Proper inequality constraints and maximization of index vectors

For obtaining the set of all quasi-supremal index vectors (or all maximal index vectors, or all Pareto-optimal solutions) of a multiple-objective optimization problem, we present, in this paper, the method of proper inequality constraints, which does not rely on any convexity condition at all, but by which one can obtain the entire desired set. This method is based on the observation that optimizing the index of one of the objectives, with some arbitrary bounds assigned to all other objectives, may still result in inferior solutions, unless these bounds areproper. Various necessary and/or sufficient conditions are presented for the properness test.This work was supported by the National Science Foundation under Grant No. GK-32701.     

Multicriteria optimization of a composite cylindrical shell subjected to longitudinal thermal stresses and buckling under the action of torque

The multicriteria optimization of the structure and geometry of a multilayer cylindrical shell under the action of external torque and longitudinal thermal stresses is considered. From known monolayer properties of the composite and given values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined. The criteria to be optimized — the critical external torque and thermal stresses — depend on two variable parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 223–230, March–April, 2009.     

Postoptimal analysis of the multicriteria combinatorial median location problem

We consider a multicriteria variant of the well-known combinatorial minisum facility location problem (median problem) with Pareto and lexicographic optimality principles. Necessary and sufficient conditions of a solution stability to the initial data perturbations in such problems are formulated in terms of binary relations. Numerical examples are given.     

多目标供应链网络平衡模型

针对生产商、零售商和消费群三层决策者问题建立了一个多目标供应链网络均衡模型.给出此模型的均衡条件,并讨论了(弱)均衡解和标量化解之间的关系.最后,给出具体的例子说明此模型.     

Hierarchical modeling in multibody dynamics

Summary In this paper a hierarchical approach using several mechanical models with different complexities and modeling depths to describe a single engineering system is presented. The mechanical models are derived from (but not limited to) multibody dynamics. The computer power available and improvements in theoretical understanding allow today not only to perform analyses but also to attack the problem of multimodel synthesis. Therefore, hierarchical modeling is used as a basis to analyze simultaneously models with different complexities and different excitations, and to optimize the performance with the most appropriate model for an investigated mechanical effect. Since only one single engineering system is investigated, its different models must be coupled by shared parameters, and the different criteria have to be combined with multicriteria optimization algorithms in order to obtain a single feasible design. An example taken from vehicle dynamics demonstrates the application of the approach. Received 14 January 1997; accepted for publication 11 September 1997     

An Experimental Evaluation of Some Classification Methods

The classification problem is of major importance to a plethora of research fields. The outgrowth in the development of classification methods has led to the development of several techniques. The objective of this research is to provide some insight on the relative performance of some well-known classification methods, through an experimental analysis covering data sets with different characteristics. The methods used in the analysis include statistical techniques, machine learning methods and multicriteria decision aid. The results of the study can be used to support the design of classification systems and the identification of the proper methods that could be used given the data characteristics.     

Multicriteria equilibrium programming: Extraproximal methods

Multicriteria equilibrium optimization is an efficient tool for mathematical modeling of various situations in operations research, design automation, control, etc. In this paper, a formal formulation of the problem of multicriteria equilibrium optimization is given, and an approach to solving this problem is examined.     

Investigation of polynomial algorithms for solving the multicriteria three-index planar assignment problem

Under certain additional conditions imposed on the coefficients of the vector objective function in the three-index planar assignment problem, a large series of computational experiments aimed at the investigation of four polynomial algorithms for finding an asymptotically optimal solution of this problem is carried out.     

The Edgeworth-Pareto principle in terms of a fuzzy choice function

The Edgeworth-Pareto Principle, the simplest version of which has been known since the 19th century, is stated in general terms of a fuzzy choice function. The application of the principle is justified for a wide class of fuzzy multicriteria choice problems described by certain axioms of the rational behavior. These results bring the axiomatic substantiation of the Edgeworth-Pareto principle performed previously by the author to the most general form and make it possible to reveal the boundaries of that class of multicriteria choice problems for which the application of this principle is required. Based on scalarization methods as applied to multicriteria problems, upper bounds are derived for the unknown set of selected vectors.     

Multiattribute evaluation of greek banking performance

Ordinal regression analysis is proposed as a means for evaluating banking performance over multiple attributes in the presence of non-monotonic preferences. First, a multivariate statistical analysis is applied to measure the banking performance on the basis of financial ratios that derive from the study of financial statements of a sample of Greek banks for the period 1989–1992. Then, an additive utility model is assessed to obtain the final ranking of a representative sample of Greek banks.