人机交互的演化设计方法及其在航天器舱布局方案设计中的应用
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摘要
本论文主要研究复杂工程系统总体布局方案设计的理论方法及其在大型航天器舱布局优化设计中的应用。
航天器舱布局方案优化设计是研究在满足各种工程技术条件的前提下，如何将各种仪器和设备最优的布置在航天器舱体内(或外)，使得总体布局的某一项或几项评价指标达到最优。这是一个亟待解决而又未很好解决的重要工程课题。布局问题的NP-困难性和航天器设计本身的巨大复杂性使得该问题的解决既有理论上的开拓性和挑战性，又存在工程实践上的艰难性和复杂性。
航天器舱布局方案优化设计属带性能约束的三维布局优化问题，属具有不确定性、高度非线性、既有定性又有定量问题的复杂工程系统问题，单纯依靠人或计算机算法(包括人工智能技术)去解决都是非常困难的。1991年Lenat、Feigenbaum提出的人机合作(Man-Machine Synergy)和同年钱学森、戴汝为等提出的人机结合(Human-Machine Cooperation)思想和方法论，被认为是21世纪解决复杂工程问题的重要途径、自动化设计的重要发展方向，但其可操作性问题一直未很好解决。本论文以航天器舱布局方案优化设计为应用背景，遵循“人机合作”、“人机合作”思想，充分发挥工程技术人员和现代计算机技术各自特长，提出人机交互的遗传算法，使“人”“机”在算法层面有机结合并具有可操作性；进而结合网络协同设计技术，给出一套以人机交互遗传算法为基础的人机交互演化协同设计理论方法，发挥多人设计和决策的优越性，以缓解组合最优化计算量过大(组合爆炸)问题，并增强上述理论方法的工程实用性。大量数值计算以及在航天器舱方案设计中的应用表明了本论文理论方法的可行性和有效性。
本论文的主要工作如下：
1．稳定、收敛、高效的优化算法是求解复杂布局优化问题的基础，是布局优化理论研究发展水平的重要标志。本论文提出一种改进的粗粒度遗传算法——混合粗粒度遗传算法，该算法将各染色体按适应度函数值大小排序并分组，对不同的染色体分组采用不同的惩罚系数、交叉算子与变异算子，并在进化过程中采用同种互斥和最优解保留策略。大量算例表明，本算法优于经典粗粒度遗传算法。该混合粗粒度遗传算法是实现本论文人机结合演化设计思想的算法基础。
2．为充分发挥人和计算机各自的特长，使“人机合作”与“人机结合”思想在工程应用中具有可操作性，提出人机交互的遗传算法。该算法将人
大连理工大学博上学位论文 摘要
工设计的个体作为初始染色体群体的组成部分，并在遗传运算过程中实时
地将人工设计的新个体加入到染色体群体中，以代替群体中的较差个体，
参与遗传运算（复制、交叉、变异X实现人与算法在基因层面的结合。该
人机交互遗传算法系统是实现网络下演化协同设计的基本单元。
3．将人机交互的遗传算法与网络协同设计技术相结合，考虑工程因素，
形成网络环境下的人机交互演化协同设计系统，以简化传统协同设计中数
据库构建，解决增强协同人之间柔性协同问题。该系统分为设计层和决策
层两个模块，采用S。eke网络编程技术，通过客户机用＆务器模式，实现进
程间的异步通信；同时采用ODBC数据库技术，利用综合评价仲裁系统和
人机交互的思想进行协同设计。
4．人机交互演化设计方法在航天器舱布局方案设计中的应用。为达到
本论文理论方法在多舱段大型航天器舱布局优化中的工程实用化，本论文
采取如下策略：首先将待布物模型化，简化为规则形状的几何体，建立返
回式人造卫星回收舱和空间站舱布局优化的数学模型和仿真模型的复合模
型；利用人机交互的遗传算法和人机交互演化协同进行布局优化设计，给
出航天器舱优化布局的“骨架”；利用美国的Prohogineer软件将模型中待
布物还原成实际形状的物体，进行模装布局和性能仿真；利用人机交互方
法进行布局调整，直至得到满意工程布局。最后将上述方法和策略应用于
我国卫星舱和空间实验站总体布局方案设计预研工作，同时也是对本文理
论方法的验证。
本课题属国家自然科学基金项目“复杂布局自动化设计理论、方法及
其应用”（N＊69974002L“人机结合演化协同及在航天器舱总装方案设
计中的应用”（N趴60073030和国家‘℃63”计划航天领域高技术项目：“多
舱段大型航天器（载人飞船、空间站）三维动力布局优化研究”（N。
863205石S人本课题涉及到航天器设计、机械工程、计算机、数学、力学
等学科，属交叉学科前沿课题的基础理论和应用基础研究。航天舱布局较
一般机械布局更复杂、更典型，本论文理论方法可望推广应用于工程机械、
组合机床、机器人、火箭、坦克、潜艇和水下悬浮工程等相关领域。因此
本课题的研究具有重要的科学价值、经济效益和社会效益。
The concern of this paper is the optimization theory and strategy of layout scheme design of complex engineering systems and their applications to layout optimization of the vessels of complex spacecraft.
The layout scheme design of spacecraft vessel is to study how to arrange the instruments and equipment inside (or outside) the vessel while satisfying all kinds of engineering constraints. It is an engineering subject of great importance and urgency and the researches on it are far from enough. Great challenges and barriers exist in both theory and practice due to the NP-hard of layout problems in computation complexity and alarming difficulties in the design of spacecraft themselves.
The layout scheme design of spacecraft vessel belongs to 3D packing problem with behavioral constraints, and it is also a complex engineering system problems with inscrutability, uncertainty, high nonlinearity, quality and quantity. It is almost impossible to solve it completely by human or computer alone. The idea of "Man-Machine Synergy" originated from Lenat and Feigenbaum in 1991 and the similar concept of "Man-Machine Cooperation" proposed by Xueshen Qian and Ruwei Dai at the very year turn out to be a promising approach to complex engineering problems and automatic design in 21st century. But there is a key problem that has not been commendably solved yet. That is how to practically implement the cooperation between man and computer. Against the background of layout optimization of spacecraft vessels, frist this paper proposes a human-computer interaction genetic algorithm (HCIGA) which combines the advantages of human and computer at a level of algorithm. Then a strategy of human-computer cooperation
design based on HCIGA is developed to solve combinatoral explosion hi optimization problems and layout scheme design in complex engineer system. The proposed methodologies demonstrate superior performance on numerical examples and their application to spacecraft vessel scheme design.
In this dissertation, some original concepts and theories are proposed which are summarized in the following.
1. A optimization algorithm plays a dominant role in solving layout optimization problems and is also an important factor in evaluating a research work. This paper proposes a hybrid coarse-grained genetic algorithm (HCGGA) in which all chromosomes are ranked according to their fitness values and divided into several subgroups. Each subgroup, whose values of punishment
coefficient, crossover and mutation operators are different from other subgroups, operates independently. Otherwise the strategies of "the same exclude" and "the best live" are adopted. Enough examples indicate that HCGGA is better than coarse-grained genetic algorithm. It is very HCGGA that human-computer interactive genetic algorithm (HCIGA) in this paper bases on.
2. To make the best of human and computer and practice the ideas of "man-machine synergy" and "man-machine cooperation", a human-computer interactive genetic algorithm is put forward. In HCIGA, the artificial individuals (AIs) are taken as a part of the original chromosome population, and then the worse individuals are replaced by new AIs real-timely during computation process. The cooperation between human and computer is carried out by genetic operations, including selection, crossover and mutation. The HCIGA is just a cell in the following cooperation design method.
3. In order to realize multi-person design and decision, as well as to ensure the characteristic of cooperative operation can be fully exerted, the thought of cooperative design is combined with HCIGA. Consequently human-computer interactive evolutionary cooperation design (HCIECD) is constructed, which can simplify the conformation of database and enforce flexible cooperation among many persons in conventional collaboration design. There are two modules in the method, which are design layer and decision layer modules. The socket technology of network programming, and client/server mode are introduced to constitute a
航天器舱布局方案优化设计是研究在满足各种工程技术条件的前提下，如何将各种仪器和设备最优的布置在航天器舱体内(或外)，使得总体布局的某一项或几项评价指标达到最优。这是一个亟待解决而又未很好解决的重要工程课题。布局问题的NP-困难性和航天器设计本身的巨大复杂性使得该问题的解决既有理论上的开拓性和挑战性，又存在工程实践上的艰难性和复杂性。
航天器舱布局方案优化设计属带性能约束的三维布局优化问题，属具有不确定性、高度非线性、既有定性又有定量问题的复杂工程系统问题，单纯依靠人或计算机算法(包括人工智能技术)去解决都是非常困难的。1991年Lenat、Feigenbaum提出的人机合作(Man-Machine Synergy)和同年钱学森、戴汝为等提出的人机结合(Human-Machine Cooperation)思想和方法论，被认为是21世纪解决复杂工程问题的重要途径、自动化设计的重要发展方向，但其可操作性问题一直未很好解决。本论文以航天器舱布局方案优化设计为应用背景，遵循“人机合作”、“人机合作”思想，充分发挥工程技术人员和现代计算机技术各自特长，提出人机交互的遗传算法，使“人”“机”在算法层面有机结合并具有可操作性；进而结合网络协同设计技术，给出一套以人机交互遗传算法为基础的人机交互演化协同设计理论方法，发挥多人设计和决策的优越性，以缓解组合最优化计算量过大(组合爆炸)问题，并增强上述理论方法的工程实用性。大量数值计算以及在航天器舱方案设计中的应用表明了本论文理论方法的可行性和有效性。
本论文的主要工作如下：
1．稳定、收敛、高效的优化算法是求解复杂布局优化问题的基础，是布局优化理论研究发展水平的重要标志。本论文提出一种改进的粗粒度遗传算法——混合粗粒度遗传算法，该算法将各染色体按适应度函数值大小排序并分组，对不同的染色体分组采用不同的惩罚系数、交叉算子与变异算子，并在进化过程中采用同种互斥和最优解保留策略。大量算例表明，本算法优于经典粗粒度遗传算法。该混合粗粒度遗传算法是实现本论文人机结合演化设计思想的算法基础。
2．为充分发挥人和计算机各自的特长，使“人机合作”与“人机结合”思想在工程应用中具有可操作性，提出人机交互的遗传算法。该算法将人
大连理工大学博上学位论文 摘要
工设计的个体作为初始染色体群体的组成部分，并在遗传运算过程中实时
地将人工设计的新个体加入到染色体群体中，以代替群体中的较差个体，
参与遗传运算（复制、交叉、变异X实现人与算法在基因层面的结合。该
人机交互遗传算法系统是实现网络下演化协同设计的基本单元。
3．将人机交互的遗传算法与网络协同设计技术相结合，考虑工程因素，
形成网络环境下的人机交互演化协同设计系统，以简化传统协同设计中数
据库构建，解决增强协同人之间柔性协同问题。该系统分为设计层和决策
层两个模块，采用S。eke网络编程技术，通过客户机用＆务器模式，实现进
程间的异步通信；同时采用ODBC数据库技术，利用综合评价仲裁系统和
人机交互的思想进行协同设计。
4．人机交互演化设计方法在航天器舱布局方案设计中的应用。为达到
本论文理论方法在多舱段大型航天器舱布局优化中的工程实用化，本论文
采取如下策略：首先将待布物模型化，简化为规则形状的几何体，建立返
回式人造卫星回收舱和空间站舱布局优化的数学模型和仿真模型的复合模
型；利用人机交互的遗传算法和人机交互演化协同进行布局优化设计，给
出航天器舱优化布局的“骨架”；利用美国的Prohogineer软件将模型中待
布物还原成实际形状的物体，进行模装布局和性能仿真；利用人机交互方
法进行布局调整，直至得到满意工程布局。最后将上述方法和策略应用于
我国卫星舱和空间实验站总体布局方案设计预研工作，同时也是对本文理
论方法的验证。
本课题属国家自然科学基金项目“复杂布局自动化设计理论、方法及
其应用”（N＊69974002L“人机结合演化协同及在航天器舱总装方案设
计中的应用”（N趴60073030和国家‘℃63”计划航天领域高技术项目：“多
舱段大型航天器（载人飞船、空间站）三维动力布局优化研究”（N。
863205石S人本课题涉及到航天器设计、机械工程、计算机、数学、力学
等学科，属交叉学科前沿课题的基础理论和应用基础研究。航天舱布局较
一般机械布局更复杂、更典型，本论文理论方法可望推广应用于工程机械、
组合机床、机器人、火箭、坦克、潜艇和水下悬浮工程等相关领域。因此
本课题的研究具有重要的科学价值、经济效益和社会效益。
The concern of this paper is the optimization theory and strategy of layout scheme design of complex engineering systems and their applications to layout optimization of the vessels of complex spacecraft.
The layout scheme design of spacecraft vessel is to study how to arrange the instruments and equipment inside (or outside) the vessel while satisfying all kinds of engineering constraints. It is an engineering subject of great importance and urgency and the researches on it are far from enough. Great challenges and barriers exist in both theory and practice due to the NP-hard of layout problems in computation complexity and alarming difficulties in the design of spacecraft themselves.
The layout scheme design of spacecraft vessel belongs to 3D packing problem with behavioral constraints, and it is also a complex engineering system problems with inscrutability, uncertainty, high nonlinearity, quality and quantity. It is almost impossible to solve it completely by human or computer alone. The idea of "Man-Machine Synergy" originated from Lenat and Feigenbaum in 1991 and the similar concept of "Man-Machine Cooperation" proposed by Xueshen Qian and Ruwei Dai at the very year turn out to be a promising approach to complex engineering problems and automatic design in 21st century. But there is a key problem that has not been commendably solved yet. That is how to practically implement the cooperation between man and computer. Against the background of layout optimization of spacecraft vessels, frist this paper proposes a human-computer interaction genetic algorithm (HCIGA) which combines the advantages of human and computer at a level of algorithm. Then a strategy of human-computer cooperation
design based on HCIGA is developed to solve combinatoral explosion hi optimization problems and layout scheme design in complex engineer system. The proposed methodologies demonstrate superior performance on numerical examples and their application to spacecraft vessel scheme design.
In this dissertation, some original concepts and theories are proposed which are summarized in the following.
1. A optimization algorithm plays a dominant role in solving layout optimization problems and is also an important factor in evaluating a research work. This paper proposes a hybrid coarse-grained genetic algorithm (HCGGA) in which all chromosomes are ranked according to their fitness values and divided into several subgroups. Each subgroup, whose values of punishment
coefficient, crossover and mutation operators are different from other subgroups, operates independently. Otherwise the strategies of "the same exclude" and "the best live" are adopted. Enough examples indicate that HCGGA is better than coarse-grained genetic algorithm. It is very HCGGA that human-computer interactive genetic algorithm (HCIGA) in this paper bases on.
2. To make the best of human and computer and practice the ideas of "man-machine synergy" and "man-machine cooperation", a human-computer interactive genetic algorithm is put forward. In HCIGA, the artificial individuals (AIs) are taken as a part of the original chromosome population, and then the worse individuals are replaced by new AIs real-timely during computation process. The cooperation between human and computer is carried out by genetic operations, including selection, crossover and mutation. The HCIGA is just a cell in the following cooperation design method.
3. In order to realize multi-person design and decision, as well as to ensure the characteristic of cooperative operation can be fully exerted, the thought of cooperative design is combined with HCIGA. Consequently human-computer interactive evolutionary cooperation design (HCIECD) is constructed, which can simplify the conformation of database and enforce flexible cooperation among many persons in conventional collaboration design. There are two modules in the method, which are design layer and decision layer modules. The socket technology of network programming, and client/server mode are introduced to constitute a
引文
[1] Lenat D.B, Feigenbaum E.A. On the thresholds of knowledge. Artificial Intelligence, 1991,47(1) : 185-230
[2] 戴汝为.“人机结合”大成智慧.模式识别与人工智能, 1994,7(3) : 181-190
[3] Dowsland K.A., Dowsland W.B. Packing problems. European Journal of Operational Research, 1992, 56(1) : 2-14
[4] Dowsland K.A., Dowsland W.B. Solution approaches to irregular nesting problems. European Journal of Operational Research, 1995, 84(3) : 506-521
[5] Faggioli E., Bentivogio C.A. Heuristic and exact methods for the cutting sequencing problem. European Journal of Operational Research, 1998, 110(3) : 564-575
[6] Vasko F.J., Newhart D.D., Stott K.L. A hierachical approach for one-dimensional cutting stock problems in the steel industry that maximizes yield and minimizes overgrading. European Journal of Operational Research, 1999,114(1) : 72-82
[7] Nitsche C., Scheithauer G, Teruo J. Tighter relaxations for the cutting problem. European Journal of Operational Research, 1999,112(3) : 654-663
[8] Petridis Vassilios, Kazarlis Spyrons, Bakirtzis Anastasios. Varying fitness function in
genetic algorithm constrained optimization: The cutting stock and unit commitment problems. IEEE Transactions on System, Man, and Cybernetics-Part B: Cybernetics, 1998,28(5) : 629-639
[9] Gilmore P.C., Gomery R.E. Multistage cutting stock problems of two and more dimensions. Operations Research, 1965, 13: 94-120
[10] Ghandforoush Parviz, Daniels John J. Heuristic algorithm for the guillotine constrained cutting stock problem. ORSA Journal on Computing, 1992, 4(3) : 351-356
[11] Wang P.Y. Two algorithms for constrained two-dimensional cutting stock problems. Operations Research, 1983,31(3) : 573-586
[12] Oliveria J.F., Ferreira J.S. An improved version of Wang's algorithm for two-dimensional cutting problems. European Journal of Operational Research, 1990,44: 256-266
[13] Eleni Hadjiconstantnou, Nicos Christofides. An exact algorithm for general, orthogonal, two-dimensional knapsack problems. European Journal of Operational Research, 1995,83: 39-56
[14] Loris Faina. An application of simulated annealing to the cutting stock problem. European Journal of Operational Research, 1999,114: 542-556
[15] Terno Johannes, Scheithauer Guntram, et al. Efficient approach for the multi-pallet loading problem. European Journal of Operational Research, 2000, 123: 372-381
[16] Liu Fuh-Hwa, Hsiao Chih-Jen. Pallet loading method for single-size boxes with optimal stability. Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering, 1997,21(6) : 591-600
[17] Bhattacharya S., Roy R. and Bhattacharya S. An exact depth-first algorithm for the pallet-loading problem. European Journal of Operational Research, 1998,110(3) : 610-625
[18] 段国林,查建中,林建平.底盘装载问题的一种启发式算法.河北工业大学学报, 1998,3 27(1) :1-6
[19] Younis Nazar A., Cavalier Tom M. On locating part bins in a constrained layout area for an automated assembly process. Computers & Industrial Engineering, 1990,18(2) : 111-118
[20] Fujita Kikuo, Akagi Shinsuke, Shimazaki Sadao. Optimal space partitioning method based on rectangular duals of planar graphs. Nippon Kikai Gakkai Ronbunshu, Chen/ Transaction of the Japan Society of Mechanical Engineers, 1994,60: 3662-3669
[21] Tarn Yukon, Wu Yuliang, Huang Wenqi, Wong Chakkuen. Effective quasi-human based heuristic for solving rectangle packing problem. IEEE Asia-Pacific Conference on Circuits and Systems-Proceedings, IEEE, 1998:137-140
[22] Murata Hiroshi, Fujiyoshi Kunihiro, Nakatake Shigetoshi, Kajitani Yoji. Rectangle-packing-based module placement. IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, IEEE, 1995: 472-479
[23] Georgis N., Petrou M., Kittler J. On the constrained rectangle packing problem.
International Journal of Modelling and Simulation, 2000,20(4):293-299
[24]Hwang Shianmiin, Kao Chengyan, Horng Jorngtzong. On solving rectangle bin packing problems using genetic algorithms. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 1994:1583-1590
[25]王金敏，马丰宁，初楠，查建中．基于构造的布局启发式方法．天津大学学报，1998，31(1)：17-22
[26]王爱虎，查建中，王金敏，鄂明成．矩形物体布局的并行算法．天津大学学报，1997，30(2)：199-204
[27]王爱虎，鄂明成，查建中．基于空间分解的二维布局问题的启发式算法．天津大学学报，1996，29(6)：840-846
[28]王爱虎，戴佐，查建中．一种基于二叉树结构表达的矩形物体布局的启发式方法．软件学报，1996，4(2)：252-257
[29]王金敏，马丰宁，陈东祥，查建中．一种基于约束的布局求解算法．计算机辅助设计与图形学学报，1998．10(2)：156-160
[30]晏敏，张昌期，刘育骐．空间布局的计算机设计．小型微型计算机系统．1988，9(12)：1-13
[31]晏敏，张昌期，刘育骐．平面布局的一个拓扑模型：方图．小型微型计算机系统．1989，10(2)：23-32
[32]晏敏，张昌期，刘育骐．平面布局方图模型的尺寸计算．小型微型计算机系统．1989，10(6)：25-30
[33]晏敏，张昌期，翟贤，刘育骐．用于平面布局的专家系统．华中理工大学学报．1989，17(4，增刊)：31-37
[34]晏敏，张昌期，翟贤，刘育骐．平面布局专家系统的尺寸推理机制．华中理工大学学报．1989，17(4，增刊)：39-44
[35]晏敏，张昌期，翟贤，刘育骐．平面布局专家系统的自学习智能回溯搜索策略．华中理工大学学报，1989，17(4，增刊)：45-50
[36]刘德全，滕弘飞．装填布局拓扑模式变换的遗传算法．大连理工大学学报，1997，37(3)：295-300
[37]刘德全，滕弘飞．矩形件排样问题的遗传算法求解．小型微型计算机系统，1998，19(12)：20-25
[38]Liu Dequan, Teng Hongfei. An improved BL-Algorithm for genetic algorithm of the orthogonal packing of rectangles. European Journal of Operational Research, 1999,112:413-420
[39]John A., George Jennifer M., George Bruce W. Lamar. Packing different-sized circles into a rectangular container. European Journal of Operational Research, 1995,84:693-712
[40]Appelbaum J., Weiss Y. Packing of circles on a hemisphere. Measurement Science and Technology, 1999.10(11):1015-1019
[41]Graham R. L., Lubachevsky B. D., Nurmela K. J., Ostergard P. R. J. Dense packings of congruent circles in a circle. Discrete Mathematics, 1998,181(15):139-154
[42]Arai Makoto, Minagawa Masaaki, Kakazu Yukinori. Strategy for packing circles: vibration control approach. Intelligent Engineering Systems Through Artificial Neural Networks, 1997,7:931-938
[43]黄文奇，詹叔浩．求解Packing问题的拟物方法．应用数学学报，1979，2(2)：176-180
[44]黄文奇，陈亮．求解有关空间利用的调度问题的拟物方法．中国科学(A辑)，1991，(3)：325-331
[45]许如初，黄文奇．解不等园packing问题拟物拟人算法初态选取．华中理工大学，1998，26(4)：1-3
[46]黄文奇，许如初，陈卫东，张京芬．解Packing及CNF—SAT问题的拟物拟人方法．华中理工大学学报，1998,26(9)：5-7
[47]陆一平，周济，钟毅芳，平面约束圆集布局的膨胀算法．华中理工大学学报．1998,26(10)：45-47
[48]Teng Hongfei, Sun Shoulin, Ge Wenhai, Zhong Wanxie. Layout optimization for the dishes installed on a rotating table. Science In China (Series A), 1994,37(10):1212-1218
[49]邓四二，滕弘飞，邢玉生，钟万勰．一类带性能约束的二维几何布局优化．大连理工大学学报,1991，31(2)：169-176
[50]唐飞，滕弘飞．一种改进的遗传算法及其在布局优化中的应用．软件学报，1999，10(10)：1096-1102
[51]唐飞，滕弘飞，带作用力约束的二维布局问题——航天器复杂插座布局的优化设计．宇航学报，2000，21(2)：50-57
[52]Ismall H. S., Hon K. K. B. New approaches for the nesting of two-dimensional shapes for press tool design. International Journal of Production Research, 1992,30(4): 825-837
[53]Jain P., Fenyes P., Ritchter R. Optimal blank nesting using simulated annealing. Transactions of the ASME, 1992,114:160-165
[54]Stefan Jakobs. On genetic algorithms for the packing of polygons. European Journal of Operational Research, 1996,88:165-181
[55]刘德全．计算机辅助排样的理论方法及其实现[博士论文]．大连：大连理工大学，1998
[56]Dowsland William B. Three-dimensional packing-solution approaches and heuristic development. International Journal of Production Research, 1991, 29(8): 1673-1685
[57]Mohanty Bidhu B., Mathur Kamlesh, Ivancic Nancy J. Value considerations in three-dimensional packing - a heuristic procedure using the fractional knapsack problem. European Journal of Operational Research, 1994, 74(1): 143-151
[58]Saginaw D. J., Perakis A. N. A decision support system for container ship stowage planning. Marine Technology, 1989,26(1): 47-61
[59]Dickinson John K., Knopf George K. Moment based metric for 2-D and 3-D packing. European Journal of Operational Research, 2000, t 22(1): 133-144
[60]Kawakami T., Minagawa M., Kakazu Y. Auto tuning of 3-D packing rules using Genetic Algorithms. NASA Technical Memorandum, 1990, 1319-1324
[61]Kawakami Takashi, Kakazu Yukinori. Strategy acquisition of the 3-D packing problem in multiagent environment. Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, 1994,60:3219-3225
[62]Herrera F., Lozano M., Moraga C. Hierarchical distributed genetic algorithms. International Journal of Intelligent Systems, 1999, 14( 11): 1099-1121
[63]Peng Hanchuan, Long Fuhui, Chi Zheru, Siu Wanchi. Hierarchical distributed genetic algorithm for image segmentation. Proceedings of the IEEE Conference on Evolutionary Computation, 2000,1: 272-276
[64]Tang K.S., Man K.F., Istepanian Robert S.H. Teleoperation controller design using hierarchical genetic algorithm. Proceedings of the IEEE International Conference on Industrial Technology, IEEE Industrial Electronics Society, 2000,1:707-711
[65]刘来福，曾文艺．数学模型与数学建模．北京：北京师范大学出版社，1997
[66]周义仓，郝孝良．数学建模实验．西安：西安大学出版社，1999
[2] 戴汝为.“人机结合”大成智慧.模式识别与人工智能, 1994,7(3) : 181-190
[3] Dowsland K.A., Dowsland W.B. Packing problems. European Journal of Operational Research, 1992, 56(1) : 2-14
[4] Dowsland K.A., Dowsland W.B. Solution approaches to irregular nesting problems. European Journal of Operational Research, 1995, 84(3) : 506-521
[5] Faggioli E., Bentivogio C.A. Heuristic and exact methods for the cutting sequencing problem. European Journal of Operational Research, 1998, 110(3) : 564-575
[6] Vasko F.J., Newhart D.D., Stott K.L. A hierachical approach for one-dimensional cutting stock problems in the steel industry that maximizes yield and minimizes overgrading. European Journal of Operational Research, 1999,114(1) : 72-82
[7] Nitsche C., Scheithauer G, Teruo J. Tighter relaxations for the cutting problem. European Journal of Operational Research, 1999,112(3) : 654-663
[8] Petridis Vassilios, Kazarlis Spyrons, Bakirtzis Anastasios. Varying fitness function in
genetic algorithm constrained optimization: The cutting stock and unit commitment problems. IEEE Transactions on System, Man, and Cybernetics-Part B: Cybernetics, 1998,28(5) : 629-639
[9] Gilmore P.C., Gomery R.E. Multistage cutting stock problems of two and more dimensions. Operations Research, 1965, 13: 94-120
[10] Ghandforoush Parviz, Daniels John J. Heuristic algorithm for the guillotine constrained cutting stock problem. ORSA Journal on Computing, 1992, 4(3) : 351-356
[11] Wang P.Y. Two algorithms for constrained two-dimensional cutting stock problems. Operations Research, 1983,31(3) : 573-586
[12] Oliveria J.F., Ferreira J.S. An improved version of Wang's algorithm for two-dimensional cutting problems. European Journal of Operational Research, 1990,44: 256-266
[13] Eleni Hadjiconstantnou, Nicos Christofides. An exact algorithm for general, orthogonal, two-dimensional knapsack problems. European Journal of Operational Research, 1995,83: 39-56
[14] Loris Faina. An application of simulated annealing to the cutting stock problem. European Journal of Operational Research, 1999,114: 542-556
[15] Terno Johannes, Scheithauer Guntram, et al. Efficient approach for the multi-pallet loading problem. European Journal of Operational Research, 2000, 123: 372-381
[16] Liu Fuh-Hwa, Hsiao Chih-Jen. Pallet loading method for single-size boxes with optimal stability. Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering, 1997,21(6) : 591-600
[17] Bhattacharya S., Roy R. and Bhattacharya S. An exact depth-first algorithm for the pallet-loading problem. European Journal of Operational Research, 1998,110(3) : 610-625
[18] 段国林,查建中,林建平.底盘装载问题的一种启发式算法.河北工业大学学报, 1998,3 27(1) :1-6
[19] Younis Nazar A., Cavalier Tom M. On locating part bins in a constrained layout area for an automated assembly process. Computers & Industrial Engineering, 1990,18(2) : 111-118
[20] Fujita Kikuo, Akagi Shinsuke, Shimazaki Sadao. Optimal space partitioning method based on rectangular duals of planar graphs. Nippon Kikai Gakkai Ronbunshu, Chen/ Transaction of the Japan Society of Mechanical Engineers, 1994,60: 3662-3669
[21] Tarn Yukon, Wu Yuliang, Huang Wenqi, Wong Chakkuen. Effective quasi-human based heuristic for solving rectangle packing problem. IEEE Asia-Pacific Conference on Circuits and Systems-Proceedings, IEEE, 1998:137-140
[22] Murata Hiroshi, Fujiyoshi Kunihiro, Nakatake Shigetoshi, Kajitani Yoji. Rectangle-packing-based module placement. IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, IEEE, 1995: 472-479
[23] Georgis N., Petrou M., Kittler J. On the constrained rectangle packing problem.
International Journal of Modelling and Simulation, 2000,20(4):293-299
[24]Hwang Shianmiin, Kao Chengyan, Horng Jorngtzong. On solving rectangle bin packing problems using genetic algorithms. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 1994:1583-1590
[25]王金敏，马丰宁，初楠，查建中．基于构造的布局启发式方法．天津大学学报，1998，31(1)：17-22
[26]王爱虎，查建中，王金敏，鄂明成．矩形物体布局的并行算法．天津大学学报，1997，30(2)：199-204
[27]王爱虎，鄂明成，查建中．基于空间分解的二维布局问题的启发式算法．天津大学学报，1996，29(6)：840-846
[28]王爱虎，戴佐，查建中．一种基于二叉树结构表达的矩形物体布局的启发式方法．软件学报，1996，4(2)：252-257
[29]王金敏，马丰宁，陈东祥，查建中．一种基于约束的布局求解算法．计算机辅助设计与图形学学报，1998．10(2)：156-160
[30]晏敏，张昌期，刘育骐．空间布局的计算机设计．小型微型计算机系统．1988，9(12)：1-13
[31]晏敏，张昌期，刘育骐．平面布局的一个拓扑模型：方图．小型微型计算机系统．1989，10(2)：23-32
[32]晏敏，张昌期，刘育骐．平面布局方图模型的尺寸计算．小型微型计算机系统．1989，10(6)：25-30
[33]晏敏，张昌期，翟贤，刘育骐．用于平面布局的专家系统．华中理工大学学报．1989，17(4，增刊)：31-37
[34]晏敏，张昌期，翟贤，刘育骐．平面布局专家系统的尺寸推理机制．华中理工大学学报．1989，17(4，增刊)：39-44
[35]晏敏，张昌期，翟贤，刘育骐．平面布局专家系统的自学习智能回溯搜索策略．华中理工大学学报，1989，17(4，增刊)：45-50
[36]刘德全，滕弘飞．装填布局拓扑模式变换的遗传算法．大连理工大学学报，1997，37(3)：295-300
[37]刘德全，滕弘飞．矩形件排样问题的遗传算法求解．小型微型计算机系统，1998，19(12)：20-25
[38]Liu Dequan, Teng Hongfei. An improved BL-Algorithm for genetic algorithm of the orthogonal packing of rectangles. European Journal of Operational Research, 1999,112:413-420
[39]John A., George Jennifer M., George Bruce W. Lamar. Packing different-sized circles into a rectangular container. European Journal of Operational Research, 1995,84:693-712
[40]Appelbaum J., Weiss Y. Packing of circles on a hemisphere. Measurement Science and Technology, 1999.10(11):1015-1019
[41]Graham R. L., Lubachevsky B. D., Nurmela K. J., Ostergard P. R. J. Dense packings of congruent circles in a circle. Discrete Mathematics, 1998,181(15):139-154
[42]Arai Makoto, Minagawa Masaaki, Kakazu Yukinori. Strategy for packing circles: vibration control approach. Intelligent Engineering Systems Through Artificial Neural Networks, 1997,7:931-938
[43]黄文奇，詹叔浩．求解Packing问题的拟物方法．应用数学学报，1979，2(2)：176-180
[44]黄文奇，陈亮．求解有关空间利用的调度问题的拟物方法．中国科学(A辑)，1991，(3)：325-331
[45]许如初，黄文奇．解不等园packing问题拟物拟人算法初态选取．华中理工大学，1998，26(4)：1-3
[46]黄文奇，许如初，陈卫东，张京芬．解Packing及CNF—SAT问题的拟物拟人方法．华中理工大学学报，1998,26(9)：5-7
[47]陆一平，周济，钟毅芳，平面约束圆集布局的膨胀算法．华中理工大学学报．1998,26(10)：45-47
[48]Teng Hongfei, Sun Shoulin, Ge Wenhai, Zhong Wanxie. Layout optimization for the dishes installed on a rotating table. Science In China (Series A), 1994,37(10):1212-1218
[49]邓四二，滕弘飞，邢玉生，钟万勰．一类带性能约束的二维几何布局优化．大连理工大学学报,1991，31(2)：169-176
[50]唐飞，滕弘飞．一种改进的遗传算法及其在布局优化中的应用．软件学报，1999，10(10)：1096-1102
[51]唐飞，滕弘飞，带作用力约束的二维布局问题——航天器复杂插座布局的优化设计．宇航学报，2000，21(2)：50-57
[52]Ismall H. S., Hon K. K. B. New approaches for the nesting of two-dimensional shapes for press tool design. International Journal of Production Research, 1992,30(4): 825-837
[53]Jain P., Fenyes P., Ritchter R. Optimal blank nesting using simulated annealing. Transactions of the ASME, 1992,114:160-165
[54]Stefan Jakobs. On genetic algorithms for the packing of polygons. European Journal of Operational Research, 1996,88:165-181
[55]刘德全．计算机辅助排样的理论方法及其实现[博士论文]．大连：大连理工大学，1998
[56]Dowsland William B. Three-dimensional packing-solution approaches and heuristic development. International Journal of Production Research, 1991, 29(8): 1673-1685
[57]Mohanty Bidhu B., Mathur Kamlesh, Ivancic Nancy J. Value considerations in three-dimensional packing - a heuristic procedure using the fractional knapsack problem. European Journal of Operational Research, 1994, 74(1): 143-151
[58]Saginaw D. J., Perakis A. N. A decision support system for container ship stowage planning. Marine Technology, 1989,26(1): 47-61
[59]Dickinson John K., Knopf George K. Moment based metric for 2-D and 3-D packing. European Journal of Operational Research, 2000, t 22(1): 133-144
[60]Kawakami T., Minagawa M., Kakazu Y. Auto tuning of 3-D packing rules using Genetic Algorithms. NASA Technical Memorandum, 1990, 1319-1324
[61]Kawakami Takashi, Kakazu Yukinori. Strategy acquisition of the 3-D packing problem in multiagent environment. Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, 1994,60:3219-3225
[62]Herrera F., Lozano M., Moraga C. Hierarchical distributed genetic algorithms. International Journal of Intelligent Systems, 1999, 14( 11): 1099-1121
[63]Peng Hanchuan, Long Fuhui, Chi Zheru, Siu Wanchi. Hierarchical distributed genetic algorithm for image segmentation. Proceedings of the IEEE Conference on Evolutionary Computation, 2000,1: 272-276
[64]Tang K.S., Man K.F., Istepanian Robert S.H. Teleoperation controller design using hierarchical genetic algorithm. Proceedings of the IEEE International Conference on Industrial Technology, IEEE Industrial Electronics Society, 2000,1:707-711
[65]刘来福，曾文艺．数学模型与数学建模．北京：北京师范大学出版社，1997
[66]周义仓，郝孝良．数学建模实验．西安：西安大学出版社，1999