界

At first the typical die and mould components and their standard processing technique,and the types of facilities were defined.Then the integer programming model of the facility planning was established and the branch and bound method was used to give a solution to the model cases.

定义了模具典型零件、设备类及模具典型零件标准工艺；建立了设备资源规划的整数规划数学模型；采用分枝—定界法对给定实例进行求解；计算结果证明了模型的有效性及实用性。

Moreover object convergence approach also may with cutting plane method, branch and Bound Method and so on the method unify the use, thus acceleration solution process.

而且目标收敛法还可与割平面法、分枝估界等方法结合起来使用，从而加速求解过程。

We study the optimal properties of the problem 1 |p_j=a or a+b_j, d |∑w_jC_j and according to it a kind of GA implement and a kind of Branch and Bound method are given.

本章考虑了单机分段恶化排序问题1| p_j= a or a+b_j， d |∑w_jC_j根据最优解的性质给出了遗传算法和分支定界法。

For the above problem, two heuristic methods and a hybrid optimal algorithm that incorporates the branch and bound method with active schedule constru〓n algorithm are presented Computational results show the effectiveness of these methods.

对上述问题，给出了两个启发式方法和一个将分支定界法和活动调度构造算法相结合的混合最优算法。

Although departed methods such as dynamic programming, integer programming, and branch bound method can solve small scale problems, the rise in execution time of these methods is exponential with the number of generating units.

虽然在以往的研究中，已有许多方法使用在此问题上，例如动态规划法、整数规划法及支界法等，但是由於这些方法所需的求解时间会随机组数的增加呈指数关系成长，因此都比较适合於小规模系统上使用。

Moreover, if the optimization problem has certain special feature, the simpler relaxation methods can be provided. For example, considering a generalized geometric programming problem, relevant relaxation linear programming can be obtained using its special structure. Based on the branch and bound method, a linear relaxation algorithm of global optimization is presented for generalized geometric programming, and the convergence of the algorithm is also proven.

此外，当优化问题具有某种特殊性质时，我们能给出更加简便的松弛化方法，如考虑广义几何规划问题，能充分利用其特殊结构，建立了广义几何规划问题的松弛线性规划问题；在分枝定界技术的基础上，提出了一个求广义几何规划全局解的线性松弛算法；证明了算法的收敛性。

The given Branch and Bound method can find out the optimal solution of the problem in small size while the given GA implement can quickly find out the approximate optimal solution of the problem in large size. The given GA implement proves to be very effective by numerical experiments and examples.

对于问题的较小规模情形分支定界法能精确地求得最优解；对于问题的较大规模情形遗传算法能很快地求得近似最优解；算例及大量实验表明用遗传算法来求问题的近似解是成功的。

By means of Heuristic Search, Branch and Bound method and Voronoi Diagram, the algorithm analyzes occlusion on complicated denture models precisely and quickly, which solved the practical problem in the application of VR technologies in dentistry.

通过推广基于分离轴定理的经典碰撞检测算法，借助启发式搜索、分支定界和Voronoi图等手段，算法可以在较短的时间内对复杂牙列模型完成高精度的定量咬合分析任务，解决了虚拟现实技术在口腔医学领域应用中的实际问题。

Second, according to model characteristic, such as non-linear, non-convex, multiple-peaked and so on, the paper discusses limitation of traditional solving algorithm, such as branch and bound method, GBD method and OA method, puts forward penalty function-makeup integer algorithm and genetic algorithm, analyses procedures of genetic algorithm, such as selection, crossover and mutation, brings forward modifications for specific realized problems of genetic algorithm, such as selection of initial points, operator design, adoptive value adjustment, constraint treatment and so on, and works out correlated solving program.

其次针对该模型非线性、非凸、多峰等特点，讨论了分支定界法、GBD法和OA法等传统求解算法的局限性，提出了罚函数一凑整算法和遗传算法的求解思路，对遗传算法的选择、交叉、变异等过程进行分析，对遗传算法初始点选择、算子设计、适应值调整和约束处理等具体实现问题提出了改进措施，并编制了相关的求解程序。

The first model is the optimization problems with s linear objective function subject to a system of fuzzy relation equations and a system of fuzzy relation inequalities, which are solved by using path method and 0-1 integer programming with branch and bound method.

第一种为约束为模糊关系方程和模糊关系不等式的具有线性目标函数的优化问题，采用路径法及0-1整数规划中的分枝定界法对其求解；第二种为约束为模糊关系方程和模糊关系不等式的格线性规划问题，采用直接法、路径法及0-1整数规划法对其求解；第三种为模糊关系不等式为模糊的，即约束中有一个可接受的容差，采用容差法及正负理想法对其求解；第四种是一种新的可能性模糊线性规划问题，采用模糊数大小比较法、"切片-粘贴"法及正负理想法，并设计了随机模拟的遗传算法对其求解；第五种为期望值模型，利用期望值将其转化为清晰约束系数的线性规划问题的方法。

James, son of Zebedee, and John the brother of James, whom he named Boanerges, that is, sons of thunder

载伯德的儿子雅各伯和雅各伯的弟弟若望，并为他们起名叫"波纳尔革"，就是"雷霆之子"

The southern Hungarian university city of Szeged will host part of the project, amounting to 40 percent of the total investment, which will mostly be paid for through Hungary's EU structural funds.

位于塞格德南部的匈牙利大学将负责部分项目，总计占总投入资金的40%。大部分资金将由匈牙利的欧盟结构基金会支付。