三维自动布局系统的研究与应用
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摘要
布局问题就是将一些物体按一定要求合理地放置在一个空间内，且使所占空间尽量地小。其中，物体称为布局物体，空间称为布局容器。三维布局问题广泛地用于机械生产和交通运输等行业当中。三维布局问题属于组合最优化问题和NP完全问题，具有高度复杂性，用一般的数学方法根本无法求解，目前解决三维布局问题多为各种启发式方法，本文在对启发式方法进行深入探讨的基础上，采用了用于解决一般三维布局问题的模拟退火算法作为布局系统的操作算法。
模拟退火算法(Simulated annealing，SA)是模拟热力学中经典粒子系统的降温过程，来求解规划问题的极值。模拟退火法(Kirkpatrick等，1983)是一种随机的优化技术，它是零阶算法，不需要导数信息，广泛地用于解决连续的、有序离散及多模态优化问题。本文对传统的SA算法进行了改进，在算法的搜索策略和变动策略中应用了启发式方法，由定邻域搜索变为变邻域搜索，平移和旋转变动交替进行，既保证了解的精度又提高了其收敛速度，取得了良好的布局效果。
本文基于ObjectARX技术，以AutoCAD数据库为操作背景，用VC++作为开发语言，根据模拟退火法构建了多目标函数，通过面向对象技术对布局类进行了特征描述，设计了一系列的操作模块和干涉检验的算法，完成了对无约束的任意形状三维实体的布局。布局系统主要由用户输入模块、自动布局模块、布局结果输出模块、布局数据显示等模块组成。
在任意三维实体布局系统的基础上，本文对机床主轴箱系统的特征以类的形式进行了描述，将该布局系统应用于机床主轴箱的实例验证当中(在主轴箱实例验证中，又特别增加了布局约束模块)，通过将齿轮简化为圆柱体，在AutoCAD环境下建立了主轴箱的CAD模型，增加了任意实体布局系统中所没有的同轴约束，并对有啮合要求的实体进行变动限制，这种约束和限制是根据用户实时选择有相关要求的齿轮对来实现的，使布局实体在有约束的情况下，达到布局密度和布局总厚度等衡量指标的优化值。
文章最后，总结了全文的工作并对进一步的研究作了展望。
The packing problem is to put some objects into a defined space according to the specified need and to make the occupation as small as possible. The object is called packing object and the space is called container. Three-dimensional packing (TDP) is a combinatorial optimization and HP-complete problem and applied widely to the mechanical manufacture and traffic transportation industries. Up to now there are varieties of heuristic algorithms to solve the TDP because of its high complication, we discuss the heuristic algorithm deeply in this paper and apply the simulated annealing (SA) algorithm to the packing system.
SA algorithm is to simulate the classical particles in the Thermodynamics in order to seek the extreme value of the design problem. SA is a stochastic optimization technique and a zero-order algorithm requiring no derivative information and has been used extensively to solve continuous, ordered discrete and multi-modal optimization. In this paper we improved the traditional SA algorithm, and the heuristic algorithm is applied to the search and move schedule. The neighborhood is changed from the fixable to the alterable, the operation of moving and rotating is alternate, and the precision of the solution is then guaranteed as well as its convergence speed. We have applied the improved SA to test the three-dimensional packing problem and received a good result.
In this paper, a generic objective function consisting of multiple design objectives according to SA is formed. The TDP system is based on the ObjectARX technique, AutoCAD database and the VC++ development language. The characteristics of the configuration class is described based on the object-oriented technology and series of modules and algorithm of detecting interference are designed. In the end, the packing result without constraints of the arbitrary geometry component is realized. The packing system consists of the following modules: the input module, the automatic packing module, the output of the packing result module, and the output of the packing datum module etc.
On the basis of the above-mentioned packing system, the characters of the gear box is described in the form of "class", the packing system is then applied to test the example of the gear box (in the gear box verification, we add a constraint module to deal with the specified problem). The gears are simplified to cylinders and the module is formed in AutoCAD. At the end of the paper, we get an optimal value of the packing density and the whole thickness by
adding the constraints of gears with the same axes, and constrain the moves of the gears meshed with each other, which are not appeared in the former system and can be selected by the user. At last, a simple prospect for the possible application is given.
模拟退火算法(Simulated annealing，SA)是模拟热力学中经典粒子系统的降温过程，来求解规划问题的极值。模拟退火法(Kirkpatrick等，1983)是一种随机的优化技术，它是零阶算法，不需要导数信息，广泛地用于解决连续的、有序离散及多模态优化问题。本文对传统的SA算法进行了改进，在算法的搜索策略和变动策略中应用了启发式方法，由定邻域搜索变为变邻域搜索，平移和旋转变动交替进行，既保证了解的精度又提高了其收敛速度，取得了良好的布局效果。
本文基于ObjectARX技术，以AutoCAD数据库为操作背景，用VC++作为开发语言，根据模拟退火法构建了多目标函数，通过面向对象技术对布局类进行了特征描述，设计了一系列的操作模块和干涉检验的算法，完成了对无约束的任意形状三维实体的布局。布局系统主要由用户输入模块、自动布局模块、布局结果输出模块、布局数据显示等模块组成。
在任意三维实体布局系统的基础上，本文对机床主轴箱系统的特征以类的形式进行了描述，将该布局系统应用于机床主轴箱的实例验证当中(在主轴箱实例验证中，又特别增加了布局约束模块)，通过将齿轮简化为圆柱体，在AutoCAD环境下建立了主轴箱的CAD模型，增加了任意实体布局系统中所没有的同轴约束，并对有啮合要求的实体进行变动限制，这种约束和限制是根据用户实时选择有相关要求的齿轮对来实现的，使布局实体在有约束的情况下，达到布局密度和布局总厚度等衡量指标的优化值。
文章最后，总结了全文的工作并对进一步的研究作了展望。
The packing problem is to put some objects into a defined space according to the specified need and to make the occupation as small as possible. The object is called packing object and the space is called container. Three-dimensional packing (TDP) is a combinatorial optimization and HP-complete problem and applied widely to the mechanical manufacture and traffic transportation industries. Up to now there are varieties of heuristic algorithms to solve the TDP because of its high complication, we discuss the heuristic algorithm deeply in this paper and apply the simulated annealing (SA) algorithm to the packing system.
SA algorithm is to simulate the classical particles in the Thermodynamics in order to seek the extreme value of the design problem. SA is a stochastic optimization technique and a zero-order algorithm requiring no derivative information and has been used extensively to solve continuous, ordered discrete and multi-modal optimization. In this paper we improved the traditional SA algorithm, and the heuristic algorithm is applied to the search and move schedule. The neighborhood is changed from the fixable to the alterable, the operation of moving and rotating is alternate, and the precision of the solution is then guaranteed as well as its convergence speed. We have applied the improved SA to test the three-dimensional packing problem and received a good result.
In this paper, a generic objective function consisting of multiple design objectives according to SA is formed. The TDP system is based on the ObjectARX technique, AutoCAD database and the VC++ development language. The characteristics of the configuration class is described based on the object-oriented technology and series of modules and algorithm of detecting interference are designed. In the end, the packing result without constraints of the arbitrary geometry component is realized. The packing system consists of the following modules: the input module, the automatic packing module, the output of the packing result module, and the output of the packing datum module etc.
On the basis of the above-mentioned packing system, the characters of the gear box is described in the form of "class", the packing system is then applied to test the example of the gear box (in the gear box verification, we add a constraint module to deal with the specified problem). The gears are simplified to cylinders and the module is formed in AutoCAD. At the end of the paper, we get an optimal value of the packing density and the whole thickness by
adding the constraints of gears with the same axes, and constrain the moves of the gears meshed with each other, which are not appeared in the former system and can be selected by the user. At last, a simple prospect for the possible application is given.
引文
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[2] Dowsland K A, Dowsland W B. Packing problems. European Journal of Operational Research. 1992, 56: 2-14.
[3] Simon Szykman. Optimization as a Driver for Design Space Exploration. Proceedings of the Optimization in Industry Conference, March 23-27, 1997, Palm Coast, Florida.
[4] Szykman S, Cagan J. A simulated annealing approach to three-dimensional component packing. ASME Journal of Mechanical Design. 1995, 117 (2 (A)): 308-314.
[5] Szykman S, Cagan J. Synthesis of optimal non-orthogonal routes. ASME Journal of Mechanical Design. 1996, 118 (3): 419-424.
[6] Kolli A, Cagan J, R A. Packing of genetic three-dimensional components based on multi-resolution modeling. In Proceedings of the 1996 ASME Design Engineering Technical Conferences and Computers in Engineering Conference: Design Automation Conference, 96-DETC/DAC-1479, Irbine, CA, 1996: 18-22.
[7] Cagan J, Degentesh D, Su Yin. A simulated annealing-based algorithm using hierarchical models for general three-dimensional component layout. Computer-Aided Design. 1998, 30 (10): 781-790.
[8] Loris Faina. A global optimization algorithm for the three-dimensional packing problem. European journal of operational research.2000, 126 (2): 340-354.
[9] Szykman S, Cagan J. Constrained three-dimensional component layout using simulated annealing. ASME Journal of Mechanical Design. 1997, 119: 28-35.
[10] Su Yin, Jonathan Cagan. An extended pattern search algorithm for three-dimensional component layout. Journal of Mechanical Design. 2001, 122 (1): 102-108.
[11] Teng Hong-fei, Sun Shou-lin, Liu De-quan et al. Layout optimization for the objects located within a rotating vessel—a three-dimensional packing problem with behavioral constraints. Computers & operations research. 2001, 28 (6): 521-535.
[12] Teng Hong-fei, Sun Zhi-guo, Liu De-quan et al. Complex layout optimization problem: layout scheme design of spacecraft module. Journal of Dalian University of Technology.2001, 41(5): 581-588.
[13] Tiziana Calamoneri, Annalisa Massini. Optimal three-dimensional layout of interconnection networks. Theoretical computer science.2001, 255(1-2): 263-279.
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