﻿ 基于蚁群算法和极限学习机的舰船电子装备备件优化模型
 舰船科学技术  2022, Vol. 44 Issue (5): 158-161    DOI: 10.3404/j.issn.1672-7649.2022.05.034 PDF

1. 华中农业大学 信息学院，湖北 武汉 430070;
2. 河南工业职业技术学院 电子信息工程学院，河南 南阳 473000

Optimization model of ship electronic equipment spare parts based on ant colony algorithm and limit learning machine
LI Qiao-jun1,2
1. School of Information, Huazhong Agricultural University, Wuhan 430070, China;
2. School of Electronic and Information Engineering, Henan Polytechnic Institute, Nanyang 473000, China
Abstract: According to the use characteristics of ship electronic equipment obtained from the analysis, a spare parts optimization model of ship electronic equipment is established, which includes two parts: fixed reliability spare parts optimization and fixed cost spare parts optimization. Taking the ratio of reliability to cost as the objective function, the ant colony algorithm is used to improve the limit learning machine to solve the model, taking the initial weight and threshold of the limit learning machine as the crawling path node of each ant in the ant colony algorithm, the global optimal solution is obtained through the optimal path search to realize the optimization of ship electronic equipment spare parts. The experimental results show that when the diversity of the results obtained from the model is high and the ship reliability is certain, the total cost of spare parts in stock is always kept at the lowest; This method can effectively ensure the availability of electronic equipment at any time during the whole ship navigation.
Key words: ant colony     extreme learning machine     ship electronic equipment     spare parts optimization     fixed reliability     objective function
0 引　言

1 蚁群算法和极限学习机的舰船电子装备备件优化模型 1.1 舰船电子装备备件优化模型构建 1.1.1 舰船电子装备使用特点分析

1）舰船电子装备能够循环利用，每次利用后若想使其恢复到规定状态[6]，仅需进行适当的维护保养即可。

2）对舰船电子装备的使用频率进行约束，是因为各电子装备均具有有限的使用寿命，假设各舰船电子装备最大使用次数用 ${N_0}$ 描述，当超过该值时，则停止使用对应的舰船电子装备。

3）舰船电子装备故障率用 $\lambda$ 描述，在一次使用时电子装备的寿命满足 $\lambda$ 的指数分布[7]N为舰船电子装备使用次数用，N的分布率表示为 ${p^n} = \Pr \left\{ {N = n} \right\}$ 。一般情况下，N满足以下概率分布：

 $P\left( {N = n\left| {N \leqslant {N_0}} \right.} \right) = \frac{{{\rho ^n} - {\rho ^{n + 1}}}}{{1 - {\rho ^{{N_0} + 1}}}} ，$ (1)

N0取较大值的条件下，使用舰船电子装备的概率可以近似为 $\rho$

1.1.2 舰船电子装备备件优化模型

 $\begin{split} {R_i} =& \sum\limits_{j = 0}^{{x_i}} {{e^{ - {\lambda _i}T}}\frac{1}{{j!}}\lambda _i^j{T^j}} = \\ &{e^{ - {\lambda _i}T}} \left[ {1 + {\lambda _i}T + \left( {\frac{1}{{2!}} + \cdots + \frac{1}{{{x_i}!}}} \right)\left( {\lambda _i^2{T^2} + \cdots + \lambda _i^{{x_i}}{T^{{x_i}}}} \right)} \right] 。\end{split}$ (2)

${R_s}$ 为整个舰船系统的可靠度，计算公式为：

 ${R_s} = \prod\limits_{i = 1}^n {{R_i}} = \prod\limits_{i = 1}^n {\sum\limits_{j = 0}^{{x_i}} {{e^{ - {\lambda _i}T}}\frac{1}{{j!}}\lambda _i^j{T^j}} }，$ (3)

1）定可靠度备件优化模型

 $\begin{gathered} \min {C_s} = \sum\limits_{i = 1}^n {{c_i}{x_i}} ，\hfill \\ {\rm{ s.t.}}\mathop {}\limits_{} {R_s} \geqslant {R_0} ，\hfill \\ \end{gathered}$ (4)

2）定费用备件优化模型

 $\max {R_s}\mathop {}\limits_{} {\rm{s.t.}}\mathop {}\limits_{} \sum\limits_{i = 1}^n {{c_i}{x_i} \leqslant {C_0}}，$ (5)

 $\begin{split} &\max \frac{{{R_s}}}{{{C_s}}}，\hfill \\ & {\rm{s.t}}\mathop {}\limits_{} {C_s} = \sum\limits_{i = 1}^n {{c_i}{x_i}}，\hfill \\ &{R_s} = \prod\limits_{i = 1}^n {\prod\limits_{j = 0}^{{x_i}} {{e^{ - {\lambda _i}T}}\frac{1}{{j!}}\lambda _i^j{T^j}} } 。\hfill \end{split}$ (6)
1.2 基于蚁群算法和极限学习机的模型求解 1.2.1 基于极限学习机的模型求解

 $\begin{split} &\min \left( {\frac{{\beta _L^T{\beta _L} + \gamma {\varepsilon ^T}\varepsilon }}{2}} \right)，\hfill \\ & {\rm{s.t.}}\mathop {}\limits_{} {t_j} = \sum\limits_{i = 1}^L {{\beta _i}f\left( {{a_i}{x_j} + {c_i}} \right) - {\varepsilon _i}}。\hfill \end{split}$ (7)

 $L\left( {w,\varepsilon ,{\beta _L}} \right) = \frac{{\beta _L^T{\beta _L} + \gamma {\varepsilon ^{\rm{T}}}\varepsilon }}{2} - w{H_L}{\beta _L} + T + \varepsilon。$ (8)

 $\left\{ \begin{gathered} L/{\beta _L} \to \beta _L^T = w{H_L} ，\hfill \\ L/\varepsilon \to \gamma {\varepsilon ^{\rm{T}}} + w = 0，\hfill \\ L/w \to {H_L}{\beta _L} - \left( {T + \varepsilon } \right) = 0。\hfill \\ \end{gathered} \right.$ (9)

 ${\beta _L} = \frac{{\gamma H_L^TT}}{{\gamma H_L^T{H_L} + {I_L}}}。$ (10)

 $t = \sum\limits_{i = 1}^L {{\beta _i}f\left( {{a_i}x + {c_i}} \right)}。$ (11)

1.2.2 基于蚁群算法优化的极限学习机

1）参数初始化

Y(0)为初始种群，其内包含的蚂蚁数量为Mmgn分别为进化代数和节点数；fiti为路径i的适应度；两节点ij的启发度代表启发因子 ${\eta _{ij}}$ ，其求解过程表示为 ${\eta _{ij}} = \dfrac{1}{{{d_{ij}}}}$ ；针对边(i,j)，其中的信息素量和蚂蚁k残留的信息素量分别用 ${\tau _{ij}}$ $\Delta \tau _{ij}^k$ 描述； $\rho$ 为信息素量蒸发系数； $P_{ij}^k\left( t \right)$ 为第k只蚂蚁在t时刻从节点i爬行到节点j的几率。

2）适应度计算

 $\begin{split} &fit\left( y \right) = {\left[ {{y_1},{y_2},\cdots,{y_M}} \right]^{\rm{T}}}，\hfill \\ & {y_i} = \frac{1}{m}\sum\limits_{j = 1}^m {O_j^2 - 2{O_j}{T_j} + T_j^2} 。\hfill \end{split}$ (12)

3）利用适应度完成信息素的释放

 $\begin{split} &{\tau }_{ij}\left(t+n\right)={\tau }_{ij}\left(t\right)-\rho {\tau }_{ij}\left(t\right)+\Delta {\tau }_{ij}，\\ & \Delta {\tau }_{ij}={\displaystyle \sum _{k=1}^{m}\Delta {\tau }_{ij}^{k}}，\\ & \Delta {\tau }_{ij}^{k}=\left\{\begin{array}{l}Q/fi{t}_{k},{{\displaystyle }}^{}蚂蚁k行走经过\left(i,j\right)，\\ 0,{{\displaystyle }}^{}{{\displaystyle }}^{}{{\displaystyle }}^{}蚂蚁k行走不经过\left(i,j\right)。\end{array}\right.\end{split}$ (13)

4）蚁群移动可通过信息素完成

 $P_{ij}^k = \frac{{{{\left[ {{\tau _{ij}}\left( t \right){\eta _{ij}}\left( t \right)} \right]}^{\alpha \beta }}}}{{\beta \displaystyle \sum\limits_{s \in {J_k}\left( i \right)} {{{\left[ {{\tau _{is}}\left( t \right)} \right]}^\alpha }\left[ {{\eta _{is}}\left( t \right)} \right]} }} 。$ (14)

5）将当前迭代的路径及最佳路径保存

2 结果分析

 图 1 库存备件总费用和舰船可靠度优化结果 Fig. 1 Optimization results of total cost of spare parts in stock and ship reliability

 图 2 舰船电子装备的任务可用度结果 Fig. 2 Mission availability results of ship electronic equipment
3 结　语

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