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A class of order-based genetic algorithm for flow shop scheduling

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Abstract

A class of order-based genetic algorithm is presented for flow shop scheduling that is a typical NP-hard combinatorial optimisation problem with a strong engineering background. The proposed order-based genetic algorithm borrows from the idea of ordinal optimisation to ensure the quality of the solution found with a reduction in computation effort and applies the evolutionary searching mechanism and learning capability of genetic algorithms to effectively perform exploration and exploitation. Under the guidance of ordinal optimisation and with an emphasis on order-based searching and elitist-based evolution in the proposed approach, a solution that is "good enough" can be guaranteed with a high confidence level and reduced level of computation. The effectiveness of the proposed algorithm is demonstrated by numerical simulation results based on benchmarks, and its optimisation quality is much better than that of the classic genetic algorithm, the well-known NEH heuristic, as well as being better than a pure blind search. Moreover, the effects of some parameters on optimisation performance are discussed.

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Abbreviations

n :

number of jobs

m :

number of machines

p ij :

processing time of job i on machine j

C max, C* :

makespan, optimal makespan value or lower bound value

P k , |P k |:

population at kth iteration and its size

S, |S|:

search space and its size

p 0 :

initial desired solution quality for G

p e :

final desired solution quality for G

p s0 :

initial desired probability that at least one of the selected solutions is in G

p se :

final desired probability that at least one of the selected solutions is in G

G :

the set consist of the p percent "best" feasible solutions

L :

sampling number

p mut, p′ mut :

The first and second mutation probabilities

l :

best l solution selected from population

k :

iteration number

a[], b[]:

parent strings

f :

fitness value

M :

a positive number large enough

c[], d[]:

children strings

RE :

the relative error of the result obtained to C*

BRE :

the relative error of the best result obtained to C*

ARE :

the relative error of the average result obtained to C*

WRE :

the relative error of the worst result obtained to C*

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Acknowledgement

The authors would like to thank Prof. Y. C. Ho (Harvard Univ.) for his helpful discussion on OO. This research is partially supported by National Science Foundation of China (60204008) and the Basic Research Foundation of Tsinghua University, as well as 973 program (2002CB312200).

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Authors and Affiliations

  1. Department of Automation, CFINS, Tsinghua University, 100084, Beijing, P.R. China

    L. Wang

  2. Department of Automation, CFINS, Tsinghua University, 100084, Beijing, P.R. China

    L. Zhang & D.-Z. Zheng

Authors
  1. L. Wang
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  2. L. Zhang
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  3. D.-Z. Zheng
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Correspondence to L. Wang.

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Wang, L., Zhang, L. & Zheng, DZ. A class of order-based genetic algorithm for flow shop scheduling. Int J Adv Manuf Technol 22, 828–835 (2003). https://doi.org/10.1007/s00170-003-1689-8

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  • DOI: https://doi.org/10.1007/s00170-003-1689-8

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