Andrzej P. Wierzbicki

The Use of Reference Objectives in Multiobjective Optimization

The paper presents a survey of known results and some new developments in the use of reference objectives—that is, any reasonable or desirable point in the objective space—instead of weighting coefficients or utility (value) functions in multiobjective optimization. The main conclusions are as follows: Any point in the objective space—no matter whether it is attainable or not, ideal or not—can be used instead of weighting coefficients to derive scalarizing functions which have minima at Pareto points only. Moreover, entire basic theory of multiobjective optimization--necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, etc.—can be developed with the help of reference objectives instead of weighting coefficients or utility (value) functions. Reference objectives are very practical means for solving a number of problems such as Pareto-optimality testing, scanning the set of Pareto-optimal solutions, computer-man interactive solving of multiobjective problems, group assessment of solutions of multiobjective optimization or cooperative game problems, or solving dynamic multiobjective optimization problems.

A mathematical basis for satisficing decision making

This paper presents a conceptual and mathematical model of the process of satisficing decision making under multiple objectives in which the information about decision makers preferences is expressed in the form of aspiration levels. The mathematical concept of a value (utility) function is modified to describe satisficing behavior; the modified value function (achievement scalarizing function) should possess the properties of order preservation and order approximation. It is shown that the mathematical basis formed using aspiration levels and achievement scalarizing functions can be used not only for satisficing decision making but also for Pareto optimization, and thus provides an alternative to approaches based on weighting coefficients or typical value functions. This mathematical basis, which can also be regarded as a generalization of the goal programming approach in multiobjective optimization, suggests pragmatic approaches to many problems in multiobjective analysis.

On the completeness and constructiveness of parametric characterizations to vector optimization problems

SummaryMotivated by recent reviews of characterizations of optimal solutions to vector optimization problems and by applications to decision support systems, this paper presents a methodological approach to comparing such characterizations. After specifying attributes of constructiveness, alternative classes of characterizations are reviewed. Characterization theorems are quoted or presented in more detail in cases that supplement those given in recent reviews. One of alternative classes of characterizations — by aspiration levels and order-consistent achievement functions — is discussed in more detail. An impossibility theorem of complete and robustly computable characterization of efficient (as opposed to weakly or properly efficient) solutions to vector optimization problems is presented.ZusammenfassungAngeregt durch neuere Übersichten der Charakterisierung von optimalen Lösungen von Vektoroptimierungsproblemen und durch Anwendungen auf Entscheidungsunterstützungssysteme wird in diesem Beitrag ein methodischer Ansatz zum Vergleich solcher Charakterisierungen dargestellt. Nach der Spezifizierung von Attributen der Konstruktivität werden alternative Klassen von Charakterisierungen betrachtet. Charakterisierungstheoreme werden entweder zitiert oder, in Ergänzung neuerer Übersichten, dargestellt. Eine der alternativen Klassen der Charakterisierungen wird näher diskutiert. Ein Unmöglichkeitstheorem einer vollständigen und robust berechenbaren Charakterisierung von effizienten (im Gegensatz zu schwach oder streng effizienten) Lösungen der Vektoroptimierungsprobleme wird dargelegt.

Introduction to Multiobjective Optimization: Noninteractive Approaches

We give an introduction to nonlinear multiobjective optimization by covering some basic concepts as well as outlines of some methods. Because Pareto optimal solutions cannot be ordered completely, we need extra preference information coming from a decision maker to be able to select the most preferred solution for a problem involving multiple conflicting objectives. Multiobjective optimization methods are often classified according to the role of a decision maker in the solution process. In this chapter, we concentrate on noninteractive methods where the decision maker either is not involved or specifies preference information before or after the actual solution process. In other words, the decision maker is not assumed to devote too much time in the solution process.

Reference Point Approaches

This chapter presents a summary of reference point methodology in vector optimization and decision support. The methodology has been developed at the International Institute for Applied Systems Analysis (IIASA) since 1980 and found numerous applications, both in IIASA and elsewhere. The chapter presents methodological foundations, basic concepts and notation, reference points and achievement functions, neutral and weighted compromise solutions, issues of modeling for multi-objective analysis, some basic applications of reference point methods and a discussion of a decision process type supported by reference point methodology.

Aspiration Based Decision Support Systems

This book focuses the methodology of decision analysis and support related to the principle of reference point optimization (developed by the editors of this volume and called also variously: aspiration-led decision support, quasi-satisfying framework of rationality, DIDAS methodology etc.). The selection principle applied for this volume was to concentrate on advances of theory and methodology, related to the focusing theme, to supplement them by experiences and methodological advances gained through wide applications and tests in one particular application area - the programming of development of industrial structures in chemical industry, and finally to give a very short description of various software products developed in the contracted study agreement.

Knowledge management and knowledge creation in academia: a study based on surveys in a Japanese research university

Purpose – This study aims to pose one major research question, i.e. why and how to use knowledge management methods in order to enhance knowledge creation in academia – at universities and research institutes?Design/methodology/approach – The paper defines KM in academia as any systematic activity related to support and enhancement of the creation of scientific knowledge and achievement of research goals, including both social process and relevant computer technology tools. Two surveys and case studies were carried out to achieve the research purpose at Japan Advanced Institute of Science and Technology (JAIST). The first survey focused on knowledge management in academia and investigated the current KM situations, special and diverse requirements from researchers. The second survey concentrated on supporting the creative processes of academic research and investigated which aspects of knowledge creation processes should be supported in particular. Based on survey findings, the practical solutions are fur...

On the Role of Intuition in Decision Making and Some Ways of Multicriteria Aid of Intuition

Practical experiences in decision-making—including the experience in the reform of the system of funding of scientific research in Poland—lead to the conclusion that it is important to understand better the role of intuition in decision-making processes. For this purpose a more specific definition of intuition is proposed. One of the conclusions from this definition is that multicriteria aid for decisions should concentrate more on supporting earlier stages of decision processes that precede choice. The role of and possible tools for multicriteria aid for model simulation and analysis are presented.

A parallel multiple reference point approach for multi-objective optimization

This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed within a region that covers the Pareto Frontier. An evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space. Computational experiments are performed on a bi-objective flow-shop scheduling problem. Results, quality measures as well as a statistical analysis are reported in the paper.

DIDASS — Theory, Implementation and Experiences

The purpose of this paper is to report on the progress made in the System and Decision Sciences (SDS) research group at IIASA on the development of the decision support system DIDASS (Dynamic Interactive Decision Analysis and Support System). This system is based on methodology derived from the paradigm of satisficing decision making and the methodology of linear and nonlinear programming. The mathematical background to this approach (based on aspiration formation and the concept of scalarizing functions) is outlined in Section 2. Methods of implementation and computational aspects are discussed in Section 3. The fourth section summarizes three applications of DIDASS, and the paper ends with some conclusions.