群决策中两类三端点区间数判断矩阵的集结方法

研究群决策过程中三端点区间数互反判断矩阵和三端点区间数互补判断矩阵的集结. 采用OWA(Ordered weighted averaging) 方法将决策者的偏好信息集结为两个三端点区间数判断矩阵. 基于三端点区间数判断矩阵的完全一致性概念, 建立三端点区间数判断矩阵的权重求解模型. 根据群决策背景下专家群最大一致的目标, 建立求解专家群体偏好权重的模型. 在第二阶段建立群偏好权重分布范围估计模型, 最后通过可能度方法以排定各方案的最终优劣顺序.     

基于模糊判断矩阵的两阶段群决策方法

针对多属性群决策问题,提出一种两阶段决策分析方法。通过分析积型模糊一致性判断矩阵和模糊判断矩阵的排序向量之间的偏差,建立并求解一个规划模型,得到专家模糊判断矩阵的排序向量。由最小化专家模糊判断矩阵的排序向量与专家群组排序向量的偏差,再次建立并求解一个规划模型,得到反映专家群组偏好的排序向量,从而得出基于模糊判断矩阵的两阶段群决策方法。通过2个算例说明了该方法的可行性与有效性。     

一种基于残缺语言判断矩阵的群决策模型

研究了偏好信息为残缺语言判断矩阵的群决策问题。通过创建一个转换公式,将加性语言判断矩阵转化为互补判断矩阵,探讨了判断矩阵转换的一致性;应用转换公式将专家个体的加性残缺语言判断矩阵转化为残缺互补判断矩阵,并利用残缺互补判断矩阵排序向量的和行归一法,求出专家个体的排序向量;根据专家个体的排序向量,通过建立并求解一个非线性规划模型,得到专家群组的排序向量,从而实现备选方案的排序和择优。通过算例说明了方法的可行性与有效性.     

区间Pythagorean模糊前景多阶段多属性应急决策方法

针对属性权重未知且决策信息为区间Pythagorean模糊语言的应急决策问题,提出一种基于组合赋权和前景理论的多阶段多属性决策方法。根据方案信息熵确定属性权重范围,并以区间Pythagorean模糊熵最小为目标构建模型并求解,以确定属性权重。定义正负理想点作为参考点,运用前景理论求出每一阶段各状态下的前景值,并考虑前一阶段方案对后一阶段状态概率的影响,求出方案链的前景值。在此基础上,以方案链的前景值最大和成本最小为目标构建优化模型,并将多目标转化为单目标,求解模型以确定各阶段的最优方案。以某传染病疫情防控应急决策问题为算例验证了该方法的可行性,并将多阶段决策效果与单一阶段的决策结果进行比较分析,验证了该方法的有效性。     

一种基于GA-FAHP的软件漏洞风险评估方法

针对软件系统中漏洞的风险等级确定等问题,提出了一种利用遗传模糊层次分析法(GA-FAHP)评估软件漏洞风险的方法。该方法首先利用改进的模糊层次分析法求出各风险因素权重,并建立模糊判断矩阵;其次将模糊判断矩阵的一致性检验与修正计算过程转化为带约束的非线性系统优化问题,并利用遗传算法求解;最后,通过GA-FAHP算法求出软件漏洞的风险值。实验结果表明,该方法具有较好的准确性和有效性,为软件漏洞风险评估提供了一种可行的途径。     

基于一致性指标的两类不确定偏好信息集结

研究了两类区间数判断矩阵偏好信息的集结问题.首先,基于Saaty提出的数字互反判断矩阵一致性检验指标(CR),给出了区间数互反判断矩阵的满意一致性条件;然后利用互反与互补判断矩阵之间的关系求解出数字互补判断矩阵的一致性指标(CGCI),并在此基础上给出了区间数互补判断矩阵的满意一致性条件;最后建立了一致性指标最大的两类区间数判断矩阵偏好信息的集结模型,并用此模型解决了供应链中伙伴企业的选择问题.     

FMEA环境下区间梯形二型模糊群体判断聚合方法研究

针对失效模式和影响分析高度不确定的复杂群体判断环境,提出一种新的区间梯形二型模糊(IT2 TF)群体判断聚合方法。通过深度挖掘数据信息求解信息的集中趋势和波动范围,构建隶属函数参数模型,将含有个体判断不确定性的一组区间判断信息聚合成IT2 TF群体判断结果,从而量化群体判断的一致性意见并记录实际存在的不确定性信息。算例分析结果验证了该聚合方法的有效性及实用性,并表明其能提高群体判断结果的准确度。     

基于模拟退火粒子群算法的AHP排序权值计算

层次分析法( AHP)中根据判断矩阵求解排序权重问题本质上为一个使一致性指标最小化的优化问题.针对现有解决方法中的不足,提出一种结合粒子群和模拟退火原理,并且根据AHP的特点引入特征粒子来求解判断矩阵排序权重的算法,同时,针对一致性不满足条件的矩阵或者残缺矩阵,在一致性指标中引入可信度参数,使算法能够动态修正不一致判断矩阵或者残缺矩阵,应用的范围更加广泛.文中对判断矩阵求解排序权重以及一致性检验、模拟退火粒子群算法解决AHP排序问题进行了介绍,并给出了实验数据以及分析.实例结果表明,算法可行且有效,计算结果精度高,稳定性好.     

基于粒子群算法的模糊层次分析模型

针对模糊层次分析法中存在的模糊判断矩阵一致性检验和修正困难、元素权重计算繁琐的问题,从模糊判断矩阵的定义角度出发,构建了基于粒子群算法的模糊层次分析模型(PSO-FAHP),提出了包含模糊判断矩阵一致性修正及各元素排序过程的非线性带约束优化问题,引入粒子群算法实现了问题的求解,并分析了模型的合理性。最后通过数值算例对比了模型的计算结果,验证了模型的正确性。对模糊层次分析法的实践应用具有一定的指导意义。     

群决策中两类不确定偏好信息的集结方法研究

研究区间数互反判断矩阵和区间数互补判断矩阵的集结,采用UOWA算子将决策者的偏好信息集结为区间数互反判断矩阵和互补判断矩阵两种形式,结合决策者给出的允许偏差,定义群满意度隶属函数,建立求解群偏好一致程度最大化的权重模型．为解决模型存在多组最优解问题,在第2阶段建立群偏好权重分布范围估计模型,研究模型所具有的性质,最后通过区间数比较的可能度方法排定各方案的最终优劣顺序。     

A direct method for synthesis of optimum distributed systems

The present paper is concerned with the numerical solution of the synthesis problem for optimal linear distributed control systems, via a specific direct method. For this method the control function is represented by a finite number of conveniently chosen functions. In this work an example of a linear diffusion system with boundary control is considered, which is worked out entirely, including numerical results. Proper proof are given for the consistency, stability, and convergence of the numerical solution by that direct method. Also, a procedure is indicated for estimating the approximation error in the computed optimal control.     

Solving algebraic equations on a microcomputer

Equation-solving programs for microcomputers make the numerical solution of algebraic equations an easy task. It is no longer necessary to learn or to program algorithms for the solution of many different types of equations. A single equation or a set of simultaneous equations may simply be entered into the computer and numerically solved for unknowns without concern as to whether the equations are linear or non-linear. Several examples of possible applications of equation-solving programs are discussed. Solution times for these examples are given for SEQS on the Apple II and Macintosh computers. The example sets of equations, which include chemical equilibrium and enzyme kinetics problems, have been chosen to demonstrate important aspects of the uses and limitations of equation solving. The four examples discussed are: a two-compartment pharmacokinetic model, citric acid ionization in aqueous solution, an enzyme inhibition model, and an example of the application of an equation-solving program in doing a simple non-linear regression problem.     

Modern modeling of a classic multiperiod problem

In this paper we discuss the integration of modeling and programming in order to solve problems in operations research and decision support. Our goal is to integrate modeling into the larger programming scheme of things and, conversely, to inject programming into modeling. This integration leads to a technologically open way to handle problems in OR, AI, etc. since the full programming arsenal can be brought to bear on these problems and since both problem solving and model management can be abetted by software engineering techniques. Here, by means of variations on a single example, we will illustrate the solution of a linear program, a goal program, a disjunctive program, a hill climbing search, a branch and bound search, and a parallel solution to a stochastic problem.     

有库存约束的有保质期产品经济批量模型

研究了库存容量有限、需求动态变化且确定的有保质期产品的经济批量问题.在准备成本、单位成本、库存持有成本和损耗成本均为线性的情况下,建立了问题的数学模型,目标是最小化总成本.提出了求解该问题的启发式算法,在无库存约束下用Wagner-Whitin算法求出解的下界,通过对各周期的数量移动消除不可行周期以满足库存约束.给出了数值计算实例.     

User friendly micro computer program for solving fractional and linear programming problems

Fractional Linear Programming (FLP) has many applications in management science as well as in engineering. We have developed a microcomputer program to solve linear and FLP problems. It is written in TURBO PASCAL which can be used on a wide variety of microcomputers. Because data entry constitutes a large proportion of the total computer solution time, careful attention has been placed on the human factors of human-computer interaction in that stage of program development. A test example is presented to demonstrate the usefulness of this program.     

Probabilistic cost estimation in advance of production in a computerized manufacturing system through stochastic geometric programming

A mathematical model for stochastic cost optimization has been developed. The model contains cost terms such as inventory cost, penalty cost for due date violation, and the machining cost. The probable range of cost has been estimated by a stochastic geometric program. If an exact solution is desired, a two stage stochastic geometric program has to be solved. This is mathematically tedious and requires great computational effort. However, managers are often concerned with a policy decision which can be based on the probable lower and upper bounds on the cost function. The probability level on the lower bound of cost has been calculated through the theory of error propagation. This approach is explained through an example.     

Linear programming with fuzzy coefficients in constraints

This paper presents a new method for solving linear programming problems with fuzzy coefficients in constraints. It is shown that such problems can be reduced to a linear semi-infinite programming problem. The relations between optimal solutions and extreme points of the linear semi-infinite program are established. A cutting plane algorithm is introduced with a convergence proof, and a numerical example is included to illustrate the solution procedure.     

PI控制中衰减度与H∞指标的相容性

研究n阶线性定常系统在PI控制下衰减度与H∞指标的相容性问题.首先基于D-分割法和边界穿越定理,分别推导了描述PI控制器参数稳定域边界、PI控制器满足期望的衰减度指标的参数边界和期望的H∞指标的参数边界的解析表达式.再应用满意控制思想,对上述期望指标的相容性进行了分析,给出了相容指标较好的取值范围.当上述两类指标相容时,可以迅速得到整个PI控制器相容性解集(满意解集).用一个算例说明了所提出的设计方法的有效性.     

An effective subgradient algorithm for the generalized assignment problem

A modified subgradient algorithm is presented for the generalized assignment problem, which, like the classical assignment problem, is concerned with the minimum cost assignment of agents to jobs. The generalized assignment problem, however, permits differences in job performance efficiencies among agents and thereby allows the possibility that each agent may be assigned more than a single job, as long as each job is ultimately assigned and the total resources available to every agent are not exceeded. A two stage heuristic algorithm using a modified subgradient approach and branch and bound is developed for solving the problem. By computing step sizes precisely and using the dual as a bound, the algorithm is shown to be particularly effective and easy to program and implement. A numerical example is presented to illustrate the model and method, and computational experience is cited for problems containing up to 12,000 0–1 variables.     

Assessment of a non-adaptive deterministic global optimization algorithm for problems with low-dimensional non-convex subspaces

The optimum and at least one optimizing point for convex nonlinear programs can be approximated well by the solution to a linear program (a fact long used in branch and bound algorithms). In more general problems, we can identify subspaces of ‘non-convex variables’ such that, if these variables have sufficiently small ranges, the optimum and at least one optimizing point can be approximated well by the solution of a single linear program. If these subspaces are low-dimensional, this suggests subdividing the variables in the subspace a priori, then producing and solving a fixed, known number of linear programs to obtain an approximation to the solution. The total amount of computation is much more predictable than that required to complete a branch and bound algorithm, and the scheme is ‘embarrassingly parallel’, with little need for either communication or load balancing. We compare such a non-adaptive scheme experimentally to our GlobSol branch and bound implementation, on those problems from the COCONUT project Lib1 test set with non-convex subspaces of dimension four or less, and we discuss potential alterations to both the non-adaptive scheme and our branch and bound process that might change the scope of applicability.