117–132CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ruochen Liu
    • 1
  • Xu Niu
    • 1
  • Jing Fan
    • 1
  • Caihong Mu
    • 1
  • Licheng Jiao
    • 1
  1. 1.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of ChinaXidian UniversityXi’anPeople’s Republic of China

Personalised recommendations