The LBS package - a microcomputer implementation of the Light Beam Search method for the multiple -objective non-linear mathematical programming

Jaszkiewicz, A. & Slowinski, R. (1994). The LBS package - a microcomputer implementation of the Light Beam Search method for the multiple -objective non-linear mathematical programming. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-94-007

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Abstract

The paper presents the LBS package which is a microcomputer implementation of the Light Beam Search method. The software has been designed to support interactive analysis of multiple-objective continuous non-linear mathematical programming problems. At the decision phase of the interactive procedure, a sample of points, composed of the current point and a number of alternative proposals, is presented to the decision maker (DM). The sample is constructed to ensure a relatively easy evaluation of the sample by the DM. To this end an outranking relation is used as a local preference model in a neighborhood of the current point. The outranking relation is used to define a sub-region of the non-dominated set where the sample presented to the DM comes from. The DM has two possibilities to move from one sub-region to another which better fits his/her preferences. The first possibility consists in specifying a new reference point which is then projected onto the non-dominated set in order to find a better non-dominated point. The second possibility consists in shifting the current point to a selected point from the sub-region. In both cases, a new sub-region is defined around the updated current point. This technique can be compared to projecting a focused beam of light from a spotlight at the reference point onto the non-dominated set; the highlighted sub-region changes when either the reference point or the point of interest in the non-dominated set are changed.

The LBS package has been implemented in Turbo Pascal within the MS-Windows environment. The package includes two versions of the LBS executable program and a set of example problems. The LBS program is composed of three modules: the problem definition module, the solver module and the interactive analysis module. The problem definition module allows for defining multiple-objective non-linear problems in a natural text form. It supports also checking the correctness of the problem definition and compilation of a problem defined in a text form to an internal format. The solver module is exchangeable and any non-linear optimizer fining to the specified interface can be used in this module. The two versions of the LBS program differ just by the solver used. The first one, coming from the PINOKIO package, is an implementation of the Generalized Reduced Gradient method (GRG). The second one, coming from the DIDAS-N package is an implementation of the Penalty Shifting Method. The interactive analysis module makes an extensive use of computer graphics to help in the perception of a large amount of information. The graphical windows environment allows for simultaneous presentation of different kinds of information and mixing of textual, numerical and graphical forms of presentation.

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