一种凸非球面镜补偿检验的新方法

凸非球面检验是光学检验中一个比较困难的问题。结合一块Φ110mm的凸双曲面镜,在分析几种传统检验方法的基础上,提出了一种用透镜组补偿检验凸非球面的新方法。令球差系数∑S1=0,用三级像差理论求解光学系统的初始结构,并通过Zemax光学设计软件对初始结构进行优化,克服了传统检验方法的缺点和不足。从设计结果可以看出,系统的像差得到了很好的校正,使得凸双曲面达到了很高的检验精度,从而使非球面的检验更加方便。     

Optimization over the efficient set

This paper deals with the problem of maximizing a function over the efficient set of a linear multiple objective program. The approach is to formulate a biobjective program with an appropriate efficient set. The penalty function approach is motivated by an auxiliary problem due to Benson.     

On the Multilevel Structure of Global Optimization Problems

In this paper we will discuss the multilevel structure of global optimization problems. Such problems can often be seen at different levels, the number of which varies from problem to problem. At each level different objects are observed, but all levels display a similar structure. The number of levels which can be recognized for a given optimization problem represents a more complete measure of the difficulty of the problem with respect to the standard measure given by the total number of local minima. Moreover, the subdivision in levels will also suggest the introduction of appropriate tools, which will be different for each level but, in accordance with the fact that all levels display a similar structure, will all be based on a common concept namely that of local move. Some computational experiments will reveal the effectiveness of such tools.     

On Method for Uncertain Multiple Attribute Decision Making Problems with Uncertain Multiplicative Preference Information on Alternatives

The uncertain multiple attribute decision making (UMADM) problems are investigated, in which the information about attribute weights is known partly and the attribute values take the form of interval numbers, and the decision maker (DM) has uncertain multiplicative preference information on alternatives. We make the decision information uniform by using a transformation formula, and then establish an objective-programming model. The attribute weights can be determined by solving the developed model. The concept of interval positive ideal point of alternatives (IPIPA) is introduced, and an approach based on IPIPA and projection to ranking alternatives is proposed. The method can avoid comparing and ranking interval numbers, and can reflect both the objective information and the DMs subjective preferences.     

权监督多级模糊优选模型

本从多级模糊优选概念出发，建立一种以决策经验，偏好为监督，在方案优选确定过程中融合主、客观权重，同时确定评价指标权重和决策方案优属度的权监督多级模糊优选算法。     

Feedback Competitive Advertising Strategies with a General Objective Function

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max–min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.     

关于最短路问题的一个双目标优化问题

本文研究了一个双目标最短路问题的变形问题,在该变形问题中,一个目标函数还是路的长度,另一个目标函数则是路的容量,在Pareto-optimal最优解的意义下,本文给出了一个时间复杂性为O（n^3 )的算法,在字典序最优解的意义下,本文给出了一个时间复杂性为O(n^3)的算法。     

A dual approach to solve the fuzzy linear programming problem

A concept of fuzzy objective based on the Fuzzification Principle is presented. In accordance with this concept, the Fuzzy Linear Mathematical Programming problem is easily solved. A relationship of duality among fuzzy constraints and fuzzy objectives is given. The dual problem of a Fuzzy Linear Programming problem is also defined.     

Multiple objective linear programming models with interval coefficients – an illustrated overview

In most real-world situations, the coefficients of decision support models are not exactly known. In this context, it is convenient to consider an extension of traditional mathematical programming models incorporating their intrinsic uncertainty, without assuming the exactness of the model coefficients. Interval programming is one of the tools to tackle uncertainty in mathematical programming models. Moreover, most real-world problems inherently impose the need to consider multiple, conflicting and incommensurate objective functions. This paper provides an illustrated overview of the state of the art of Interval Programming in the context of multiple objective linear programming models.     

A multiplicative version of Promethee II applied to multiobjective optimization problems

The method Promethee II has produced attractive results in the choice of the most satisfactory optimal solution of convex multiobjective problems. However, according to the current literature, it may not work properly with nonconvex problems. A modified version of this method, called multiplicative Promethee, is proposed in this paper. Both versions are applied to some analytical problems, previously optimized by an evolutionary algorithm. The multiplicative Promethee got much better results than the original Promethee II, being capable of solving convex and nonconvex problems, with continuous and discontinuous Pareto fronts.