业务流程管理中的大规模整数规划问题求解

对从企业业务流程管理中抽象出来的大规模整数规划问题的计算机求解方法进行讨论。提出一种内存优化管理方法,能更高效地存储海量数据。同时对求解整数规划问题的经典算法——分枝定界算法进行研究,利用人工智能的搜索思想,给出分枝定界法的改进算法,使其能快速求解大规模整数规划问题。     

基于遗传分枝定界算法的Flow-shop调度问题

Flow shop调度问题属于NP难题,传统的方法很难求出精确最优解,提出了一种遗传分枝定界算法,即在遗传算法中引入分枝定界算法保持对优化解有贡献的工件部分顺序,求解3机Flow shop调度问题,该算法与常用的遗传局部算法和遗传动态规划算法类似,用随机方法测试例子,与目前著名的Taillard的禁忌搜索算法和Reeves的遗传算法两种改进算法进行比较,大量的数据实验证实了遗传分枝定界算法的有效性。     

3机Flow-shop调度问题研究

提出了一种遗传分枝定界算法求解3机Flow-s hop调度问题，该算法类似于常用的遗传局部算法和遗传动态规划算法．用随机方法生成测 试例子，通过与著名的Taillard的禁忌搜索算法和Reeves的遗传算法进行比较，实验结果证 实了遗传分枝定界算法的有效性．     

航天测控调度分枝定界算法

通过分析航天测控调度问题的测控需求,建立了航天测控调度整数规划模型,引入了拉格朗日松弛思想并与分枝定界算法结合,设计了基于拉格朗日松弛的分枝定界算法求解航天测控调度问题。通过对两个场景的仿真实验,得到了两个场景的航天测控调度问题最优值,验证了基于拉格朗日松弛的分枝定界算法的有效性。     

基于遗传分枝定界算法的F1ow—shop调度问题

F1ow—shop调度问题属于NP难题，传统的方法很难求出精确最优解，提出了一种遗传分枝定界算法，即在遗传算法中引入分枝定界算法保持对优化解有贡献的工件部分顺序，求解3机F1ow—shop调度问题，该算法与常用的遗传局部算法和遗传动态规划算法类似，用随机方法测试例子，与目前著名的Taillard的禁忌搜索算法和Reeves的遗传算法两种改进算法进行比较，大量的数据实验证实了遗传分枝定界算法的有效性。     

单机序列相关Setup最小化最大拖期算法

研究了一个具有序列相关Setup带交货期的单机调度NP问题,优化目标是最小化最大拖期。提出了一个求解该问题的分枝定界枚举算法,其中包括确定问题上界和下界的方法,以及两条优势规则。计算实验证明了本文提出算法的有效性。     

基于约束传播的HFS调度研究

将约束传播技术同分枝定界法相结合求解优化目标为最小最大完工时间的混合流水车间调度问题。算法核心是根据资源松弛度确定关键阶段,通过在分枝定界算法中嵌入动态可调的开工时间窗口,用顺序传播、资源传播、上下游工序传播,动态修改每个操作的开工时间窗上下界,并在算法特点基础上给出相应的剪枝下界,以减小搜索空间,提高分枝定界法的优化能力。实验结果证明了算法的有效性。     

求解具0－1变量的两级决策问题的分枝－定界优化方法

在一类具０－１变量的两级决策问题基础上，研究了求解该问题的分枝－定界优化方法，分析了算法中定界的设计和分枝准则的选择。文中示例的仿真结果表明，该算法是有效的。     

求解具0—1变量的两级决策问题的分枝—定界优化方法

在一类具０－１变量的两级决策问题基础上，研究了求解该问题的分枝－定界优化方法，分析了算法中定界的设计和分枝准则的选择。文中示例的仿真结果表明，该算法是有效的。     

复合并行机排序问题的启发式算法研究

为有效解决复合并行机排序的极小化最大完成时间问题,提出了分支定界算法和改进的启发式动态规划算法。利用分支定界算法的3个工具:分支模型、边界和优先规则,构建出分支搜索树。按优先规则进行定界搜索,从而减小了问题求解规模。将原始作业转换为虚拟作业,根据Johnson法则,求解出原问题的最优排序。改进的动态规划算法复杂度分析和计算实验表明,这两个算法可靠性高并且可以解决实际问题。     

A scalable FETI-DP algorithm for a semi-coercive variational inequality

We develop an optimal algorithm for the numerical solution of semi-coercive variational inequalities by combining dual-primal FETI algorithms with recent results for bound and equality constrained quadratic programming problems. The discretized version of the model problem, obtained by using the FETI-DP methodology, is reduced by the duality theory of convex optimization to a quadratic programming problem with bound and equality constraints, which is solved by a new algorithm with a known rate of convergence given in terms of the spectral condition number of the quadratic problem. We present convergence bounds that guarantee the scalability of the algorithm. These results are confirmed by numerical experiments.     

Global minimization of indefinite quadratic problems

A branch and bound algorithm is proposed for finding the global optimum of large-scale indefinite quadratic problems over a polytope. The algorithm uses separable programming and techniques from concave optimization to obtain approximate solutions. Results on error bounding are given and preliminary computational results using the Cray 1S supercomputer as reported.     

FETI based algorithms for contact problems: scalability,large displacements and 3D Coulomb friction

Theoretical and experimental results concerning FETI based algorithms for contact problems of elasticity are reviewed. A discretized model problem is first reduced by the duality theory of convex optimization to the quadratic programming problem with bound and equality constraints. The latter is then optionally modified by means of orthogonal projectors to the natural coarse space introduced by Farhat and Roux in the framework of their FETI method. The resulting problem is then solved either by special algorithms for bound constrained quadratic programming problems combined with penalty that imposes the equality constraints, or by an augmented Lagrangian type algorithm with the inner loop for the solution of bound constrained quadratic programming problems. Recent theoretical results are reported that guarantee certain optimality and scalability of both algorithms. The results are confirmed by numerical experiments. The performance of the algorithm in solution of more realistic engineering problems by basic algorithm is demonstrated on the solution of 3D problems with large displacements or Coulomb friction.     

A heuristic-based branch and bound algorithm for unconstrained quadratic zero-one programming

In this paper we describe a branch and bound algorithm for solving the unconstrained quadratic 0–1 programming problem. The salient features of it are the use of quadratic programming heuristics in the transformation of subproblems and exploiting some classes of facets of the polytope related to the quadratic problem in deriving upper bounds on the objective function. We develop facet selection procedures that form a basis of the bound computation algorithm. We present computational experience on four series of randomly generated problems and 14 real instances of a quadratic problem arising in design automation. We remark that the same ideas can also be applied to some other combinatorial optimization problems.     

Computational aspects of a branch and bound algorithm for quadratic zero-one programming

In this paper we describe computational experience in solving unconstrained quadratic zero-one problems using a branch and bound algorithm. The algorithm incorporates dynamic preprocessing techniques for forcing variables and heuristics to obtain good starting points. Computational results and comparisons with previous studies on several hundred test problems with dimensions up to 200 demonstrate the efficiency of our algorithm.     

A New Optimal Force Distribution Scheme of Multiple Cooperating Robots Using Dual Method

A new optimal force distribution scheme of multiple cooperating robots is proposed, in which the duality theory of nonlinear programming (NLP) is combined with the quadratic programming (QP) approach. The optimal force distribution problem is formulated as a QP problem with both linear and quadratic constraints, and its solution is obtained by an efficient algorithm. The use of the quadratic constraints is important in that it considerably reduces the number of constraints, thus enabling the Dual method of NLP to be used in the solution algorithm. Moreover, it can treat norm constraints without approximation, such as bound of the norm of the force exerted by each robot. The proposed scheme is more efficient in terms of speed than any other method. Numerical examples of two PUMA robot task using the proposed method and a well-known fast method are compared, and the results indicate the capability of real time application of our method.     

A branch-and-bound algorithm for single machine scheduling with quadratic earliness and tardiness penalties

This paper considers the problem of scheduling a single machine, in which the objective function is to minimize the weighted quadratic earliness and tardiness penalties and no machine idle time is allowed. We develop a branch and bound algorithm involving the implementation of lower and upper bounding procedures as well as some dominance rules. The lower bound is designed based on a lagrangian relaxation method and the upper bound includes two phases, one for constructing initial schedules and the other for improving them. Computational experiments on a set of randomly generated instances show that one of the proposed heuristics, used as an upper bound, has an average gap less than 1.3% for instances optimally solved. The results indicate that both the lower and upper bounds are very tight and the branch-and-bound algorithm is the first algorithm that is able to optimally solve problems with up to 30 jobs in a reasonable amount of time.     

Interval Methods for Sinusoidal Parameter Estimation: A Comparative Analysis

In this paper, we address the problem of determining maximum-likelihood estimates of sinusoid parameters from a signal that consists of sinusoids and additive noise. We present three algorithms that integrate interval methods for global optimization with procedures that decompose the problem into smaller ones. Interval methods represent a global optimization technique that is based upon the branch and bound principle. More specifically, we decompose the problems via the expectation-maximization algorithm and variations of the coordinate descent algorithm. Although, we have not proven that the proposed algorithms converge to the global optimum, their performance in our simulation example was much superior to that of the popular iterative quadratic maximum likelihood (IQML) method.     

Maximum-likelihood detection based on branch and bound algorithm for MIMO systems

Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual subproblem. In order to reduce the complexity further, the Cholesky factorization update is presented to solve the linear system at each iteration of active set algorithm efficiently. By relaxing the pruning conditions, we also present the quasi branch and bound algorithm which implements a good tradeoff between performance and complexity. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.     

A parametric branch and bound approach to suboptimal explicit hybrid MPC

In this article we present a parametric branch and bound algorithm for computation of optimal and suboptimal solutions to parametric mixed-integer quadratic programs and parametric mixed-integer linear programs. The algorithm returns an optimal or suboptimal parametric solution with the level of suboptimality requested by the user. An interesting application of the proposed parametric branch and bound procedure is suboptimal explicit MPC for hybrid systems, where the introduced user-defined suboptimality tolerance reduces the storage requirements and the online computational effort, or even enables the computation of a suboptimal MPC controller in cases where the computation of the optimal MPC controller would be intractable. Moreover, stability of the system in closed loop with the suboptimal controller can be guaranteed a priori.