Test Problem Generator for the Multidimensional Assignment Problem

The multidimensional assignment problem (MAPs) is a higher dimensional version of the standard linear assignment problem. Test problems of known solution are useful in exercising solution methods. A method of generating an axial MAP of controllable size with a known unique solution is presented. Certain characteristics of the generated MAPs that determine realism and difficulty are investigated.     

A new algorithm for pole assignment of single-input linear systems using state feedback

In this paper we present a new algorithm for the single-input pole assignment problem using state feedback. This algorithm is based on the Schur decomposition of the closed-loop system matrix, and the numerically stable unitary transformations are used whenever possible, and hence it is numerically reliable.The good numerical behavior of this algorithm is also illustrated by numerical examples.     

Traffic assignment in communication satellites

A high capacity communication satellite interconnects scores of ground stations simultaneously. Under the Satellite-Switched/Time Division Multiple Access (SS/TDMA) system, each channel of the satellite is allocated to a pair of ground stations for a certain time period, after which the whole set of allocations (called a switch) is changed simultaneously. The problem we address is to minimize the time length of the entire sequence of switches, subject to a limit on the number of switches. We formulate this as a 3-index bottleneck-sum assignment problem, and solve it by a heuristic that obtains consistently better results than earlier methods based on different formulations.     

Blocking probability analysis of survivable routing in WDM optical networks with/without sparse-wavelength conversion

In this paper, a new algorithm for wavelength assignment has been proposed and its performance is evaluated in terms of blocking probability and fairness. It has been shown that the proposed algorithm offers the least blocking probability. The blocking performance of wavelength division multiplexing (WDM) network has been analyzed for the network having 10 nodes and for varying loads. As the load per link (in Erlangs) increases, the blocking probability increases. The result shows that the performance of first-fit algorithm is better than random algorithm whereas the proposed algorithm offers the least blocking.     

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.     

求解二次分配问题的新的流量模型

二次分配问题是具有广泛应用背景的经典组合优化难题之一。本文在二次分配问题已有线性化模型的基础上,提出了一种新的基于流量的线性化模型。数值试验结果表明,新模型无论从时间上还是计算节点数都更具有优势。     

Optimizing the marriage market: An application of the linear assignment model

Research shows that the success of marriages and other intimate partnerships depends on objective attributes such as differences in age, cultural background, and educational level. This article proposes a mathematical approach to optimizing marriage by allocating spouses in such a way as to reduce the likelihood of divorce or separation. To produce our optimization model, we use the assumption of a central “agency” that would coordinate the matching of couples. Based on a representative and longitudinal sample of 1074 cohabiting and married couples living in Switzerland, we estimate various objective functions corresponding to age, education, ethnicity, and prior divorce concerning every possible combination of men and women. Our results show that the current state of marriages or partnerships is well below the social optimum. We reallocate approximately 68% of individuals (7 out of 10) to a new couple that we posit has a higher likelihood of survival. From this selection of new partners, we obtain our final “optimal” solutions, with a 21% reduction in the objective function.     

调剂问题的Vague指派方法研究

调剂工作是硕士研究生招生录取过程中一项非常重要的工作.论文以硕士研究生调剂工作为例,通过分析基本特征,将其转化为指派问题进行研究.并借助于Vague集思想,运用面试投票的方法获得效益矩阵.根据评价者的不同偏好特征采用记分函数将Vague值转化为实数,得到了实数满意度矩阵.进而不仅实现了学生和录取单位的共赢,也实现了资源的优化配置.该方法一方面为此类问题的解决提供了一种有效途径,另一方面也在理论上找到了Vague指派的一般步骤,通过数据计算保证了该方法在问题解决上的有效性和可行性.     

Assignments of Nonexchangeable Proton Resonances and the Solution Structures of d–TGGGT

In this paper, we report the studies of the solution structures of synthetic pentadeoxyribonucleotide d-TGGGT(NH₄ ⁺ salt) using 2D–NMR. The 1H–NMR experiments with different temperatures and concentrations reveal an equilibrium between single strand and aggregation. In the experimental condition(22°C, 13mmol/ L), the cross peaks in the COSY spectrum are mainly from single strand, and the spin systems of sugar resonances of this component can be assigned. In contrast, the cross peaks in the NOESY spectrum mainly come from aggregation and the sequential assignments of bases, sugar 1′, 2′ and 2″ protons can be carried out. From NOE connectivities, it is obvious that the aggregation adopts a right–handed helix conformation. It is suggested that the aggregation in our experiment corresponds to the tetramolecular complex.