﻿ 基于遗传模拟退火算法的舰船分段装载顺序优化设计
 舰船科学技术  2022, Vol. 44 Issue (5): 150-153    DOI: 10.3404/j.issn.1672-7649.2022.05.032 PDF

Sequence optimization design of ship sectional loading based on genetic simulated annealing algorithm
ZHANG Xiao-ling
Henan Wisdom Education and Intelligent Technology Application Engineering Technology Research Center, Zhengzhou 451460, China
Abstract: In order to reduce the frequency of interference and tool change, a sequence optimization method based on genetic simulated annealing algorithm was designed. Piecewise load sequence optimization mathematical model is built with, and set up the contact relation between the parts and components assembly sequence feasibility of intervention, by using the genetic simulated annealing algorithm by selecting fitness function, selection section load factor, crossover and mutation operation, and simulated annealing processing steps, such as solving block loading sequence optimization mathematical model of the objective function. The optimization results of ship loading sequence are obtained. Experimental results show that the optimal crossover probability and variation probability are 0.9 and 0.1, respectively. After the optimization, the cumulative interference times and the cumulative tool replacement times of ship loading sequence are reduced three times and four times, respectively. The optimization effect is significant.
Key words: genetic simulated annealing     ship sectional loading     sequential optimization design     mathematical model     feasibility conditions
0 引　言

1 舰船分段装载的顺序优化方法 1.1 分段装载顺序优化数学模型建立

 $\mathrm{min}S=({\sigma }_{1}+{\sigma }_{2}+{\sigma }_{3}+{\sigma }_{4})\cdot({f}_{1}+{f}_{2}+{f}_{3}+{f}_{4}) 。$ (1)

1.2 装配顺序可行性条件设置

 $A{S_m} = \left\{ {{Q_1},{Q_2}, \cdots ,{Q_m}} \right\} 。$ (2)

1）装载顺序零件接触关系可行性设置

$i$ 个分段零件装载之初，先考虑与该分段零件其他存在关联关系分段零件是否已经装载，若是，则第 $i$ 个分段零件在该装载顺序较为合理。反之则认为第 $i$ 个分段零件在其装载顺序内不可行[7]。舰船在分段装载时，其第一个分段零件无须考虑上述接触关系[8]，但其后续的每个零件均需考虑与之存在关联关系的是否已经装载。在判断舰船分段零件之间的关联关系时，利用矩阵形式描述，其表达式如下：

 ${M_A} = {\left[ {{M_{ij}}} \right]_{N\cdot N}} 。$ (3)

 ${M_i} = {M_i}{Q_1} \cup {M_i}{Q_2} \cup {M_i}{Q_3} \cup \cdots \cup {M_i}{Q_m}。$ (4)

2）装载顺序干涉可行性设置

 $Y = \left\{ {{b_{ijX}},{b_{ijY}},{b_{ijZ}},{b_{jiX}},{b_{jiY}},{b_{jiZ}}} \right\} 。$ (5)

 ${b_{dk}} = {\left[ {{b_{ij{d_k}}}} \right]_{N*N}} 。$ (6)

 $\left\{ \begin{gathered} + {b_{i{d_k}}} = {b_{i{Q_1}{d_k}}} \cup {b_{i{Q_2}{d_k}}} \cup \cdots {b_{i{Q_m}{d_k}}}，\hfill \\ - {b_{i{d_k}}} = {b_{{Q_1}i{d_k}}} \cup {b_{{Q_2}i{d_k}}} \cup \cdots {b_{{Q_m}i{d_k}}} 。\hfill \\ \end{gathered} \right.$ (7)

1.3 基于遗传模拟退火算法的分段装载顺序优化数学模型求解

1）适应度函数选取

 $AU = \sum\limits_{i = 1}^n {({U_{{x_{i - 1}},{x_i}}})}，$ (8)
 ${U_{{x_{i - 1}},{x_i}}} = {\alpha _i} + {\beta _i} + {\gamma _i} + {\omega _i} 。$ (9)

 $Fitness({Q_i}) = \sum\limits_{i = 1}^N {4i - \sum\limits_{i = 1}^N {({\alpha _i} + {\beta _i} + {\gamma _i} + {\omega _i})} }。$ (10)

2）分段装载因子选择

 ${E_i} = \frac{{{h_i}}}{{\displaystyle\sum\limits_{j = 1}^N {{h_j}} }}。$ (11)

 $\sum\limits_{j = 0}^{i - 1} {{E_j}} \leqslant r \leqslant \sum\limits_{j = 0}^i {{E_j}} 。$ (12)

3）交叉与变异操作

4）模拟退火处理

 ${E_a} = \left\{ \begin{gathered} 1,{F_i}(O) < {F_i}(O)，\hfill \\ \exp \left[ {\frac{{{F_i}(O)}}{T} - \frac{{{F_j}(O)}}{T}} \right],{F_i}(O) \geqslant {F_i}(O)。\hfill \\ \end{gathered} \right.$ (13)

 $O = O\cdot \xi，$ (14)

5）建立初始因子群并设置迭代终止条件。利用优先级函数和随机数函数各生成一半初始因子群，其中将随机数生成的因子作为优先级，其计算公式如下：

 ${E_i} =\left (\frac{{{l_i}{p_r}}}{{{w_i}}} + \frac{{{l_i}\cdot {w_i}\cdot {E_a}}}{{{w_i}}}\right)。$ (16)

2 实验结果分析

 图 1 自升式起重船船底边仓组件结构示意图 Fig. 1 structural diagram of bottom side bin components of jack up crane ship
2.1 交叉与变异概率确定

 图 2 交叉概率和变异概率确定结果 Fig. 2 Determination results of crossover probability and mutation probability
2.2 分段装载的顺序优化测试

 图 3 不同分段装载零件数量时优化前后所用时间 Fig. 3 time before and after optimization when loading parts in different sections
3 结　语

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