﻿ 基于物理规划的航空保障多目标优化模型
 计算机系统应用  2001, Vol. 29 Issue (9): 184-190 PDF

1. 海军参谋部办公室, 北京 100071;
2. 海军航空大学 青岛校区, 青岛 266041

Multi-Objective Optimization Model of Aviation Equipment Support Based on Physical Programming Algorithm
SHI Hai-Qing1, YANG Hang2, ZHAO Dong-Mei2
1. Office of Naval Staff, Beijing 100071, China;
2. Qingdao Campus, Naval Aeronautical University, Qingdao 266041, China
Abstract: Together with the particle swarm optimization algorithm, a physical programming-based multi-objective optimization model is developed to seek the optimal strategy for spare parts arrangement. The levels of satisfaction and the preference functions as well as the aggregate objective function for the supportability are designed which can reflect the preference of decision makers. With the proposed optimization method, the computational burden in large-scale multi-objective design problems can be greatly reduced. Meanwhile, the results from the proposed method are compared with that of single-objective optimization, demonstrating the effectiveness of the proposed model.
Key words: aviation equipment support     multi-objective optimization     physical planning     particle swarm optimization     functional framework

1 优化目标

 $A=\dfrac{\displaystyle\sum\limits_1^n{T_u}}{{n{T_0}}}$ (1)

 ${W_0} = {W_1} + {W_2} + {W_3}$ (2)
 ${W_3} = nkt$ (3)
 ${W_2} = \sum\limits_1^{{T_0}} {\sum\limits_1^i {{r_{i1}}} } + \sum\limits_1^{{T_0}} {\sum\limits_1^i {{r_{i2}}} }$ (4)

2 优化流程

 图 1 部件失效过程伪代码

(1)所有决策变量取最小值. 在这种情况下输出变量的结果如表2所示, 团修理厂、军区仓库决策备件数的变化情况和观测时间内的飞机状态变化如图3所示. 在这情况下, 虽然这种情况下, 总费用很低, 但是任务a的成功率、任务b的成功率和任务c的成功率的结果很不令人满意. 因为没有备用飞机, 团修理厂和军区仓库的积压库存量也很多, 造成了不必要的库存损失.

(2)所有决策变量取最大值. 在这种情况下输出变量的结果如表3所示, 团修理厂、军区仓库决策备件数的变化情况和观测时间内的飞机状态变化如图4所示. 在这情况下, 任务a的成功率、任务b的成功率和任务c的成功率很高, 但是总费用也很高. 实际情况中可能并没有这样的资金支持来保障这样的备件方案. 而且因为备用飞机数的增加, 系统的可用度也受到了影响. 团修理厂和军区仓库的库存量很高, 同样造成了不必要的库存损失.

 图 2 部件维修过程伪代码

 图 3 最少备件方案下备件数和飞机状态变化图

 图 4 最多备件方案下备件数和飞机状态变化图

 图 5 指标体系优化流程

 $\begin{array}{*{20}{c}} {{\rm{Min}}}&{g = \lg \left\{ {\dfrac{1}{{{n_{sc}}}}\displaystyle \sum\limits_{i = 1}^{{n_{sc}}} {\overline {{g_i}} } [{g_i}(x)]}\right\} } \end{array}$ (1)
 ${\rm{s.t. }}\;\;\;{g_5} \le {g_{55}}$ (2)
 ${g_i} \ge {g_{i5}},{\rm{ }}i = 1,2,3,4$ (3)
 图 6 粒子群算法流程图

3 计算分析

 图 7 适应度曲线

 图 8 备件数和可用飞机数量变化

 图 9 任务a成功率偏好函数

 图 10 任务b成功率偏好函数

 图 11 任务c成功率偏好函数

 图 12 可用度偏好函数

 图 13 总费用偏好函数

4 性能比较

 图 14 成功率a单目标优化

 图 15 成功率b单目标优化

 图 16 成功率c单目标优化

5 结论与展望

 图 17 可用度单目标优化

 图 18 总费用单目标优化

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