Multi-Objective Modeling and Simulation for Decision Report

Modeling and simulation of various physical, environmental or socioeconomic processes is often a preliminary step for using the resulting models in decision support. With the advancements of computing technology and the methodology of decision support, it is now necessary to revise basic approaches to modeling and simulation: from the very beginning of model construction, they should aim at multi-objective analysis of the model while taking into account various optimization, sensitivity analysis and symbolic manipulation techniques treated as tools of such an analysis, not as goals. The paper illustrates how such an approach could increase the opportunities of comprehensive analysis of a model from a selected class -- as an example, the class of nonlinear dynamic discrete-time models was chosen. A user-friendly format of formulating such models is discussed together with related problems of inverse, constrained and multi-objective simulation as well as structural differentiation and sensitivity analysis, fuzzy set processing and other related issues. As a new tool for the analysis of boundaries of sets generated by such models -- for example. the a-level sets of fuzzy membership functions -- an interactive method of using an elastic "electronic pencil" is proposed

An Experimental Multi-Objective Game - "Humble Shall be Rewarded". Rules, Analysis and Preliminary Conclusions

The paper presents an experimental multi-objective game with a simple mechanics and rather complicated payoff structure. The game has been devised as a tool of study how people learn -- not only to play a game, but to recognize new strategic perspectives, how easily they change a pre-conceived problem formulation. The game can be also applied for testing creativity and learning capabilities of students at graduate level as well as of investigating the impact of professional and cultural backgrounds on adaptive decision making. The game illustrates the fact that real-life game-like situations are often multi-objective. while some objectives and their hierarchy or preference structure might be not apparent from the beginning. Effects of multiplicity of equilibria and the possibility of conflict escalation in such cases are also illustrated by the game. The paper presents the rules of the game, an analysis of its various aspects and some preliminary conclusions

The Use of Reference Objectives in Multiobjective Optimization - Theoretical Implications and Practical Experience

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 in multiobjective optimization. The main conclusions are as follows: (1) 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 functions. (2) 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

The Role of Intuition and Creativity in Decision Making

The paper starts with a reflection on various perceptions of rationality in decision making; by concentrating on so-called deliberative decision making and examining its analogy to cognitive processes, a case for including intuitive decisions into the concept of rational decision making is made. The role of "Gestalt" images and basic concepts in perceiving reality is stressed. Intuitive decision making is operationally defined and various phases of intuitive decision processes are examined. Special attention is paid to creative decision processes, when the decision maker is facing a novel problem of strategic importance. Issues of possible empirical studies of intuitive decision making are outlined. Since this paper is constructed as a "thought experiment" (Kuhn, 1964) in order to clarify some concepts of perception related to intuition, possible implications for the philosophy of science are also indicated

Reference Point Methods in Vector Optimization and Decision Support

This paper presents a summary of reference point methodology in vector optimization and decision support. The methodology was developed at IIASA since 1980 and applied in numerous projects, both in IIASA and elsewhere. The paper 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

Multiple Criteria Games Theory and Applications

After a review of basic concepts in multiple criteria optimization, the paper presents a characterization of noncooperative equilibria in multiple criteria games in normal form either by weighted sums or by order-consistent achievement scalarizing functions, for convex and nonconvex cases. Possible applications of multiple criteria games and such characterizations of their equilibria are indicated. The analysis of multiple criteria games night be especially useful when studying reasons of possible conflict escalation processes and ways of preventing them

Negotiation and Mediation in Conflicts I.: The Role of Mathematical Approaches and Methods

There are many possible approaches to the analysis of conflict situations and ways of developing mediation or negotiation procedures. In general, we can distinguish between socio-political approaches, procedures for mediation and negotiation which have developed historically through political experience, and systems-analytical, mathematical approaches, which rely on various branches of decision and game theory or on computerized simulation or gaming models. While the socio-political approaches must remain the basis of any analysis of conflict situations, they can usefully be supplemented by more-formalized approaches; both approaches, when used separately, have their limitations. This paper, after a short review of existing systems-analytical and mathematical approaches, proposes new concepts and methods for the mathematical analysis of conflict processes. The proposed approach attempts to bridge the gap between simulation gaming models and experiments and more formal game-theoretical analysis by taking certain ideas from interactive decision supported gaming, assuming that the players have multiple objectives that they wish to satisfice (not optimize), and introducing special mediation procedures as an element of decision support during the game. The mathematical concepts used are the selection of satisficing game equilibria, the definition of constructive and destructive behavior (on the part of the players), and a formalization of conflict escalation and de-escalation processes

A Methodological Guide to Multiobjective Optimization

During the last few years, multiobjective optimization has received growing attention: the number of publications related to this subject between 1974 and 1979 exceeds 120. There are many approaches, techniques and tools related to multiobjective decision-making and optimization; however, not all approaches are equally developed, and the resulting tools are often applied because of certain traditions rather than their suitability for solving a given problem. Therefore, this paper is devoted to a comparative evaluation of various approaches and tools. This evaluation is based, however, first on a classification of problems of multiobjective decision making and optimization. Thereafter, the available approaches, methods, techniques and tools are shortly presented and evaluated in terms of suitability for various classes of problems. The final part of the paper presents a broader description of a relatively new approach based on reference objective levels, not fully developed yet but applicable in many classes of problems. A new notion of extended threshold utility functions, other basic theoretical results, applicational examples and directions of further research related to this approach are presented

The Use of Reference Objective Levels in Group Assessment of Solutions of Mulltiobjective Optimization

Many papers devoted to problems of group assessment of Pareto-optimal solutions or of compromise reaching in cooperative games were based on notions of utility functions or preference ordering identification. However, there is strong evidence that individual decision makers are apt to think in terms of goals or desirable levels of objectives rather than in terms of utility and preferences. Since reference objective levels can be used instead of weighting coefficients and utility functions to derive basic conditions for Pareto-optimality, they can also be applied to construct compromise-aiding procedures for cooperative games or for group assessment of Pareto-optimal solutions. Several variants of such compromise-aiding procedures are investigated in the paper, together with deadlock situations and deadlock-resolving procedures

Augmented Simplex: A Modified and Parallel Version of Simplex Method Based on Multiple Objective and Subdifferential Optimization Approach

In the perspective of parallel computations, new versions of basic optimization algorithms are needed. The paper presents a concept of such coarse-grained parallelization, based on a parametric imbedding into a family of problems or parametrically diversified algorithms. This general idea is exemplified for the case of the simplex algorithm of linear programming, where a linear optimization problem can be imbedded into a multiple-objective family which introduces diversified directions of search cutting through the interior of original admissible set. To improve the effectiveness of such algorithms, an initial phase of directional feasibility search by subdifferential optimization is added. The resulting augmented simplex algorithm, even without parallelization, might be competitive with interior point methods for a certain, broad class of linear programming problems. Necessary theoretical foundations, some algorithmic details and results of preliminary tests are presented