Cross Entropy Multi-objective Optimization Algorithm

  • Gerardo BeruvidesEmail author
Part of the Springer Theses book series (Springer Theses)


This chapter presents two set of modifications respect to the cross entropy multi-objective optimization algorithm (MOCE) introduced by Bekker and Aldrich (Eur J Oper Res 211(1):112–121 [1]). First, a group of modifications are introduced in the cross entropy multi-objective optimization algorithm, also called (MOCE+), based on a new procedure for addressing constraints: (i) the use of variable cutoff values for selecting the elitist population; and, (ii) filtering of the elitist population after each epoch. The second and final modifications packages are introduced in the Simple Multi-Objective Cross Entropy method (SMOCE), based on only four parameters (epoch number, working population size, histogram interval number, and elite fraction) stored in the algorithm, in order to facilitate the tuning process. The final proposed method (SMOCE) is evaluated using different test suites. Furthermore, a comparison with some other well-known optimization methods is carried out. The comparative study demonstrates the good figures of merit of the SMOCE method in complex test suites. Finally, the proposed method is validated in the multi-objective optimization of a micro-drilling process. Two conflicting targets are considered: total drilling time and vibrations on the plane that is perpendicular to the drilling axis. The Pareto front, obtained through the optimization process, is analyzed through quality metrics and the available options in the decision-making process.


  1. 1.
    Bekker J, Aldrich C (2011) The cross-entropy method in multi-objective optimisation: an assessment. Eur J Oper Res 211(1):112–121MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Rubinstein R (2008) Semi-iterative minimum cross-entropy algorithms for rare-events, counting, combinatorial and integer programming (in English). Methodol Comput Appl Prob 10(2):121–178zbMATHCrossRefGoogle Scholar
  3. 3.
    Costa A, Jones OD, Kroese D (2007) Convergence properties of the cross-entropy method for discrete optimization. Oper Res Lett 35(5):573–580MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Kroese DP, Rubinstein RY, Taimre T (2007) Application of the cross-entropy method to clustering and vector quantization. J Glob Optim 37(1):137–157zbMATHCrossRefGoogle Scholar
  5. 5.
    Rubinstein RY, Kroese DP (2013) The cross-entropy method: a unified approach to combinatorial optimization, Monte-Carlo simulation and machine learning. Springer, New YorkzbMATHGoogle Scholar
  6. 6.
    Haber RE, Del Toro RM, Gajate A (2010) Optimal fuzzy control system using the cross-entropy method. A case study of a drilling process. Inf Sci 180(14):2777–2792CrossRefGoogle Scholar
  7. 7.
    Beruvides G, Quiza R, Haber RE (2016) Multi-objective optimization based on an improved cross-entropy method. A case study of a micro-scale manufacturing process. Inf Sci 334–335:161–173CrossRefGoogle Scholar
  8. 8.
    GAMHE-Group (2015) Multi-objective optimization cross entropy (MOCE+)
  9. 9.
    Van Veldhuizen DA (1999) Scalable multi-objective optimization test problems. Ph.D., Air Force Institute of Technology, Wright-Patterson AFBGoogle Scholar
  10. 10.
    Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRefGoogle Scholar
  11. 11.
    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):477–506zbMATHCrossRefGoogle Scholar
  12. 12.
    Nebro AJ, Luna F, Alba E, Dorronsoro B, Durillo JJ, Beham A (2008) AbYSS: adapting scatter search to multiobjective optimization. IEEE Trans Evol Comput 12(4):439–457CrossRefGoogle Scholar
  13. 13.
    Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithmGoogle Scholar
  14. 14.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  15. 15.
    Li K, Kwong S, Wang R, Tang K-S, Man K-F (2013) Learning paradigm based on jumping genes: a general framework for enhancing exploration in evolutionary multiobjective optimization. Inf Sci 226:1–22MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Huo Y, Zhuang Y, Gu J, Ni S (2015) Elite-guided multi-objective artificial bee colony algorithm. Appl Soft Comput J 32:199–210CrossRefGoogle Scholar
  17. 17.
    Dai X, Yuan X, Zhang Z (2015) A self-adaptive multi-objective harmony search algorithm based on harmony memory variance. Appl Soft Comput J 35:541–557CrossRefGoogle Scholar
  18. 18.
    Ramteke M, Ghune N, Trivedi V (2015) Simulated binary jumping gene: a step towards enhancing the performance of real-coded genetic algorithm. Inf Sci 325:429–454CrossRefGoogle Scholar
  19. 19.
    Giagkiozis I, Purshouse RC, Fleming PJ (2014) Generalized decomposition and cross entropy methods for many-objective optimization. Inf Sci 282:363–387MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Qingfu Z, Hui L (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  21. 21.
    Qingfu Z, Aimin Z, Yaochu J (2008) RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans Evol Comput 12(1):41–63CrossRefGoogle Scholar
  22. 22.
    D’Addona DM, Teti R (2013) Genetic algorithm-based optimization of cutting parameters in turning processes. Procedia CIRP 7:323–328CrossRefGoogle Scholar
  23. 23.
    Quiza Sardiñas R, Rivas Santana M, Alfonso Brindis E (2006) Genetic algorithm-based multi-objective optimization of cutting parameters in turning processes. Eng Appl Artif Intell 19(2):127–133CrossRefGoogle Scholar
  24. 24.
    Dixit PM, Dixit US (2008) Modeling of metal forming and machining processes: by finite element and soft computing methods (engineering materials and processes) (engineering materials and processes). Springer, London, p 590Google Scholar
  25. 25.
    Lalwani DI, Mehta NK, Jain PK (2008) Experimental investigations of cutting parameters influence on cutting forces and surface roughness in finish hard turning of MDN250 steel (in English). J Mater Process Technol 206(1–3):167–179CrossRefGoogle Scholar
  26. 26.
    Dandekar CR, Shin YC (2012) Modeling of machining of composite materials: a review (in English). Int J Mach Tools Manuf 57:102–121CrossRefGoogle Scholar
  27. 27.
    Ren Q, Balazinski M, Baron L, Jemielniak K, Botez R, Achiche S (2014) Type-2 fuzzy tool condition monitoring system based on acoustic emission in micromilling. Inf Sci 255:121–134CrossRefGoogle Scholar
  28. 28.
    Sieben B, Wagner T, Biermann D (2010) Empirical modeling of hard turning of AISI 6150 steel using design and analysis of computer experiments (in English). Prod Eng Res Devel 4(2):115–125CrossRefGoogle Scholar
  29. 29.
    Velchev S, Kolev I, Ivanov K, Gechevski S (2014) Empirical models for specific energy consumption and optimization of cutting parameters for minimizing energy consumption during turning (in English). J Clean Prod 80:139–149CrossRefGoogle Scholar
  30. 30.
    Zain AM, Haron H, Sharif S (2011) Optimization of process parameters in the abrasive waterjet machining using integrated SA-GA (in English). Appl Soft Comput J 11(8):5350–5359CrossRefGoogle Scholar
  31. 31.
    Baskar N, Asokan P, Prabhaharan G, Saravanan R (2005) Optimization of machining parameters for milling operations using non-conventional methods (in English). Int J Adv Manuf Technol 25(11–12):1078–1088CrossRefGoogle Scholar
  32. 32.
    Yusup N, Zain AM, Hashim SZM (2012) Overview of PSO for optimizing process parameters of machining. In: 2012 international workshop on information and electronics engineering, IWIEE 2012, Harbin, vol 29, pp 914–923CrossRefGoogle Scholar
  33. 33.
    Coello CAC, Lamont GB, Veldhuizen DAV (2006) Evolutionary algorithms for solving multi-objective problems (genetic and evolutionary computation). Springer, New YorkzbMATHGoogle Scholar
  34. 34.
    Konak A, Coit DW, Smith AE (2006) Multi-objective optimization using genetic algorithms: a tutorial (in English). Reliab Eng Syst Saf 91(9):992–1007CrossRefGoogle Scholar
  35. 35.
    Mukherjee I, Ray PK (2006) A review of optimization techniques in metal cutting processes (in English). Comput Ind Eng 50(1–2):15–34CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centre for Automation and Robotic (CAR-CSIC)MadridSpain

Personalised recommendations