Improved firefly algorithm for the stochastic duration optimization of the ship maintenance
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摘要:
目的 针对船舶维修牵连工程复杂、空间干涉多、任务工时不确定，提出一种解决随机工时下船舶维修工期优化的模型和算法。 方法 基于情景理念设计维修工程的期望工期指标，构建该问题的数学模型；基于并行调度模式解码，提出一种改进萤火虫算法求解该模型；采用工程案例测试集和某船舶坞内维修工程实例，验证所提模型和算法的性能。 结果 某船舶坞内维修工程实例优化结果表明，其工期估值为89.6 d，置信度95.6%，与原方法工期相比减少13.4 d，可缩短13.1%的工期。 结论 改进的萤火虫算法可有效优化船舶维修工程的工期，为不确定条件下的船舶维修进度计划制定提供依据。 Abstract:Objective Ship maintenance projects have such characteristics as complex implicated tasks, space interference and uncertain task durations. A mathematical model and optimization algorithm are proposed to solve the stochastic duration optimization problem of ship maintenance. Method According to the scenario concept, this paper designs the expected duration as an objective function and constructs a mathematical model, then proposes an improved firefly algorithm to solve the problem. Finally, a group of benchmark projects and one dock maintenance engineering project are carried out to test the validity of the proposed method. Results The results show that the proposed method has the best performance in solving the problem. The optimized dock maintenance engineering project has 89.6 days of the expected duration and a 95.6% confidence level. Compared with the original method, the expected duration is reduced by 13.4 days and 13.1%. Conclusion This method can provide a basis for planning the schedules of ship maintenance projects. -
Key words:
- maintenance schedule /
- project scheduling problem /
- stochastic /
- scenario /
- improved firefly algorithm
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表 1 算法对比结果
Table 1. Comparison results of algorithm
序号 GA ABC PSO SOA FA J30_1 45.57 48.76 50.96 51.03 45.83 J30_2 48.66 48.33 47.71 48.21 49.79 J30_3 48.48 48.04 48.65 48.82 47.99 J30_4 62.42 63.62 64.01 63.99 63.46 J30_5 41.88 43.35 43.44 40.05 40.98 J30_6 47.91 48.32 52.02 49.21 48.30 J30_7 60.10 59.54 61.18 61.66 60.47 J30_8 56.06 55.71 57.49 55.87 55.34 J30_9 53.29 52.14 55.76 53.34 51.41 J30_10 46.48 47.35 51.33 47.87 47.53 J60_1 83.19 87.66 89.42 90.11 78.41 J60_2 80.10 83.12 79.95 80.03 74.05 J60_3 76.23 76.09 88.02 78.46 72.23 J60_4 91.40 94.77 97.65 95.2 92.01 J60_5 79.31 83.45 85.21 86.52 76.49 J60_6 66.76 71.71 71.33 70.27 66.37 J60_7 79.81 87.97 87.99 86.24 79.29 J60_8 88.76 98.42 93.67 91.56 81.84 J60_9 93.34 101.12 98.29 98.94 89.5 J60_10 83.34 89.07 89.66 84.82 81.28 J120_1 149.75 186.50 154.55 155.18 144.24 J120_2 155.47 192.88 155.69 162.83 149.00 J120_3 161.64 176.92 164.85 165.94 151.26 J120_4 136.75 166.60 152.29 131.76 133.04 J120_5 144.93 190.90 170.22 153.00 144.46 J120_6 114.88 143.79 125.51 127.43 112.17 J120_7 154.89 204.65 177.12 172.18 135.89 J120_8 140.21 171.43 151.39 149.58 147.66 J120_9 159.11 185.86 153.54 161.10 152.17 J120_10 147.62 176.66 152.52 164.14 138.65 运行时间/s 5 496 10 339 5 525 5 561 98 314 
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表 2 部分工程案例数据
Table 2. Part of the project case data
序号 名称 前置
条件工时数/d 工人 1 进坞 无 [8.5, 15.5] 32 2 左右螺旋桨桨叶清除污垢 1 [8.5, 15.5] 10 3 左右尾轴机械密封 2 [12.0, 20.0] 16 4 左右艉轴舱喷射泵 3 [0.6, 3.4] 2 5 左右艉轴舱 4 [1.3, 4.7] 2 6 舵机右舵轴轴承 1 6.0 8 7 舵叶 1 [8.5, 15.5] 14 8 1,2,3,4#液压 无 [12.0, 20.0] 10 9 舵机监控箱 无 [5.2, 10.8] 2 10 1号油缸放气阀 无 [0.1, 2.0] 1 11 应急舵进油阀 无 [0.1, 2.0] 1 12 舵机隔离旁通阀组 1 [2.0, 6.0] 2 13 舵机备用油箱 1 [0.6, 3.4] 2 14 舵机冷却水压力表 1 [0.1, 2.0] 1
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