Advertisement

Soft Computing

, Volume 18, Issue 6, pp 1177–1188 | Cite as

A block based estimation of distribution algorithm using bivariate model for scheduling problems

  • Pei-Chann ChangEmail author
  • Meng-Hui Chen
Methodologies and Application

Abstract

Recently, estimation of distribution algorithms (EDAs) have gradually attracted a lot of attention and have emerged as a prominent alternative to traditional evolutionary algorithms. In this paper, a block-based EDA using bivariate model is developed to solve combinatorial problems. Instead of generating a set of chromosomes, our approach generates a set of promising blocks using bivariate model and these blocks are reserved in an archive for future use. These blocks will be updated every other k generation. Then, two rules, i.e., AC1 and AC2, are developed to generate a new chromosome by combining the set of selected blocks and rest of genes. This block based approach is very efficient and effective when compared with the traditional EDAs. According to the experimental results, the block based EDA outperforms EDA, GA, ACO and other evolutionary approaches in solving benchmark permutation problems. The block based approach is a new concept and has a very promising result for other applications.

Keywords

Combinatorial problems Estimation of distribution algorithms Bivariate probabilistic model Artificial chromosomes 

References

  1. Ahmadizar F (2012) A new ant colony algorithm for makespan minimization in permutation flow shops. Comput Ind Eng 63(2):355–361CrossRefGoogle Scholar
  2. Bagchi TP (1999) Multiobjective Scheduling by Genetic Algorithms. Kluwer, BostonCrossRefzbMATHGoogle Scholar
  3. Baker KR (1974) Introduction to sequencing and scheduling. Wiley, New YorkGoogle Scholar
  4. Baker KR (1975) A comparative study of flow-shop algorithms. Oper Res 23(1):62–73CrossRefzbMATHGoogle Scholar
  5. Baluja S (1994) Population based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Technical Report No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, Pennsylvania, USAGoogle Scholar
  6. Ceberio J, Irurozki E, Mendiburu A, Lozano J (2012) A review on estimation of distribution algorithms in permutation-based combinatorial optimization problems. Prog Artif Intell 1(1):103–117CrossRefGoogle Scholar
  7. Chang PC, Chen SH, Fan CY (2008a) Mining gene structures to inject artificial chromosomes for genetic algorithm in single machine scheduling problems. Appl Soft Comput J 8(1):767–777Google Scholar
  8. Chang PC, Chen SH, Fan CY, Chan CL (2008b) Genetic algorithm integrated with artificial chromosomes for multi-objective flow-shop scheduling problems. Appl Math Comput 205(2):550–561Google Scholar
  9. Chang PC, Huang WH, Ting CJ (2010) Self-evolving Artificial Immune System via Developing T and B Cell for Permutation Flow-shop Scheduling Problems. Proceedings of World Academy of Science, Engineering and Technology 65:822–827Google Scholar
  10. Chang PC, Huang WH, Ting CJ (2011) A hybrid genetic-immune algorithm with improved lifespan and elite antigen for flow-shop scheduling problems. Int J Prod Res 49(17):5207–5230CrossRefGoogle Scholar
  11. Chen SH, Chen MC (2013) Addressing the advantages of using ensemble probabilistic models in estimation of distribution algorithms for scheduling problems. Int J Prod Econ 141(1):24–33Google Scholar
  12. Chen YM, Chen MC, Chang PC, Chen SH (2012) Extended artificial chromosome genetic algorithm for permutation flowshop scheduling problems. Comput Ind Eng 62(2):536–545 Google Scholar
  13. Costa WE, Goldbarg MC, Goldbarg EG (2012) New VNS heuristic for total owtime owshop scheduling problem. Expert Syst Appl 39(9):8149–8161CrossRefGoogle Scholar
  14. Dong X, Chen P, Huang HK, Nowak M (2013) A multi-restart iterated local search algorithm for the permutation flow-shop problem minimizing total flow time. Comput Oper Res 40(2):627–632CrossRefGoogle Scholar
  15. Garey MR, Johnson DS (1979) Computers and Intractibility: a Guide to the Theory of NP-Completeness. Freeman, San FranciscozbMATHGoogle Scholar
  16. Harik GR, Lobo FG, Goldberg DE (1999) The compact genetic algorithm. IEEE Trans Evolut Comput 3(4):523–528CrossRefGoogle Scholar
  17. Larrañaga PJ, Lozano A (2002) Estimation of distribution algorithms: A new tool for evolutionary computation. Kluwer Academic Publishers, BostonCrossRefGoogle Scholar
  18. Lian Z, Gu X, Jiao B (2006) A similar particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan. Appl Math Comput 175(1):773–785CrossRefzbMATHMathSciNetGoogle Scholar
  19. Liu HC, Gao L, Pan QK (2011) A hybrid particle swarm optimization with estimation of distribution algorithm for solving permutation flow-shop scheduling problem. Expert Syst Appl 38(4):4348–4360lCrossRefGoogle Scholar
  20. Paul TK, Iba H (2002) Linear and Combinatorial Optimizations by Estimation of Distribution Algorithms. 9th MPS Symposium on Evolutionary Computation, IPSJ Symposium, Japan, pp 99–106Google Scholar
  21. Pen QK, Ruiz R (2012) Local search methods for the flow-shop scheduling problem with flowtime minimization. Eur J Oper Res 222(1):31–43CrossRefGoogle Scholar
  22. Reeves CR (1995) A genetic algorithm for flow-shop sequencing. Comput Oper Res 22(1):5–13CrossRefzbMATHGoogle Scholar
  23. Tasgetiren MF, Pan QK, Suganthan PN, Chen AH (2011) A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow-shops. Inf Sci 181(1):3459–3475CrossRefMathSciNetGoogle Scholar
  24. Tsutsui S (2002) Probabilistic model-building genetic algorithms in permutation representation domain using edge histogram. Lect Notes Comput Sci 2439:224–233CrossRefGoogle Scholar
  25. Tsutsui S, Pelikan M, Goldberg DE (2006) Node Histogram vs. Edge Histogram: a Comparison of PMBGAs in Permutation Domains. Missouri Estimation of Distribution Algorithms Laboratory, MEDAL Report No. 2006009, JulyGoogle Scholar
  26. Tzeng YR, Chen CL, Chen CL (2012) A hybrid EDA with ACS for solving permutation flow-shop scheduling. Int J Adv Manuf Technol 60:1139–1147CrossRefGoogle Scholar
  27. Zhang Q (2004) On Stability of fixed points of limit models of univariate marginal distribution algorithm and factorized distribution algorithm. IEEE Trans Evol Comput 8(1):80–93CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Information ManagementYuan Ze UniversityChung-LiTaiwan, ROC

Personalised recommendations