Research Article
A Single-Machine Two-Agent Scheduling Problem by a Branch-and-Bound and Three Simulated Annealing Algorithms
Table 2
RPD of heuristic algorithms (
= 20~60).
| | Pro | | SA1 | SA2 | SA3 | CPU time | RPD | CPU time | RPD | CPU time | RPD | Mean | Std. | Mean | Std. | Mean | Std. | Mean | Std. | Mean | Std. | Mean | Std. |
| 20 | 0.25 | 25 | 0.0019 | 0.0051 | 0.45 | 1.44 | 0.0019 | 0.0051 | 0.41 | 1.19 | 0.0016 | 0.0047 | 0.51 | 1.75 | 50 | 0.0019 | 0.0051 | 1.39 | 2.67 | 0.0019 | 0.0051 | 1.87 | 5.51 | 0.0022 | 0.0055 | 0.89 | 1.88 | 75 | 0.0019 | 0.0051 | 2.86 | 4.81 | 0.0019 | 0.0051 | 4.96 | 6.80 | 0.0019 | 0.0051 | 2.01 | 3.66 | 0.5 | 25 | 0.0019 | 0.0051 | 0.02 | 0.07 | 0.0019 | 0.0051 | 0.00 | 0.01 | 0.0016 | 0.0047 | 0.01 | 0.06 | 50 | 0.0019 | 0.0051 | 0.51 | 0.81 | 0.0019 | 0.0051 | 0.39 | 0.67 | 0.0022 | 0.0055 | 0.51 | 0.78 | 75 | 0.0019 | 0.0051 | 1.05 | 1.52 | 0.0022 | 0.0055 | 1.19 | 2.08 | 0.0022 | 0.0055 | 1.30 | 2.03 | 0.75 | 25 | 0.0019 | 0.0051 | 0.00 | 0.00 | 0.0013 | 0.0043 | 0.00 | 0.00 | 0.0019 | 0.0051 | 0.00 | 0.00 | 50 | 0.0019 | 0.0051 | 0.00 | 0.00 | 0.0016 | 0.0047 | 0.00 | 0.00 | 0.0019 | 0.0051 | 0.00 | 0.00 | 75 | 0.0019 | 0.0051 | 0.50 | 0.58 | 0.0019 | 0.0051 | 0.58 | 0.75 | 0.0019 | 0.0051 | 0.34 | 0.55 |
| Average | 0.0019 | 0.0051 | 0.75 | 1.32 | 0.0018 | 0.0050 | 1.04 | 1.89 | 0.0019 | 0.0052 | 0.62 | 1.19 |
| 40 | 0.25 | 25 | 0.0066 | 0.0078 | 0.10 | 0.30 | 0.0072 | 0.0079 | 0.16 | 0.52 | 0.0066 | 0.0078 | 0.00 | 0.00 | 50 | 0.0072 | 0.0079 | 0.92 | 1.51 | 0.0078 | 0.0079 | 1.22 | 2.09 | 0.0072 | 0.0079 | 0.39 | 1.47 | 75 | 0.0078 | 0.0079 | 3.66 | 4.43 | 0.0084 | 0.0079 | 3.91 | 5.84 | 0.0081 | 0.0079 | 2.82 | 4.04 | 0.5 | 25 | 0.0066 | 0.0078 | 0.02 | 0.06 | 0.0066 | 0.0078 | 0.00 | 0.00 | 0.0066 | 0.0078 | 0.00 | 0.00 | 50 | 0.0075 | 0.0079 | 0.39 | 0.43 | 0.0078 | 0.0079 | 0.31 | 0.57 | 0.0078 | 0.0079 | 0.46 | 0.79 | 75 | 0.0084 | 0.0079 | 0.81 | 0.81 | 0.0091 | 0.0078 | 1.03 | 1.69 | 0.0091 | 0.0078 | 0.71 | 1.12 | 0.75 | 25 | 0.0066 | 0.0078 | 0.00 | 0.00 | 0.0063 | 0.0077 | 0.00 | 0.00 | 0.0063 | 0.0077 | 0.00 | 0.00 | 50 | 0.0063 | 0.0077 | 0.00 | 0.00 | 0.0063 | 0.0077 | 0.00 | 0.00 | 0.0063 | 0.0077 | 0.00 | 0.00 | 75 | 0.0072 | 0.0079 | 0.32 | 0.45 | 0.0078 | 0.0079 | 0.25 | 0.36 | 0.0081 | 0.0079 | 0.25 | 0.31 |
| Average | 0.0071 | 0.0078 | 0.69 | 0.89 | 0.0075 | 0.0078 | 0.76 | 1.23 | 0.0073 | 0.0078 | 0.51 | 0.86 |
| 60 | 0.25 | 25 | 0.0159 | 0.0022 | 0.07 | 0.20 | 0.0178 | 0.0055 | 0.09 | 0.23 | 0.0147 | 0.0037 | 0.02 | 0.11 | 50 | 0.0175 | 0.0051 | 1.48 | 2.72 | 0.0197 | 0.0069 | 1.20 | 1.88 | 0.0163 | 0.0044 | 0.28 | 0.88 | 75 | 0.0197 | 0.0069 | 2.38 | 2.51 | 0.0219 | 0.0077 | 3.74 | 5.10 | 0.0206 | 0.0074 | 2.58 | 4.10 | 0.5 | 25 | 0.0147 | 0.0037 | 0.01 | 0.03 | 0.0147 | 0.0037 | 0.00 | 0.00 | 0.0144 | 0.0043 | 0.00 | 0.00 | 50 | 0.0175 | 0.0060 | 0.39 | 0.57 | 0.0184 | 0.0061 | 0.27 | 0.35 | 0.0181 | 0.0066 | 0.23 | 0.42 | 75 | 0.0209 | 0.0075 | 0.66 | 1.03 | 0.0231 | 0.0079 | 0.62 | 0.73 | 0.0222 | 0.0078 | 0.66 | 0.90 | 0.75 | 25 | 0.0141 | 0.0047 | 0.00 | 0.00 | 0.0141 | 0.0047 | 0.00 | 0.00 | 0.0141 | 0.0047 | 0.00 | 0.00 | 50 | 0.0141 | 0.0047 | 0.00 | 0.00 | 0.0141 | 0.0047 | 0.00 | 0.00 | 0.0141 | 0.0047 | 0.00 | 0.00 | 75 | 0.0175 | 0.0051 | 0.21 | 0.27 | 0.0197 | 0.0069 | 0.22 | 0.28 | 0.0194 | 0.0067 | 0.21 | 0.25 |
| Average | 0.0169 | 0.0051 | 0.58 | 0.82 | 0.0182 | 0.0060 | 0.68 | 0.95 | 0.0171 | 0.0056 | 0.44 | 0.74 |
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