Smooth penalty function method for rigorous optimization of distillation processes

Integer decisions on stage numbers and feed locations, and global optimality are still challenging for rigorous optimization of distillation processes. In the present article, we propose a smooth penalty function method to address both these problems. The proposed method is based on the relaxation of the integer decision problem into continuous nonlinear programming (NLP) problem by adopting the bypass efficiency model developed by Dowling and Biegler. A smooth penalty term (SPT) is proposed and added to the total annual cost (TAC) function to form a new objective function, namely, the smooth penalty function. Using the new objective function, the problem is initially solved with negative weight coefficients for the SPTs regarding each column section to get an optimum near the global optimum of the SPT. Then, starting from this solution, the problem is solved again iteratively by increasing the values of the weight coefficients until all the stage numbers become integers. The performance of the method is validated by an illustrating problem and in three case studies, including a reactive distillation optimization problem.     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

基于熵的QFD在航空武器研制中的应用

由于在航空武器研发过程中很难得到准确的用户需求信息,针对这种信息的不完整和不确定性,采用了对称的模糊数据来获取用户含糊表达中的信息,并且在传统的质量功能展开(QFD)模型中引入熵的方法来确定指标权重及其相互之间的关系,建立了基于熵的QFD模型,并以某航空武器装备为例说明了该模型的实用性.     

Weak Schur numbers and the search for G.W. Walker’s lost partitions

A set A of integers is weakly sum-free if it contains no three distinct elements x,y,z such that x+y=z. Given k≥1, let WS(k) denote the largest integer n for which {1,…,n} admits a partition into k weakly sum-free subsets. In 1952, G.W. Walker claimed the value WS(5)=196, without proof. Here we show WS(5)≥196, by constructing a partition of {1,…,196} of the required type. It remains as an open problem to prove the equality. With an analogous construction for k=6, we obtain WS(6)≥572. Our approach involves translating the construction problem into a Boolean satisfiability problem, which can then be handled by a SAT solver.     

区间型灰数四则运算的直接表示

区间数是一类特殊的灰数,它的四则运算在灰数学、概率论、未确知数学中,有广泛的应用,区间数的加减法,有明显的直接表示,但乘除法,涉及变号问题,比较复杂,本文给出乘除运算的直接表示。     

2010年潮州市食品微生物抽检检测报告分析

为了解潮州市2010年食品微生物污染状况.依据国家标准GB 4789.2-2008和GB 4789.3-2008对454份样品进行菌落总数和大肠菌群的检测;结果表明食品包装材料合格率最低,干性调味料合格率最高,分别为51.28%和82.69%;省内与省外食品的大肠菌群检测合格率存在显著性差异.两者合格率分别为95.83...     

舰载导弹配送路径决策模糊熵物元模型

为确定舰载导弹配送路径的最佳方案,构建一种舰载导弹配送路径的综合物元决策模型。将模糊数学、物元分析、熵及灰色关联度等理论有机结合,在考虑影响目标决策的多种因素的基础上得到备选路径决策方案的模糊关联熵物元,并进行实例分析。分析结果证明:该物元模型清晰简洁,能为指挥决策者提供一种快速有效的辅助决策手段。     

基于FAHP及GRA的刀具优选方法研究

针对传统层次分析法(AHP)在构建刀具优选判断矩阵时没有考虑评价工程师主观判断的模糊性和指标属性的模糊性,导致刀具优选可信度和准确性降低的问题。分析了影响刀具选择的约束因素,建立了一种两级结构的多目标刀具优选模型,包括刀具的加工时间T、加工质量Q、加工成本C、资源消耗R、环境影响E五个优化目标;提出并设计了基于三角模糊数的模糊层次分析法(FAHP)及灰色关联分析(GRA)法进行求解刀具优选层次模型的算法,在三角模糊数互补判断矩阵传统计算权重方法的基础上,进行了算法优化。结合某航空制造企业叶片榫头铣削刀具优化选择的案例,证明了该方法用于刀具优选是可行且有效的。     

Fast modular exponentiation of large numbers with large exponents

In many problems, modular exponentiation |x^b|_m is a basic computation, often responsible for the overall time performance, as in some cryptosystems, since its implementation requires a large number of multiplications.It is known that |x^b|_m=|x^|b|_(m)|_m for any x in [1,m−1] if m is prime; in this case the number of multiplications depends on (m) instead of depending on b. It was also stated that previous relation holds in the case m=pq, with p and q prime; this case occurs in the RSA method.In this paper it is proved that such a relation holds in general for any x in [1,m−1] when m is a product of any number n of distinct primes and that it does not hold in the other cases for the whole range [1,m−1].Moreover, a general method is given to compute |x^b|_m without any hypothesis on m, for any x in [1,m−1], with a number of modular multiplications not exceeding those required when m is a product of primes.Next, it is shown that representing x in a residue number system (RNS) with proper moduli m_i allows to compute |x^b|_m by n modular exponentiations |x_i^b|_mi in parallel and, in turn, to replace b by |b|_(mi) in the worst case, thus executing a very low number of multiplications, namely log₂m_i for each residue digit.A general architecture is also proposed and evaluated, as a possible implementation of the proposed method for the modular exponentiation.     

区间数互补判断矩阵排序的一种新方法

研究了决策信息以区间数互补判断矩阵形式给出的多目标决策问题．给出了区间数一致性互补判断矩阵的概念及其判定定理；建立了一个目标规划模型，通过求解该模型得到区间数互补判断矩阵的权重向量；利用已有的可能度公式对方案进行排序与择优．提出了区间数互补判断矩阵排序的目标规划法，该方法具有操作简便和易于上机实现的特点．