User Guide to a Mathematical Programming Package for Multicriteria Dynamic Linear Problems Hybrid Version 3.1

Makowski, M. ORCID: https://orcid.org/0000-0002-6107-0972 & Sosnowski, J.S. (1988). User Guide to a Mathematical Programming Package for Multicriteria Dynamic Linear Problems Hybrid Version 3.1. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-88-111

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Abstract

This paper is one of the series of 11 Working Papers presenting the software for interactive decision support and software tools for developing decision support systems. These products constitute the outcome of the contracted study agreement between the System and Decision Sciences Program at IIASA and several Polish scientific institutions. The theoretical part of these results is presented in the IIASA Working Paper WP-88-071 entitled "Theory, Software and Testing Examples in Decision Support Systems", which contains the theoretical and methodological backgrounds of the software system developed within the project.

This paper presents the HYBRID system for solving linear multiple criteria optimization problems, utilizing the reference point technique. This method, originally developed by the authors, is the non-simplex one and is based on the augmented Lagrangian technique with conjugate gradient optimization. Due to special properties of the method it was possible to make the implementation especially efficient for solving dynamic problems. In such cases the HYBRID outperforms such known packages, like MINOS. Since the method does not require to store large amount of information (like basis matrix in standard Simplex formulation) it is especially valuable for microcomputer applications, allowing to solve problems a magnitude bigger dimensionality than with standard methods.

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