A multistage linear array assignment problem

The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice

User-Oriented Methodology and Techniques of Decision Analysis and Support

This volume contains 26 papers selected from Workshop presentations. The book is divided into two sections; the first is devoted to the methodology of decision analysis and support and related theoretical developments, and the second reports on the development of tools -- algorithms, software packages -- for decision support as well as on their applications. Several major contributions on constructing user interfaces, on organizing intelligent DSS, on modifying theory and tools in response to user needs -- are included in this volume

Fast approximation schemes for multi-criteria combinatorial optimization

Cover title.Includes bibliographical references (p. 38-44).by Hershel M. Safer, James B. Orlin

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast

Theory, Software and Testing Examples in Decision Support Systems

This volume summarizes the results of a four-year cooperative contracted study "Theory, Software and Testing Examples for Decision Support Systems" conducted in Poland by four institutions: the Institute of Automatic Control, Warsaw University of Technology, the System Research Institute of the Polish Academy of Sciences, the Institute of Control and Systems Engineering, Academy of Mining and Metallurgy in Cracow, and the Institute of Informatics, University of Warsaw in cooperation with the Methodology of the Decision Analysis Project of the System and Decision Sciences Program at IIASA. This research was supported mostly by IIASA funds in Polish national currency, but also by other sources and research grants in Poland, such as the grant RP.1.02 of the Ministry of Education for research in optimization and automatic control; totally, it represents the results of a part-time work of about 30 researchers from these institutions. This volume concentrates on the theoretical and methodological advances of this cooperative study, although it describes also experiences of applications in the area of programming the development of chemical industry together with a decision support system for such purposes as well as presents short descriptions of eight software packages (prototype decision support systems, multiobjective mathematical programming packages and a pilot negotiation support system) that are available together with more detailed documentation as scientific software constituting a part of results of this study. The research on the Polish side was coordinated by Professor Andrzej P. Wierzbicki and on IIASA's side by Dr. Andrzej Lewandowski, the project leader of the Methodology of Decision Analysis; they served also as the editors of this volume

Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

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

Theory, Software and Testing Examples for Decision Support Systems

Research in methodology of Decision Support Systems is one of the activities within the System and Decision Sciences Program which was initiated seven years ago and is still in the center of interests of SDS. During these years several methodological approaches and software tools have been developed; among others the DIDAS (Dynamic Interactive Decision Analysis and Support) and SCDAS (Selection Committed Decision Analysis and Support). Both methodologies gained a certain level of popularity and have been successfully applied in other IIASA programs and projects as well as in many scientific institutions. Since development and testing the software and methodologies on real life examples requires certain -- rather high -- resources, it was decided to establish a rather extensive international collaboration with other scientific institutions in various NMO countries. This volume presents the result of the second phase of such a cooperation between the SDS Program and the four scientific institutions in Poland. The research performed during this stage related mostly to converting the decision support software developed during the previous phase, from the mainframe to the microcomputer, ensuring simultaneously high level of rebustness, efficiency and user friendliness. Several new theoretical developments, like new non-simplex algorithm for linear programming, new algorithms for mixed-integer programming and job shop scheduling are also described in the volume. Finally, it presents also new theoretical developments relating to supporting the processes of negotiations as well as the methodological issues on application the Decision Support Systems in industry management