Generalized Scalarizing Problems GENS and GENSLex of Multicriteria Optimization

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making".

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Classification-Based Method of Linear Multicriteria Optimization

The paper describes a classification-based learning-oriented interactive method for solving linear multicriteria optimization problems. The method allows the decision makers describe their preferences with greater flexibility, accuracy and reliability. The method is realized in an experimental software system supporting the solution of multicriteria optimization problems.

MultiDecision-2: A Multicriteria Decision Support System

The paper presents a multicriteria decision support system, called MultiDecision-2, which consists of two independent parts - MKA-2 subsystem and MKO-2 subsystem. MultiDecision-2 software system supports the decision makers (DMs) in the solving process of different problems of multicriteria analysis and linear (continues and integer) problems of multicriteria optimization. The two subsystems MKA-2 and MKO-2 of of MultiDecision-2 are briefly described in the paper in the terms of the class of the problems being solved, the system structure, the operation with the interface modules for input data entry and the information about DM’s local preferences, as well as the operation with the interface modules for visualization of the current and final solutions.

A Multicriteria Decision Support System MultiDecision-1

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making."

Multicriteria Evaluation and Optimization of Hierarchical Systems

It is shown that any multicriteria problem can be represented by a hierarchical system. Separate properties of the object are evaluated at the lower level of the system, using a criteria vector, and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriteria problems of evaluation and optimization. It is based on nested scalar convolutions of vector- valued criteria and allows simple structural and parametrical synthesis of multicriteria hierarchical systems.