Soft Computing

, Volume 21, Issue 20, pp 5883–5891 | Cite as

Hyper multi-objective evolutionary algorithm for multi-objective optimization problems

Focus

Abstract

Multi-objective optimization problems (MOPs) are very common in practice. To solve MOPs, many kinds of multi-objective evolutionary algorithms (MOEAs) are proposed. However, different MOEAs have different performances for different MOPs. Therefore, it is a time-consuming task to choose a suitable MOEA for a given problem. To pursue a competitive performance for various kinds of MOPs, in this paper, we propose a framework named hyper multi-objective evolutionary algorithm (HMOEA). In this framework, more than one MOEAs are employed, which is more adaptive to different problems. In HMOEA, the population will be randomly divided into several groups. In each group, a selected MOEA will be implemented. Therefore in the framework, the number of groups is equal to the number of the employed MOEAs. The size of each group, namely the size of sub-population in each group, is adjusted according to the corresponding MOEA’s performance. If a MOEA performs well, its corresponding group will have a large size group, which means the MOEA obtains more computational resources. On the contrary, if a MOEA has a poor performance in current generation, its corresponding group will obtain only a few individuals. Although a MOEA does not perform very well in current generation, the framework will not abandon this MOEA, but provide it a group that has predefined small size. The reason is that an involvement of different MOEAs will increase the diversity of algorithms in the hyper framework, which is helpful for HMOEA to avoid local optima and also can help HMOEA be adaptive to different phases in the whole optimization process. To compare MOEAs’ performances, coverage rate (CR) metric is used to evaluate the quality of MOEA and therefore decides the size of group for each MOEA. In numerical experiments, ZDT benchmarks are employed to test the proposed hyper framework. Several classic MOEAs are also used in comparisons. According to the comparison results, HMOEA can achieve very competitive performances, which demonstrates that the design is feasible and effective to solve MOPs.

Keywords

Multi-objective optimization problems Hyper multi-objective evolutionary algorithm Group Coverage rate 

References

  1. Aggelogiannaki E, Sarimveis H (2007) A simulated annealing algorithm for prioritized multi-objective optimization implementation in an adaptive model predictive control configuration. IEEE Trans Syst Man Cybern Part B 37(4):902–915CrossRefGoogle Scholar
  2. Agrawal G, Kawajiri Y (2012) Comparison of various ternary simulated moving bed separation schemes by multi-objective optimization. J Chromatogr 1238:105–113CrossRefGoogle Scholar
  3. Ahmadi P, Almasi A, Shahriyari M, Dincer I (2012) Multi-objective optimization of a combined heat and power (CHP) system for heating purpose in a paper mill using evolutionary algorithm. Int J Energy Res 36(1):46–63CrossRefGoogle Scholar
  4. Asadzadeh M, Tolson B (2013) Pareto archived dynamically dimensioned search with hyper volume-based selection for multi-objective optimization. Eng Optim 45(12):1489–1509MathSciNetCrossRefGoogle Scholar
  5. Attea BA, Khali EA, Cosar A (2015) Multiobjective evolutionary routing protocol for efficient coverage in mobile sensor network. Soft Comput 19(10):2983–2995CrossRefGoogle Scholar
  6. Chang J, Shi P (2011) Using investment satisfaction capability index based particle swarm optimization to construct a stock portfolio. Inf Sci 181(14):2989–2999MathSciNetCrossRefGoogle Scholar
  7. Chiandussi G, Codegone M, Ferrero S et al (2012) Comparison of multi-objective optimization methodologies for engineering applications. Comput Math Appl 63(5):912–942MathSciNetCrossRefMATHGoogle Scholar
  8. Chen BJ, Shu HZ, Coatrieux G, Chen G, Xun XM, Coatrieux JL (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51:124–144MathSciNetCrossRefMATHGoogle Scholar
  9. Deb K (1999) Multi-objective genetic algorithm: problem difficulties and construction of test problems. Evol Comput 7:205–230CrossRefGoogle Scholar
  10. Deb K, Pratap A, Agarwal S, Meyarivan T (2000) A fast elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  11. Farmani R, Savic DA, Walters GA (2005) Evolutionary multi objective optimization in water distribution network design. Eng Optim 37(2):167–183CrossRefGoogle Scholar
  12. Fu ZJ, Sun XM, Liu Q, Zhou L, Shu JG (2015) Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud date supporting parallel computing. IEICE Trans Commun E98B(1):190–200Google Scholar
  13. Garcia J, Florez JE, Torralba A, Borrajo D, Lopez CL, Garcia-Olaya A, Saenz J (2013) Combining linear programming and automated planning to solve intermodal transportation problems. Eur J Oper Res 227(1):216–226MathSciNetCrossRefMATHGoogle Scholar
  14. Gong M, Jiao L, Du H, Bo L (2008) Multiobjective immune algorithm with nondominated neighbor-based selection. Evol Comput 16(2):225–255CrossRefGoogle Scholar
  15. Guo W, Wang L, Ge SS, Ren H, Mao Y (2015) Drift analysis of mutation operations for biogeography-based optimization. Soft Comput 19:1881–1892CrossRefMATHGoogle Scholar
  16. Guo W, Wang L, Wu Q (2016) Numerical comparisons of migration models for multi-objective biogeography based optimization. Inf Sci 328:302–320CrossRefGoogle Scholar
  17. Horn J, Horn J, Nafpliotis N, Nafpliotis N, Goldberg DE (1993) Multi-objective optimization using the niched pareto genetic algorithm. Technical reportGoogle Scholar
  18. Jararweh Y, Al-Ayyoub M, Darabseh A, Benkhelifa E, Vouk M, Rindos A (2016) Software defined cloud: survey, system and evaluation. Future Gener Comput Syst Int J Escience 56:56–74Google Scholar
  19. Li J, Li XL, Sun XM (2015) Segmentation-based image copy-move forgery detection scheme. IEEE Trans Inf Forensics Secur 10(3):507–518Google Scholar
  20. Ma TH, Zhou JJ, Tang ML, Tian Y, AL-Dhelaan A, AL-Rodhaan M, Lee S, (2015) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans Inf Syst 98 (4):902–910Google Scholar
  21. Pan ZQ, Zhang Y, Kwong S (2015) Efficient motion and disparity estimation optimization for low complexity multiview video coding. IEEE Trans Broadcast 61(2):166–176CrossRefGoogle Scholar
  22. Rahimi-Vahed A, Mirghorbani SM, Rabbani M (2007) A new particle swarm algorithm for a multi-objective mixed-model assembly line sequencing problem. Soft Comput 11(10):997–1012CrossRefMATHGoogle Scholar
  23. Sarker R, Abbass HA (2004) Differential evolution for solving multi-objective optimization problems. Asia Pac J Oper Res 21(2):225–240MathSciNetCrossRefMATHGoogle Scholar
  24. Schaffer JD(1984) Some experiments in machine learning using vector evaluated genetic algorithms. PhD thesis, Nashville, Vanderbilt UniversityGoogle Scholar
  25. Shen J, Tan HW, Wang J, Wang JW, Lee S, (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178Google Scholar
  26. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  27. Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2:221–248CrossRefGoogle Scholar
  28. Suresh S, Sujit PB, Rao AK (2007) Particle swarm optimization approach for multi-objective composite box-beam design. Compos Struct 81(4):598–605Google Scholar
  29. Tan KC, Lee TH, Khor EF (2002) Evolutionary algorithms for multi-objective optimization: performance assessments and comparisons. Artif Intell Rev 17(4):253–290CrossRefMATHGoogle Scholar
  30. Veldhuizen DAV (1998) Multiobjective evolutionary algorithm research: a history and analysis. Technical report, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OHGoogle Scholar
  31. Wang WM, Zmeureanu R, Rivard H (2005) Applying multi-objective genetic algorithms in green building design optimization. Build Environ 40(11):1512–1525CrossRefGoogle Scholar
  32. Wang L, Singh C (2007) Environmental/economic power dispatch using a fuzzied multi-objective particle swarm optimization algorithm. Electr Power Syst 77(12):1654–1664CrossRefGoogle Scholar
  33. Wen XZ, Shao L, Xue Y, Fang W (2015) A rapid leanring algorithm for vehicle classification. Inf Sci 295:395–406CrossRefGoogle Scholar
  34. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle Scholar
  35. Xia ZH, Wang XH, Sun XM, Wang Q (2016) A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parallel Distrib Syst 27(2):340–352Google Scholar
  36. Xie SD, Wang YX (2014) Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wirel Pers Commun 78:231–246Google Scholar
  37. Yen GG, He Z (2014) Performance metric ensemble for multi-objective evolutionary algorithms. IEEE Trans Evol Comput 18(1):131–144CrossRefGoogle Scholar
  38. Zhang G, Shao X, Li P (2009) An effective hybrid particle swarm optimization algorithm for multi-objective flexible jobshop scheduling problem. Comput Ind Eng 56(4):1309–1318CrossRefGoogle Scholar
  39. Zhang Q, Li H (2007) MOEA/D: a multi-objective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  40. Zheng Y, Jeon B, Xu DH, Wu JQM, Zhang H (2015) Image segmentation by generalized hierarchical fuzzy C-means algorithm. J Intell Fuzzy Syst 28:961–973Google Scholar
  41. Zitzler E, Deb K, Thiele L (2000) Comparison of multi-objective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRefGoogle Scholar
  42. Zitzler E, Thiele L (1999) Multi-objective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Sino-German College of Applied ScienceTongji UniversityShanghaiChina
  2. 2.Department of Electronics and Information EngineeringTongji UniversityShanghaiChina

Personalised recommendations