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A moving block sequence-based evolutionary algorithm for resource investment project scheduling problems

  • * Corresponding author: Jing Liu

    * Corresponding author: Jing Liu 
Abstract Full Text(HTML) Figure(6) / Table(5) Related Papers Cited by
  • Inspired by the representation designed for floorplanning problems, in this paper, we proposed a new representation, namely the moving block sequence (MBS), for resource investment project scheduling problems (RIPSPs). Since each activity of a project in RIPSPs has fixed duration and resource demand, we consider an activity as a rectangle block whose width is equal to the duration of the activity and height the resource needed by the activity. Four move modes are designed for activities, by using which the activity can move to the appropriate position. Therefore, the new representation of the project of RIPSPs consists of two parts: an activity list and a move mode list. By initializing the move modes randomly for each activity and moving it appropriately, the activity list can be decoded into valid solutions of RIPSPs. Since the decoding method of MBS guarantees that after moved, each activity is scheduled in the left-most and bottom-most position within a coordinate, which means that each activity in the corresponding project is arranged as early as possible when the precedence constraints and resource demands are satisfied. In addition, the multiagent evolutionary algorithm (MAEA) is employed to incorporate with the newly designed MBS representation in solving RIPSPs. With the intrinsic properties of MBS in mind, four behaviors, namely the crossover, mutation, competition, and self-learning operators are designed for agents in MAEA. To test the performance of our algorithm, 450 problem instances are used and the experimental results demonstrate the good performance of the proposed representation.

    Mathematics Subject Classification: 90C59.

    Citation:

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  • Figure 1.  An example of precedence graph

    Figure 2.  An example of precedence graph

    Figure 3.  The types of overlaps. (a) All kinds of top-overlaps, (b) all kinds of right-overlaps

    Figure 4.  Relative positions of $CoverLeftX$ and $CoverRightX$. (a) and (b) are the cases without violating precedence constraints. (c) and (d) are the cases violating precedence constraints

    Figure 5.  The decoding process

    Figure 6.  The agent lattice of MBS$_{\rm {MAEA}}$-RIPSP

    Table 1.  The Percentages of Finding Optimal Solutions for MBS$_{\rm MAEA}$-RIPSP on Möhring Instances with 1000 Evaluations

    $C_1/C_2/C_3/C_4$$\theta = 1.0$$\theta = 1.1$$\theta = 1.2$$\theta = 1.3$$\theta = 1.4$$\theta = 1.5$
    1/1/1/11.001.001.001.000.0670.033
    3/1/1/11.000.900.900.800.1330.067
    1/3/1/11.001.001.000.800.7000.333
    1/1/3/11.001.001.001.000.9500.067
    1/1/1/31.001.001.000.601.000.067
    3/3/1/11.000.500.800.800.000.333
    3/1/3/11.001.000.900.850.600.333
    3/1/1/31.000.750.950.750.5330.067
    1/3/3/11.001.001.001.000.700.033
    1/3/1/31.001.001.001.000.800.00
    1/1/3/31.001.001.001.000.600.00
    3/3/3/11.001.000.901.000.3330.20
    3/3/1/31.000.451.000.750.1330.033
    3/1/3/31.001.000.950.850.1670.067
    1/3/3/31.001.001.001.000.700.067
     | Show Table
    DownLoad: CSV

    Table 2.  The Comparison of Numbers of Generation to Reach to the Optimal Solutions between MBS$_{\rm MAEA}$-RIPSP and GA for Möhring Test Sets

    $C_1/C_2/C_3/C_4$$\theta = 1.0$$\theta = 1.1$$\theta = 1.2$$\theta = 1.3$$\theta = 1.4$$\theta = 1.5$
    MBSGAMBSGAMBSGAMBSGAMBSGAMBSGA
    1/1/1/111121116621141
    3/1/1/111611212720271
    1/3/1/1121331411243131
    1/1/3/11111111112343
    1/1/1/31111132112145
    3/3/1/11112812125171
    3/1/3/11111121181189
    3/1/1/31212162198102
    1/3/3/11111182111523
    1/3/1/31112111186201
    1/1/3/313131212537121
    3/3/3/111121212914131
    3/3/1/31141113288221
    3/1/3/3121211121311845
    1/3/3/3121213311934923
     | Show Table
    DownLoad: CSV

    Table 3.  Parameter Settings for J10, J14 and J20 Test Sets

    Test Set#AgentMaxGenExcuteNum$SelfLTime$$P_{cro}$$P_{mut}$$P_{com}$
    J10$20\times 20$1010120.950.850.9
    J14$20\times 20$108120.950.851.0
    J20$20\times 19$108120.950.851.0
     | Show Table
    DownLoad: CSV

    Table 4.  Experimental Results of MBS$_{\rm MAEA}$-RIPSP for J10, J14 and J20 Test Sets

    $\theta$J10J14J20
    Opt.%Dev.%Eva.Opt.%Dev.%Eva.Opt.%Dev.%Eva.
    1.040.06.8896698876.50.7970371932.54.91267135
    1.141.03.4006722563.01.0457498135.05.43357327
    1.255.02.5922582143.1252.5851768333.04.92587273
    1.351.52.4822617049.3752.2975736943.02.61737188
    1.456.02.8036606547.51.9321677143.02.00797279
    1.568.51.8743449655.01.8272746543.01.97287154
     | Show Table
    DownLoad: CSV

    Table 5.  Comparisons between MBS$_{\rm MAEA}$-RIPSP and GA for J10, J14 and J20 Test Sets

    Test SetOpt.%Dev.%
    MBSGAMBSGA
    J1052.0048.203.34040.23
    J1455.7540.001.74740.32
    J2038.2533.333.64454.68
     | Show Table
    DownLoad: CSV
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