Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

非同类机极小化最大完工时间的保密排序问题

提出并研究了一类非同类机的极小化最大完工时间的保密排序问题Rm||Cmax.该问题的模型参数分为若干组,每个组都由一个不愿意共享或公开自己数据的单位所拥有.基于随机矩阵变换构造了一个不泄露私有数据且与原问题等价的安全规划模型,求解该安全模型可以获得问题的最优解,而且各单位的隐私数据仍然保持不被泄露.     

汽配件颜色喷涂顺序问题的TSP转化与建模

汽配件颜色喷涂顺序问题通常以生产线上相邻汽配件颜色切换次数少为最优目标,以进一步降低生产成本.该类问题具有所有汽配件都必须喷涂一次且只喷涂一次的特点,为此提出了TSP转化与建模的方法.将待喷涂汽配件定义为TSP顶点,任意两个待喷涂汽配件的颜色切换定义为顶点的距离,仿照TSP问题构建0-1规划模型;类似于顶点距离,将某些汽配件的颜色或类别不相邻要求定义为0-1矩阵,巧妙地构造了喷涂生产的约束条件.该建模方法简单快速,通用性高,适用于具有类似特点的各类生产实践问题.     

基于线性规划的高温超导磁体线圈设计方法

电子真空回旋器件是一种对磁场精度要求较高的微波源装置, 一般采用超导磁体提供磁场环境. 超导磁体的应用中, 磁场分布的实现是超导磁体设计的核心问题. 提供回旋器件磁场的高温超导磁体包含较复杂的磁体绕组, 为了解决此类设计计算问题, 本文提出了一种包含设计区域约束的线性优化方法进行回旋器件高温超导绕组的设计优化, 通过分步的约束和线性优化计算, 可得到同时满足设计要求和绕组可实现的设计磁场电流分布设计. 计算实例的结果给出了一个提供磁场强度1 .3 Tesla, 长度285 mm 的均匀磁场区域, 同时满足多位置的磁场要求, 设计结果与要求一致度较好, 精度满足应用需求. 该计算方法是一种可适用于较复杂磁场要求和超导绕组结构的设计优化方法.     

Graph-like compacta: Characterizations and Eulerian loops

A compact graph-like space is a triple $\left(X,V,E\right)$, where $X$ is a compact, metrizable space, $V\subseteq X$ is a closed zero-dimensional subset, and $E$ is an index set such that $X⧹V\cong \text{◂+▸}E\times \left(0,1\right)$. New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta.     

Geometrical methods for analyzing the optimal management of tipping point dynamics

Natural resources are not infinitely resilient and should not be modeled as being such. Finitely resilient resources feature tipping points and history dependence. This paper provides a didactical discussion of mathematical methods that are needed to understand the optimal management of such resources: viscosity solutions of Hamilton–Jacobi–Bellman equations, the costate equation and the associated canonical equations, exact root counting, and geometrical methods to analyze the geometry of the invariant manifolds of the canonical equations. Recommendations for Resource Managers

• Management of natural resources has to take into account the possible breakdown of resilience and induced regime shifts.
• Depending on the characteristics of the resource and on its present and future economic importance, either for all initial states the same kind of management policy is optimal, or the type of the optimal management policy depends on the initial state.
• Modeling should reflect the finiteness of the data.

     

A benchmark of optimally folded protein structures using integer programming and the 3D-HP-SC model

The Protein Structure Prediction (PSP) problem comprises, among other issues, forecasting the three-dimensional native structure of proteins using only their primary structure information. Most computational studies in this area use synthetic data instead of real biological data. However, the closer to the real-world, the more the impact of results and their applicability. This work presents 17 real protein sequences extracted from the Protein Data Bank for a benchmark to the PSP problem using the tri-dimensional Hydrophobic-Polar with Side-Chains model (3D-HP-SC). The native structure of these proteins was found by maximizing the number of hydrophobic contacts between the side-chains of amino acids. The problem was treated as an optimization problem and solved by means of an Integer Programming approach. Although the method optimally solves the problem, the processing time has an exponential trend. Therefore, due to computational limitations, the method is a proof-of-concept and it is not applicable to large sequences. For unknown sequences, an upper bound of the number of hydrophobic contacts (using this model) can be found, due to a linear relationship with the number of hydrophobic residues. The comparison between the predicted and the biological structures showed that the highest similarity between them was found with distance thresholds around 5.2–8.2 Å. Both the dataset and the programs developed will be freely available to foster further research in the area.     

一带一路背景下企业地域影响力发展的规划研究

面对一个分布在新地理区域的新市场,合理规划区域服务影响力的发展战略对企业至关重要。本文假设企业的服务影响力在地理区域上的发展可以用其地理上分布的立足点来表示。单个立足点覆盖有限范围内的地理区域,并且在一个特定时刻用所有立足点所覆盖地理区域的总和来表示企业该时刻的发展状态。由于资源限制,企业对经济发展迅速的区域的覆盖必须在一定时间内逐步完成。因此,在发展时期内如何确定立足点的位置并使其位于知名城市中,是企业管理者亟待解决的问题。针对这个问题,本文首先基于时间序列预测方法建立了区域经济指标评估模型;然后使用集合覆盖理论提出了以成本和满意度为目标的选址优化模型并使用分支定界算法求解该模型;最后,使用从“一带一路”地区收集的数据对模型进行了检验。结果表明,该方法对有相关问题的企业具有较大的参考价值。