Parallel Decomposition of Multistage Stochastic Programming Problems

A new decomposition method for multistage stochastic linear programming problems is proposed by the author. The method combines the ideas of the regularized decomposition method for two-stage programs and dynamic programming. With each node of the decision tree of the multistage stochastic problem a certain regularized subproblem is associated which generates decisions for its successors and some backward information for its predecessor. The subproblems are solved in parallel and exchange information in an asynchronous way through special buffers. After a finite time the method either finds an optimal solution to the problem or discovers its inconsistency. This method is especially convenient for implementation on a parallel computer

Parallel minimum norm solution of sparse block diagonal column overlapped underdetermined systems

Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for obtaining the minimum 2-norm solution of an underdetermined system of equations. The proposed algorithm is based on the Balance scheme, which was originally developed for the parallel solution of banded linear systems. The proposed scheme assumes a generalized banded form where the coefficient matrix has column overlapped block structure in which the blocks could be dense or sparse. In this article, we implement the more general sparse case. The blocks can be handled independently by any existing sequential or parallel QR factorization library. A smaller reduced system is formed and solved before obtaining the minimum norm solution of the original system in parallel. We experimentally compare and confirm the error bound of the proposed method against the QR factorization based techniques by using true single-precision arithmetic. We implement the proposed algorithm by using the message passing paradigm. We demonstrate numerical effectiveness as well as parallel scalability of the proposed algorithm on both shared and distributed memory architectures for solving various types of problems. © 2017 ACM

Contributions to Methodology and Techniques of Decision Analysis (First Stage)

This collaborative volume reports on the results of a contracted study agreement between the System and Decision Analysis Program and its project on the Methodology of Decision Analysis at IIASA and a group of Polish institutes working in this area. The study includes research in four directions: mathematical programming techniques for decision support; applications of decision support systems new methodological developments in decision support; dissemination of results; and educational activities

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

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

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