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."The present paper describes some basic elements of the software system developed (called MultiDecision-1), which consists of two separate parts (the systems MKA-1 and MKO-1) and which is designed to support decision makers in solving different multicriteria analysis and multicriteria optimization problems. The class of the problems 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 for the two systems MKA-1 and MKO-1 are discussed

A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

Interactive methods of multiobjective optimization repetitively derive Pareto optimal solutions based on decision maker's preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the Pareto optimal set and learning about the optimization problem. However, in the case of many objective functions, the accumulation of derived solutions makes accessing the solution pool cognitively difficult for the decision maker. We propose to enhance interactive methods with visualization of the set of solution outcomes using dimensionality reduction and interactive mechanisms for exploration of the solution pool. We describe a proposed visualization technique and demonstrate its usage with an example problem solved using the interactive method NIMBUS

Distributed Performance Analysis on the Internet Using a Centric Database

In many areas of life it is useful to be able to compare one's own performance to some general benchmark data. The Internet provides a way of realizing such a comparison so that the original database can be hidden from users by locating it in a server computer and users can test their individual data in a distributed manner. An interactive and graphical user interface can be implemented with the tools of the World-Wide Web (WWW). We introduce a World-wide INTEractive Regression Analysis (WINTERA) system that operates via the Internet. The system enables a user to carry out regression analysis with an original database and evaluate the performance of the data vector of her or his own. There are two kinds of users in the system. Data suppliers enter their observation matrices to form databases. Ordinary users can evaluate observations of their own with respect to existing databases. They can also suggest their observations to be included in the databases. the data supplier decides whether (s)he accepts or rejects the information. This means that the whole database is accessible only to the data supplier. In any case, ordinary users receive information about their performance

Interactive procedure for multiobjective dynamic programming with the mixed ordered structure

The paper presents a multiobjective dynamic programming problem with the values of the criteria function in ordered structures. The first problem is a model with deterministic values; the second, one with triangular fuzzy numbers; and the third, one with discrete random variables with the k-th absolute moment finite. The fourth model is a product of the three models listed above. The aim of the paper is to present an interactive procedure which uses trade-offs and which allows to determine the final solution in the mixed ordered structure. The ordered structures and the proposed procedure are illustrated by numerical examples

Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches

A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-optimal front and also in executing a number of interactive multiobjective optimization techniques. Along with the ideal objective vector, it is also needed for the purpose of normalizing different objectives, so as to facilitate a comparison and agglomeration of the objectives. However, the task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and has been reported to be a difficult task, and importantly an unsolved and open research issue. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search toward the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, one of the proposed procedures is found to be capable of finding the nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task in the field of multiobjective optimization

Multiple Criteria Decision Making and Multiattribute Utility Theory

T his paper is an update of a paper that five of us published in 1992. The areas of multiple criteria decision making (MCDM) and multiattribute utility theory (MAUT) continue to be active areas of management science research and application. This paper extends the history of these areas and discusses topics we believe to be important for the future of these fields