带有二次约束二次规划问题的分枝定界方法

提出了一种解带有二次约束二次规划问题的新的分枝定界算法对该算法进行了收敛性分析。这种方法是用新的线性规划松弛定界技术确定最优值的下界，并且把分枝定界技术和外逼近方法有机地结合起来。     

解复杂二次整数规划问题的新型分枝定界算法

针对二次整数规划问题的特征，本文对传统分枝定界算法做了一系列的改进，其包括用HNF算法寻求初始整数可行解、对变量进行某种先验排序以确定分枝变量的选取次序、及针对变量的特性来选取分枝方向等，给出了可用于求解中大规模复杂二次整数规划问题的改进型分枝定界算法。数值试验结果表明所给算法大大改进了传统的分枝定界算法，并有广泛的适用性。     

球约束凸二次规划的一个算法

针对球约束凸二次规划问题，利用Lagrange对偶将其转化为无约束优化问题，然后运用单纯形法对其求解，获得原问题的最优解。最后，对文中给出的算法给出了论证。     

多用户检测问题的半定规划方法

在码分多址系统中，求解多用户检测问题是重要环节，介绍了多用户检测问题的应用背景和发展现状，重点综述基于半定规划模型寻求多用户的检测问题次优解的几种重要方法，包括随机扰动法，坐标下降法，半定规划的割平面法和二次规划的分枝定界法等，结合数值实验，评价比较了这些方法的优缺点。     

一类带有常系数线性乘积规划问题的分支定界缩减方法

本文给出了一种求解带有常系数线性乘积规划问题的分支定界缩减算法.我们首先利用两个变量乘积的凸包络技术,分别得到目标函数与约束函数中乘积的上界与下界估计,由此构造出原问题的一个松弛凸规划问题.在此基础之上,借助超矩形的缩减技术,提出了确定原问题全局最优值下界的分支定界缩减算法,并从理论上分析了算法的收敛性.最后,利用数值实验验证了算法的有效性与可行性.     

求解不定二次约束二次规划问题的全局优化算法

不定二次约束二次规划问题广泛应用于芯片设计、无线通信网络、财政金融和众多工程实际问题．目前尚没有通用的全局收敛准则,这使得求解该问题的全局最优解面临着极大挑战．本文使用矩阵的初等变换技巧将原问题转化为等价双线性规划问题,基于等价问题的特征和线性化松弛技巧构造了等价问题的松弛线性规划,通过求解一系列松弛规划问题的最优解逐步逼近原问题的全局最优解．证明了算法的全局收敛性,并进行数值对比和随机实验,实验结果表明算法高效可行．     

线性约束优化问题一类算法

本文基于内点算法思想,给出一类线性约束优化问题的算法,并用于求解线性规划,线性分式规划,二次规划等线性约束非线性规划问题。     

不定整数二次规划的一个新的分支定界算法

本文通过正交变换及凹函数的线性下方估计得到不定整数二次规划的可分离形式的连续凸松弛问题,然后利用Lagrangian对偶技术导出该凸松弛问题最优值的Lagrangian对偶下界,再结合超矩形整数对分,建立了一个求解不定整数二次规划新的分支定界算法。最后给出了数值试验对结果进行了比较。     

凹二次规划问题的一个融合割平面方法的分支定界混合算法

把割平面方法融于分支定界方法之中,本文提出了求解凹二次规划问题的一个融合割平面方法的分支定界混合算法,证明了该算法是收敛的.数值例子也表明这个算法是有效的,并且好于单纯形分支定界算法。     

求解垂直互补约束数学规划问题的松弛方法(英文)

垂直互补约束数学规划问题在工程设计、生产计划、优化控制等方面有很多应用.本文提出了一种求解垂直互补约束数学规划问题的松弛方法,并证明了:在垂直互补约束数学规划问题线性独立的约束规范条件下,松弛问题稳定点的任何聚点是原问题的C-稳定点.如果进一步还满足二阶必要性条件,则这些聚点是M-稳定点.基本数值结果表明提出的方法可以很好的求解垂直互补约束数学规划问题.     

带非凸二次约束的二次规划问题的全局优化方法

利用二次函数的线形下界函数对带有非凸二次约束的二次规划(QP)提出一种新的求其全局最优解的分支定界算法.为改进算法的收敛性,根据问题的最优性和可行性提出一新的区域剪枝准则以排除(QP)的可行域中不存在全局解的部分.数值算例表明该准则能有效地加速算法的收敛性.     

Mixed Variable Optimization of a Load-Bearing Thermal Insulation System Using a Filter Pattern Search Algorithm

This paper describes the optimization of a load-bearing thermal insulation system characterized by hot and cold surfaces with a series of heat intercepts and insulators between them. The optimization problem is represented as a mixed variable programming (MVP) problem with nonlinear constraints, in which the objective is to minimize the power required to maintain the heat intercepts at fixed temperatures so that one surface is kept sufficiently cold. MVP problems are more general than mixed integer nonlinear programming (MINLP) problems in that the discrete variables are categorical; i.e., they must always take on values from a predefined enumerable set or list. Thus, traditional approaches that use branch and bound techniques cannot be applied.In a previous paper, a linearly constrained version of this problem was solved numerically using the Audet-Dennis generalized pattern search (GPS) method for MVP problems. However, this algorithm may not work for problems with general nonlinear constraints. A new algorithm that extends that of Audet and Dennis by incorporating a filter to handle nonlinear constraints makes it possible to solve the more general problem. Additional nonlinear constraints on stress, mass, and thermal contraction are added to that of the previous work in an effort to find a more realistic feasible design. Several computational experiments show a substantial improvement in power required to maintain the system, as compared to the previous literature. The addition of the new constraints leads to a very different design without significantly changing the power required. The results demonstrate that the new algorithm can be applied to a very broad class of optimization problems, for which no previous algorithm with provable convergence results could be applied.     

Two-machine flow shop problem with unit-time operations and conflict graph

This paper addresses the problem of scheduling, on a two-machine flow shop, a set of unit-time operations subject to the constraints that some conflicting jobs cannot be scheduled simultaneously on different machines. In the context of our study, these conflicts are modelled by general graphs. The problem of minimising the maximum completion time (makespan) is known to be NP-hard in the strong sense. We propose a mixed-integer linear programming (MILP) model. Then, we develop a branch and bound algorithm based on new lower and upper bound procedures. We further provide a computer simulation to measure the performance of the proposed approaches. The computational results show that the branch and bound algorithm outperforms the MILP model and can solve instances of size up to 20,000 jobs.     

Spread time considerations in operational fixed job scheduling

In this study, we consider the operational fixed job scheduling problem on identical parallel machines. We assume that the jobs have fixed ready times and deadlines, and spread time constraints are imposed on machines. Our objective is to select a set of jobs for processing so as to maximise the total weight. We show that the problem is strongly NP-hard, and we investigate several special polynomially solvable cases. We propose a branch and bound algorithm that employs size reduction mechanisms, dominance conditions, and powerful lower and upper bounds. The computational results reveal that the branch and bound algorithm returns optimal solutions for problem instances with up to 100 jobs in reasonable solution times.     

Computerized Layout Design: A Branch and Bound Approach

This paper presents a computerized procedure for layout design. The layout problem is formulated as a quadratic set covering problem. A branch and bound method for optimizing the resulting problem is devised. As a result, optimal and suboptimal layouts can be provided to the layout engineer for consideration and modification.     

A STATIONARY CYCLICAL PRODUCTION SCHEDULING PROBLEM UNDER A NONADDITIVE OUTPUT FUNCTION

The purpose of this paper is to formulate and solve a nonlinear mixed zero-one integer programming problem aimed to maximize total output by scheduling the operational time of N non-identical machines. Properties of the optimal solution are identified under restrictions imposed on machine availability and various budget constraints. A branch and bound algorithm to solve the problem is suggested.     

Single machine scheduling problem with batch setups involving positional deterioration effects and multiple rate-modifying activities

This article considers a single machine scheduling problem with batch setups, positional deterioration effects, and multiple optional rate-modifying activities to minimize the total completion time. This problem is formulated as an integer quadratic programming problem. In view of the complexity of optimally solving this problem, a two-phase heuristic algorithm is proposed where an optimal but non-integer solution is obtained in the first phase by solving a continuous relaxed version of the problem. This solution serves as a lower bound for the optimal value of the total completion time. The second phase of the algorithm generates an integer solution using a simple rounding scheme that is optimum or very close to optimum for this problem. Empirical evaluation and comparison with an existing heuristic algorithm show that the proposed heuristic algorithm is substantially more effective in solving large-size problem instances.     

直运越库物流的精确算法研究

多车辆直运越库调度问题的目标是最小化所有客户中的最晚到货时间.首先,建立了描述该问题的混合整数线性规划模型,并使用运筹优化工具ILOG CPLEX进行求解;其次,构造了基于LPT规则的启发式算法,为精确算法提供了初始可行解,并对分支定界算法进行详细的分析;最后,在数值实验部分,通过数学模型与分支定界的比较及算法性能的分析后,得出分支定界算法具有更高的效率,该分支定界算法在合理的时间内能够求解到11个供应商规模的问题.