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SCIENCE CHINA Information Sciences, Volume 62 , Issue 9 : 192104(2019) https://doi.org/10.1007/s11432-018-9720-6

Solving multi-scenario cardinality constrained optimization problems via multi-objective evolutionary algorithms

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  • ReceivedJul 29, 2018
  • AcceptedNov 24, 2018
  • PublishedJul 30, 2019

Abstract


References

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  • Figure A1

    (Color online) Solution procedures of conventional EAs and Mucard. The red circles are the real optima; the other circles are the objective values of the EA individuals. (a1) Initialization and evolution direction of conventional EAs; (a2) final result of conventional EAs; (b1) initialization and evolution direction of Mucard; (b2) evolution of Mucard;protect łinebreak (b3) final results of Mucard.

  • Table 1   Configurations of the two algorithms compared in this study
    Settings SITATION GA Mucard
    Representation Set Set
    Crossover Uniform crossover RRR operator
    Mutation Greedy interchange Greedy interchange
    Repair Yes No
    Reproduction selection Tournament Tournament
    Survival selection Elitist Crowding distance operator
  • Table A1   Multiplication factors of the average results with different running settings and different numbers of selected sites on each dataset. The values highlighted in bold font are plotted in Figure 3
    $p$ KöerkelGalv ao100Galv ao150
    A B C A B CA B C
    10 0.74 0.98 0.95 0.82 0.99 1.00 0.83 1.00 1.00
    110.800.980.940.821.001.000.831.001.00
    12 0.76 0.980.94 0.82 1.00 1.00 0.81 1.001.00
    130.740.980.930.82 1.001.00 0.81 1.00 1.00
    140.76 0.98 0.93 0.83 1.00 1.00 0.811.001.00
    150.72 1.000.93 0.83 1.00 1.00 0.831.001.00
    160.780.980.92 0.83 1.00 1.00 0.82 1.00 1.00
    170.76 0.99 0.93 0.87 1.00 1.00 0.81 1.00 0.99
    18 0.77 0.99 0.94 0.85 1.00 1.000.80 1.00 0.99
    190.78 0.99 0.930.87 1.00 1.00 0.81 0.99 0.99
    20 0.78 0.980.920.87 1.00 1.00 0.810.990.99

    A: setting (20, 1) to setting (20, 100); B: setting (20, 100) to setting (220, 100); C: setting (20, 100) to setting (20, 1100).

  • Table A2   Multiplication factors of the standard deviations for different running settings and different numbers of selected sites on each dataset. The values highlighted in bold are plotted in Figure 3
    $p$ KöerkelGalv ao100Galv ao150
    A B C A B CA B C
    10 0.12 0.49 0.68 0.33 r
    0.10 0.52 0.09 1.11 0.71
    11 0.08 1.31 0.41 0.13 0.10 0.41 0.07 1.12 1.13
    12 0.11 0.720.62 0.370.38 0.360.07 0.85 0.81
    130.07 0.87 0.53 0.18 0.14 1.02 0.13 0.77 0.64
    140.07 0.66 0.34 0.08 0.04 0.16 0.20 0.41 0.24
    15 0.12 0.87 0.40 0.06 0.22 0.06 0.07 0.93 0.69
    16 0.18 0.46 0.26 0.04 0.34 0.42 0.08 0.71 1.16
    17 0.16 0.96 0.58 0.03 1.522.40 0.24 0.51 0.56
    18 0.16 0.81 0.90 0.02 2.09 1.67 0.18 0.70 0.70
    190.22 0.82 0.61 0.03 1.10 0.86 0.15 1.21 1.01
    20 0.26 0.40 0.60 0.09 0.75 0.36 0.31 0.91 0.73

    A: setting (20, 1) to setting (20, 100); B: setting (20, 100) to setting (220, 100); C: setting (20, 100) to setting (20, 1100).

  • Table 2   Comparison of the mean percentage deviation errors between Mucard and the algoriTheorem in . The small values in the first three rows are favorable
    Port1 Port2 Port3 Port4 Port5
    Row 1 0.01097 0.025240.01108 0.01933 0.00796
    Row 2 0.01560 0.036160.01680 0.033650.01066
    Row 3 0.010950.024640.007380.016720.00504
    Row 4 0.004630.010920.00573 0.014320.00270
    Row 5 $-$0.00002$-$0.00060$-$0.00369 $-$0.00260$-$0.00292