二维装箱问题毕业论文

. Tang and maximum entropy algorithm for convexprogramming,Chinese Science Bulletin，40:5（1995），. Tang and maximum entropy method for linearprogramming,Chinese J. Num. Math. Appli.，17:3（1995），54-65.（唐焕文，张立卫，线性规划的极大熵方法，计算数学，2 （1995），160-172.)3.唐焕文，王云诚，张立卫，求解一般约束极大极小问题的一个有效的近似算法，经济数学，12:1,.王云诚，张立卫，唐焕文，求解一般约束凸规划的极大熵方法，大连理工大学学报，35:6（1995），. Tang and ，Maximum entropy methods for constrainedoptimization and minimax problems,Systems Sci. Math. Sci.,9:1（1996），.王云诚，唐焕文，张立卫，求解一半无限极大极小问题的一个极大熵方法，经济数学，13:2（1996），.唐焕文，王雪华，张立卫，求解极大极小问题的极大熵方法的收敛性，运筹学杂志，14:1（1996），. Zhang，On the ABS algorithm with singular matrix and itsapplications to linear programming,Optimization Methods andSoftware,8（1997），. Xia and . Zhang,A simplified trust region methodwith projection and convergence,（1997），. . Zhang and . Tang，A maximum entropy algorithm withparameters for solving minimax problem,Archives of ControlSciences,XLⅡ：6（1997），. E. Spedicato,. Xia and . Zhang,The implicit LX method ofthe ABS class,Optimization Methods and Software,8（1997），. . Chen and factorization algorithms in thesimplex method,J. Applied Basic and Engineering Sciences,5:4（1997），. E. Spedicato,. Xia,. Zhang and K. Mirnia,ABS algorithmsfor linear equations and applications to optimization,in & E. Spedicato (eds.),Algorithms for Large Scale LinearAlgebraic Systems，Series C: Mathematical and PhysicalSciences -508,1998， Kluwer Academic Publishers,. . Zhang and . Tang,A further study on a penalty function ofBertsekas,in: Yuan Ya-Xiang ed.,Advances in Nonlinear Programming,Kluwer Academic Publishers,1998,. 张立卫，唐焕文，A theorem on the differential of the K-Sfunction，经济数学，15:1/2（1998），. 张立卫，Condition on parameter $\beta_k$ in a convergent conjugategradient method，运筹学学报，3:2 （1999），. modified version to the differential system ofEvtushenko and Zhadan for solving nonlinear programming,in:Yuan Ya-Xiang ed.,Numerical Linear Algebra and Optimization,Science Press,Beijing,New York,1999,161-- 168 .18. 郭崇惠，唐焕文，张立卫，Global convergence for a class of conjugategradient methods，运筹学学报，3:2（1999），. . He and of a dual algorithm for minimaxproblems,Archives of Control Sciences,10(XLⅥ）（2000),. 张立卫，李勤，张鑫，Two differential systems for solving nonlinearprogramming problems，运筹学学报，4:4（2000),. and . He,The convergence of a dual algorithm fornonlinear programming,Korean J. Comput. & . 7:3（2000),. E. Spedicato, and . Zhang,ABS algorithms for linearequations and optimization,J. Computational and AppliedMathematics，124（2000),. 王明征，张立卫，夏尊铨，Dennis-Wolkowicz最小改变割算法的超线性收敛性，大连理工大学学报，11（2000),645—. 夏尊铨，张士霞，张立卫，复ABS方法. 大连理工大学学报，11（2000),. . Zhang and . Xia，Newton-type methods forquasidifferentiable equations,Journal of Optimization Theory andApplications,108:2 （2001），. and . Xia,Approximations to convex-valuedmultifunctions. in: Demayano V. and Rubinov A. eds.,Quasidifferentiability and Related Topics,Kluwer AcademicPublishers,. Y. Gao,. Xia and quasidifferential for aquasidifferentiable function in two-dimensional space,Journal ofConvex Analysis,8:2（2001），. 贺素香，张立卫，A class of constructive dual algorithms forsolving nonlinear programming problems，运筹学学报，5:3（2001），. 贺素香，张立卫，求解约束优化问题的对偶算法，计算数学，23:3（2001），. . Zhang，Computing inertias of KKT matrix and reduced Hessianvia the ABS algorithm,Ricerca Operativa,Vol. 31,（2001），. . Zhang,. Liu and . Xia,Application of the ABS methodto systems of linear matrix integer equations,Ricerca Operativa,Vol. 31, （2001），. . Xia and . Zhang,ABS algorithms for solving linearlyconstrained optimization problems via the active set strategy,Ricerca Operativa,Vol. 31,（2001），. 张立卫，张鑫，求解拟可微方程组的非精确牛顿法，经济数学，18:1（2001），. . Q. Xia,Y. Gao and . Wang，Star-kernels andstar-differentials in quasidifferentiable analysis,Journal ofConvex Analysis,9:1（2002），. J. Sun and thelog-exponential trajectory of linearprogramming. Journal of Global Optimization,25:1 （2003），. 张宏伟，张立卫夏尊铨，Calculus ofgeneralized quasi-differentiablefunctions I: some results on the space of pairs of convex-setcollections，东北数学，19:1（2003），. . Xia,. Wang and derivative of aclass of set-valued mappings and its applications，Journal ofConvex Analysis,10:1（2003），. and a second order parallelvariable transformation approach,Journal of Applied Mathematicsand Computing,11:1-2,. and PVT-type algorithm forminimizing a nonsmooth convex function，Serdica Math. J. 29（2003），. and . Liu,Convergence analysis of a nonlinearLagrange algorithm for nonlinear programming withinequality constraints,Journal of Applied Mathematics & Computing,13:1-2（2003）：. . Zhang and . Hsu，A scheduling model for AGVs at thecontainer terminal,2002 Japan-USA Symposium of FlexibleAutomation,Hiroshima,Japan,July 14-19,. . Ye,. Hsu and . Huang,Two equivalentinteger programming models for dispatching vehicles at a containerterminal,Proceedings International Conference on PORT andMaritime R&D and Technology,10-12 September,Singapore,2003,. 王明征，夏尊铨，张立卫，参数凸二次规划的线性稳定性，7:1运筹学学报（2003），. 贺素香，张立卫，李兴斯，不等式约束优化问题的一个势函数，33:3数学进展（2004），. 宋秋生，张立卫，无约束拟可微优化问题信赖域方法的全局收敛性，应用数学学报，27:1（2004），. . Lin,L. W. Zhang and . Pang,Two projection-typealgorithms for solving pseudo-monotone variational inequalityproblems,OR Transactions,9:1 （2005），. . Yu and . Zhang,The augmented Lagrangian method for thepacking of unequal circles within a strip,International Journalof Pure and Applied Mathematics,18:4（2005），. L. W. Zhang,R. Ye,. Huang and W. J. Hsu,Mixed IntegerProgramming Models for Dispatchingvehicles ataContainerTerminal,Journal of Applied Mathematics & Computing,17:1-2（2005），. J. Sun,. Zhang and Y. Wu,Properties of the augmentedLagrangian in nonlinear semidefinite optimization,accepted . . Zhou and . Zhang,A differential equation approach tofinding a Kuhn-Tucker point of a nonlinear programming problem,大连理工大学学报，2005,. . Xia,. Song and . Zhang,On Fritz John and KKTnecessary conditions of constrained quasidifferentiableoptimization,International Journal of Pure and AppliedMathematics,Vol. 23 No. 3,2005,. . Zhou,. Zhang and . He,A differential equation approachto solving nonlinear complementarity problems,OR Transactions,Vol. 9 . 张宏伟，张立卫，夏尊铨，宋春玲 不等式约束的广义拟可微优化问题最优性条件，大连理工大学学报，46卷2期，2006,.贺素香，张立卫，非线性约束优化问题的一个修正Lagrangian算法，数学物理学报，26卷1期，2006,. . Yu and . Zhang,An optimization model for the two-dimensional packing problem and its augmented Lagrangian method，International Journal of Pure and Applied Mathematics,Vol. .刘勇进，张立卫，二阶锥互补问题的一类效益函数与全局误差界，大连理工大学学报， （2006），. . Liu, and . Wang,Some properties of a class ofmerit functions for symmetric cone complementarity problems,Asia-Pacific Journal of Operational Research,（2006），58. . Liu,. Zhang and . Wang,Analysis of a smoothing methodfor symmetric conic linear programming,Journal of Appliedmathematics & Computing,22:1-2（2006），. . Liu, Analysis of the AugmentedLagrangian Method for Nonlinear Second-Order Cone OptimizationProblems,to appear in Nonlinear . Jin and L. W. Zhang， Two differential equation systemsforinequality constrained optimization,to appear in AppliedMathematics and . 金丽，张立卫，肖现涛，一个求解约束非线性优化问题的微分方程方法，计算数学接收.62.金丽，张立卫，肖现涛，求解约束优化问题的两个微分方程算法，运筹学学报接收.63. L. Jin,Liwei Zhang,Adifferential system for nonlinearprogramming problems,The 6th World Congress on IntelligentControl and Automation,Dalian,China,June 2006,12⑵：. L. Jin,L. W. Zhang and X. T. Xiao. Stabledifferential equationmethods in inequality constrained optimization,to appear inInternational Journal of Pure and Applied . Y. Li,L. Jin,L. W. Zhang,A novel neural network for linearcomplementarity problems,to appear inJournal of MathematicalResearch and . 于洪霞，张立卫，二维装箱问题的非线性规划模型和算法，大连理工大学学报接收.67. 任咏红，张立卫，基于一类非线性 Lagrange函数的对偶问题，大连理工大学学报接收.68. L. W. Zhang and . Ren,A Nonlinear Lagrangian Based on Fischer-Burmeister NCP Function,to appear in Applied Mathematics . . Sun, rate of convergence ofthe augmentedLagrangian method fornonlinear semidefiniteprogramming,to appear in Mathematical and L. W. Zhang， Two differential equation systemsforequality constrained optimization,to appear in AppliedMathematics and . . Liu,. Zhang，On the convergence of the augmentedLagrangian method for nonlinear optimization problems over second-order cones,to appear in Journal of Optimization Theory . Liu,. Zhang,Extension of smoothing functions tosymmetric cone complementarity problems,高校应用数学学报接受.73. . Liu,. Zhang and . Liu,Convergence analysis of anonlinear Lagrange algorithmfor nonconvex semidefiniteprogramming,to appear in OR Transactions.

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装箱问题可分为一维装箱问题，二维装箱问题，三维装箱问题三种。现实生活中常见的应该是三维装箱问题。一维装箱问题只考虑一个因素，比如重量、体积、长度等。二维装箱问题考虑两个因素——给定一张矩形的纸（布料、皮革），要求从这张纸上剪出给定的大小不一的形状，求一种剪法使得剪出的废料的面积总和最小。常见问题包括堆场中考虑长和宽进行各功能区域划分、停车场区位划分、包装材料裁切时考虑怎样裁切使得材料浪费最少、服装布料裁切、皮鞋制作中的皮革裁切等。三维装箱问题考虑三个因素——一般指长、宽、高。装车、装船、装集装箱等要考虑这三个维度都不能超。根据目标的不同,三维装箱问题可分成以下几类：箱柜装载问题(three-dimensional bin packing problem，简称3D-BPP)：给定一些不同类型的方型箱子和一些规格统一的方型容器，问题是要把所有箱子装入最少数量的容器中。容器装载问题(three-dimensional container-packing problems，简称3D-CPP)：在该问题中，所有箱子要装入一个不限尺寸的容器中，目标是要找一个装填，使得容器体积最小。背包装载问题(three-dimensional knapsack loading problems，简称3D-KLP)：每个箱子有一定的价值，背包装载是选择箱子的一部分装入容器中，使得装入容器中的箱子总价值最大。如果把箱子的体积作为价值，则目标转化为使容器浪费的体积最小。