The Light Beam Search — Outranking Based Interactive Procedure for Multiple-Objective Mathematical Programming

  • Andrzej Jaszkiewicz
  • Roman Słowiński
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 5)


An interactive procedure for multiple-objective analysis of linear and non-linear programs is presented. At the decision phase of the 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 constnicted to ensure a relatively easy evaluation of the sample by the DM. To this end we use an outranking relation as a local preference model in a neighbourhood of the current point. The outranking relation is used to define a sub-region of the non-dominated set the sample presented to the DM comes from. The DM has two possibilities, or degrees of freedom, 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 in 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.


Decision Maker Middle Point Characteristic Neighbour Preferential Information Current Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Andrzej Jaszkiewicz
    • 1
  • Roman Słowiński
    • 1
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland

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