An algorithm for ordinal sorting based on ELECTRE with categories defined by examples

This work proposes a Progressive Assisted Sorting Algorithm (PASA) based on a multicriteria evaluation ELECTRE-type method. The purpose of the PASA is to aid a decision maker to progressively sort a set of alternatives into a set of categories, which we considered are ordered (ordinal sorting), following a consistency principle. We consider the principle that if an alternative outranks (is as good as) a second one, then it must belong to the same category or to a better category. The set of alternatives already sorted by the decision maker will implicitly define the categories, and will constrain the range of categories where other alternatives may be sorted. We show how the same idea may be used in an aggregation/disaggregation approach, considering some parameters of ELECTRE are not fixed a priori, but are constrained only by the examples provided. In this context, we establish a “convex-shape property” stating that the range of possible categories for an alternative is always an interval of categories. A discussion contrasting this approach with ELECTRE TRI is included in the conclusions.     

Asymmetric solution-phase mixture aldol reaction using oligomeric ethylene glycol tagged chiral oxazolidinones

Sorting tags are oligomeric structures that can be used as protecting groups or chiral auxiliaries enabling solution-phase mixture syntheses of multiple tagged compounds in one pot and allowing for facile and predictable chromatographic separation of products at the end of synthetic sequences. Perfluorinated hydrocarbon and oligomeric ethylene glycol (OEG) derivatives are known classes of sorting tags. Herein we describe the preparation of OEGylated chiral oxazolidinones and their use in asymmetric solution-phase mixture aldol reactions. Through the use of such oxazolidinones based on tyrosine four different individually tagged aldol adducts were obtained as a mixture, chromatographically demixed, detagged, and it was shown that these processes gave the desired aldol products in good yield and enantioselectivity.     

基于端点白化权函数聚类的水环境质量等级评价分析

为更准确地评价水环境质量,将端点三角白化权函数灰色评估引入到水质综合评价中.针对以往灰色白化权函数评估主要通过测定指标灰聚类系数判定被评价对象的优劣强弱等级进行等级识别评价,对三角白化权函数计算方法进一步扩展,完成多评价对象的准确等级定位及比较排序.将这种方法应用于山东省聊城市东昌湖水水质评价中,经实例计算证明基于三角白化权函数灰色评估评价模型的稳定性、合理性和实用性为水质评价研究方法提供了新的思路和借鉴.     

Multiobjective optimization scheme for industrial synthesis gas sweetening plant in GTL process

In industrial amine plants the optimized operating conditions are obtained from the conclusion of occurred events and challenges that are normal in the working units. For the sake of reducing the costs, time consuming, and preventing unsuitable accidents, the optimization could be performed by a computer program. In this paper, simulation and parameter analysis of amine plant is performed at first. The optimization of this unit is studied using Non-Dominated Sorting Genetic Algorithm-II in order to produce sweet gas with CO 2 mole percentage less than 2.0% and H 2 S concentration less than 10 ppm for application in Fischer-Tropsch synthesis. The simulation of the plant in HYSYS v.3.1 software has been linked with MATLAB code for real-parameter NSGA-II to simulate and optimize the amine process. Three scenarios are selected to cover the effect of (DEA/MDEA) mass composition percent ratio at amine solution on objective functions. Results show that sour gas temperature and pressure of 33.98 ? C and 14.96 bar, DEA/CO 2 molar flow ratio of 12.58, regeneration gas temperature and pressure of 94.92 ? C and 3.0 bar, regenerator pressure of 1.53 bar, and ratio of DEA/MDEA = 20%/10% are the best values for minimizing plant energy consumption, amine circulation rate, and carbon dioxide recovery.     

A flexible approach to ranking with an application to MBA Programs

We develop a model for flexibly ranking multi-dimensional alternatives/units into preference classes via Mixed Integer Programming. We consider a linear aggregation model, but allow the criterion weights to vary within pre-specified ranges. This allows the individual alternatives/units to play to their strengths. We illustrate the use of the model by considering the Financial Times Global MBA Program rankings and discuss the implications. We argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking, providing an argument for sorting or what we call flexible ranking.     

Sorting with networks of data structures

We consider the problem of sorting a permutation using a network of data structures as introduced by Knuth and Tarjan. In general the model as considered previously was restricted to networks that are directed acyclic graphs (DAGs) of stacks and/or queues. In this paper we study the question of which are the smallest general graphs that can sort an arbitrary permutation and what is their efficiency. We show that certain two-node graphs can sort in time Θ(n²) and no simpler graph can sort all permutations. We then show that certain three-node graphs sort in time Ω(n^3/2), and that there exist graphs of k nodes which can sort in time Θ(nlog_kn), which is optimal.     

上海深紫外自由电子激光装置波荡器磁场调整

 在对上海深紫外项目的波荡器建造过程中,应用亥姆霍兹线圈系统测量了全部单磁块,并使用模拟退火法对磁块进行组合排序优化,使反映磁场的成本函数下降了3个数量级。对一段波荡器进行了多次测量、调整,使积分场、峰峰值误差、位相误差等各项指标达到设计要求。     

区间数互补判断矩阵的拓扑排序方法

提出了方案之间进行比较时优于与劣于的定义,通过构造与区间数互补判断矩阵相对应的有向图的方法,将互补判断矩阵的排序问题转化为有向图中顶点的拓扑排序问题,将有向图中的顶点按照备选方案的重要性顺序输出,得到的顶点的序列即为备选方案的重要性排序,数值计算实例验证了该方法的有效性与可行性。     

An axiomatic approach to noncompensatory sorting methods in MCDM,II: More than two categories

A number of recent papers have investigated the foundations of methods allowing to sort multi-attributed alternatives between several ordered categories. This paper has a similar objective. Our analysis uses a general conjoint measurement framework, encompassing most sorting models used in MDCM, that was proposed in the literature. Within this framework, we provide an axiomatic analysis of what we call noncompensatory sorting models, with or without veto effects. These noncompensatory sorting models contain the pessimistic version of ELECTRE TRI as a particular case. Our analysis can be seen as an attempt to give a firm axiomatic basis to ELECTRE TRI, while emphasizing its specific feature, i.e., the rather poor information that this model uses on each attribute.     

A FAST TREE SOREING ALGORITHM

1IntroductionSortingisbothapracticallyimportantandtheoreticallyinterestingproblem.Therearemanysortingalgorithmsdesignedforsolvingthisproblem[11.Ingeneral,therearetwoclassesofsortingalgorithm:Oneisbasedoncomparisonsandtheothermakesuseofthespecialpropertiesofintegersorstrings.Ouralgorithmusesnotonlycomparisonsbetweenkeys,butalsothekeystructures.Somewhatlaalquicksort,thetakecomplexityintheworstcaseisnotverygood,buttheaveragetimecomplealtyismuchbetterandachievesO(nlog.n).Ouralgorithmcanbeusedasa…