A Classification Based Interactive Algorithm
of Multicriteria Linear Integer Programming
Mariana Vassileva, Krassimira Genova, Vassil Vassilev
Institute of Information Technologies, 1113 Sofia
Absract: We present a learning-oriented classification based interactive algorithm for solving multicriteria linear integer programming problems (MCLIP). At each iteration, the decision-maker (DM) classifies the set of the criteria in terms of the desired changes in the values of some of the criteria; the desired directions of change for a few of the other criteria, and the values and/or directions of the eventual deterioration of the remaining criteria. The current preferred solution and the local preferences of the DM define the reference-neighborhood. Two types of scalarizing problems are formulated - linear and mixed-integer programming problems. At most of the iterations, the algorithm finds one or more (weak) non-dominated solutions of the relaxed MCLIP problem. Only at certain iterations, solving an exact or an approximate mixed-integer scalarizing problem the algorithm finds one or more (weak) non-dominated or near (weak) non-dominated solutions close to the non-dominated surface of the MCLIP problem.