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Hybrid social spider optimization algorithm with differential mutation operator for the job-shop scheduling problem

  • * Corresponding author: Yongquan Zhou

    * Corresponding author: Yongquan Zhou 
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  • The job-shop scheduling problem is one of the well-known hardest combinatorial optimization problems. The problem has captured the interest of a significant number of researchers, but no efficient solution algorithm has been found yet for solving it to optimality in polynomial time. In this paper, a hybrid social-spider optimization algorithm with differential mutation operator is presented to solve the job-shop scheduling problem. To improve the exploration capabilities of the social spider optimization algorithm (SSO), we incorporate the DM operator (a mutation operator taken from the deferential evolutionary (DE) algorithm) into the framework of the female cooperative operator. The experimental results show that the proposed method effectiveness in solving job-shop scheduling compared to other optimization algorithms in the literature.

    Mathematics Subject Classification: Primary: 78M50, 90C27.

    Citation:

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  • Figure 1.  FT20, Size = 100

    Figure 2.  LA40, Size = 225

    Figure 3.  ORB10, Size = 100

    Figure 4.  YN04, Size = 400

    Figure 5.  FT20, Size = 100

    Figure 6.  LA40, Size = 225

    Figure 7.  ORB10, Size = 100

    Figure 8.  YN04, Size = 400

    Table 1.  Notations for the JSSP

    $ n $ the number of jobs
    $ m $ the number of operations for one job
    $ O_i $ the completion time of operation $ i $($ i=\{0, 1, 2, \dots, n*m+1\} $)
    $ t_i $ the processing time of operation $ i $ on a given machine
    $ \omega_{im} $ the flag of operation $ i $ initiated by machine $ m $
    $ P_i $ all the predecessor operations of operation $ i $
    $ A(t) $ the set of operations processed at time $ t $
    $ o_{ji} $ the $ i $th operation of job $ j $
    $ C_{\max} $ the makespan
     | Show Table
    DownLoad: CSV

    Table 2.  Simulation results for FT, LA, ORB and YN

    Name Size($ n*m $) Algorithm Best Worst Mean Std.
    FT20 20*5 PSO 1374.00 1521.00 1442.50 42.02
    IGA 1744.00 2527.00 2025.50 198.95
    DE 1456.00 1554.00 1506.00 27.64
    SSO 1527.00 1527.00 1527.00 0
    SSO-DM 1374.00 1374.00 1374.00 0
    LA40 15*15 PSO 1498.00 1732.00 1576.05 59.79
    IGA 2154.00 2803.00 2340.25 155.90
    DE 1691.00 1824.00 1767.05 36.46
    SSO 1834.00 1834.00 1834.00 0
    SSO-DM 1528.00 1528.00 1528.00 0
    ORB10 10*10 PSO 1039.00 1263.00 1150.05 48.84
    IGA 1431.00 2121.00 1761.25 158.12
    DE 1190.00 1293.00 1244.40 25.04
    SSO 1345.00 1345.00 1345.00 0
    SSO-DM 1114.00 1114.00 1114.00 0
    YN4 20*20 PSO 1340.00 1607.00 1425.15 64.84
    IGA 1826.00 2192.00 1997.90 116.48
    DE 1486.00 1601.00 1570.75 26.15
    SSO 1583.00 1583.00 1583.00 0
    SSO-DM 1492.00 1492.00 1492.00 0
     | Show Table
    DownLoad: CSV

    Table 3.  Experimental results of running time of the algorithm

    IGA PSO DE SSO SSO-DM
    FT20 4.7350 1.3626 0.6521 0.7993 0.8725
    LA40 4.2764 2.6175 1.0695 1.2537 1.2961
    ORB10 2.7547 1.8100 1.1091 1.3127 1.0230
    YN04 6.8851 3.0504 1.9461 2.3814 2.5842
     | Show Table
    DownLoad: CSV

    Table 4.  $ p $-values produced by Wilcoxon's test comparing SSO-DM vs. PSO, SSO-DM vs. IGA, SSO-DM vs. DE and SSO-DM vs. SSO, over the "average best-so-far" (Mean) values from Table 1 to Table 4

    PSO IGA DE SSO
    FT20 7.9772E-09 8.0065E-09 4.0136E-03 4.6826E-10
    LA40 7.9918E-09 7.9918E-09 8.0065E-09 4.6826E-10
    ORB10 7.9918E-09 8.0065E-09 7.9772E-09 4.6826E-10
    YN04 2.0993E-07 8.0065E-09 4.0289E-02 4.6826E-10
     | Show Table
    DownLoad: CSV
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