定界的

Corresponding to such a NP-hard problem, this paper gives some polynomial time solvable cases, and a branch and bound algorithm with a rapid method for estimating the lower bound for general case.

对这一NP-困难的排序问题，文中给出了几个多项式可解的特殊情形，一般情况下的一个快速下界估计方法以及相应的分支定界算法。

Secondly, the research methods of the pallet loading problem are induced. Branch and Bound Method is analysed. Upper bounds for the Pallet Loading Problem are summerizaed.

接着，归纳了装盘问题的研究方法，分析了分支定界方法，重点总结了装盘问题中的定界算法。

On the assumption that the constraint field is not empty and bounded, using the branch and bound theory, an algorithm is presented to solve the by branching the upper-level decision variable.

在可行域非空有界的条件下，运用分支定界方法的思想，对上层决策变量进行分支，又提出了一个求解混合整数线性双层规划的分支定界算法。

Therefore, this is an integrated optimization problem of the resource allocation and the planning of the product development process.

本文提出了一种新的基于分枝定界的算法来解决此问题并引入一个启发式规则来提高算法的搜索效率。

First, for a given integer value of the objective function, the lower and upper bounds of the variables were determined by the optimum simplex tableau of the linear programming relaxation problem. Then the conditions on the bounds were added to the constraints as cuts to the associated objective function hyperplane. Finally, a branch procedure of the branch-and-bound algorithm was applied to finding a feasible solution on the objective function hyperplane.

对于给定的目标函数整数值，首先利用线性规划松弛问题的最优单纯形表确定变量的上、下界，然后将变量的上、下界条件加入约束条件中对相应的目标函数超平面进行切割，最后应用分支定界算法中的分支方法来搜寻目标函数超平面上的可行解。

In order to ensure the strict feasibility of the optimal solution, in the lower-level of program, the constraints are imposed on the confidence upper bounds of the structural responses by constructing the "bounding ellipsoid", which can be obtained efficiently by solving some convex LSDP problems.

对于下层优化问题，本论文构造定界椭球，通过求解凸的LSDP模型来得到结构最不利响应的一个严格上界，确保了鲁棒结构优化设计的可置信性。

In this paper,a quadratic programming method based on semidefinite programming is given to solve the design of FIR filters with discrete coefficients in the light of literature 6,which can give a better bound than a semidefinite programming relaxation method.Based on the model,the Branch-and-Bound algorithm is used to solve this problem.

基于离散系数滤波器设计问题已有的半定规划松弛模型，利用文献[6]的方法给出了该问题的二次规划松弛模型，该模型能给出比半定规划模型更好的界，然后运用分支定界方法求解该模型。

Next, after analyzing the nets′relationship in three layer channel routing, setting up the objective function toward channel area minimization, we propose some new terms, for example, the withstand bound columns, valid complete cover net sets, TRACK valid routing, etc.. The conceptions and natures of static bound of nets, dynamic bound of unrouted net set and the lower bound value of the horizontal tracks are discussed; and the methods of calculating static bound, dynamic bound and lower bound are put forward.

文章接着分析了线网在三层通道区布线中的相互关系，为了以完成布线所需通道区面积最小化为目标解决三层通道区布线问题，提出了柱界列、完全有效覆盖线网集、TRACK有效布线等一些新的概念，讨论了三层通道区布线问题中线网定界、未布线网集动界和水平通道数Lower-Bound等概念和它们的性质，给出了定界、动界、Lower-Bound值的计算方法。

The multi-stage Tabu Search fits for the situation where the problem has middle size, the quality of solution is important, and the speed is not restricted too much.(4) The combined algorithm which shares the advantages of HR and TS—high speed and high quality—is the most practicable one for middle-scale problems.

通过仿真实验对分枝定界算法、基于运行的启发式算法、多阶段禁忌搜索算法和组合算法进行一系列的对比研究，得出以下几点结论：(1)分枝定界算法只适用于问题规模小且对计算时间要求不高的场合，它是一种最优化算法；(2)启发式算法适合于求解大规模问题，尤其是实际应用中遇到的大型问题，对计算时间要求较高而对解的质量只要满意即可。

Quasi-convex relaxation algorithm, which aims to solve ordinary constraint global optimization problems, is produced by a combination of branch-and-bound method with quasi-convex lower bound and quasi-concave upper bound functions developed from quasi convex-concave extension. This algorithm extends the interval algorithm with box constraint to general constraint global optimization problem.

利用拟凸-凹扩张中构造出的函数的拟凸下界函数和拟凹上界函数，与分枝定界方法相结合，建立了求一般约束全局优化问题的拟凸松弛算法，这一算法是将盒子约束的区间算法推广到一般约束优化问题中。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。