Relation betwen integer linear vector optimization and multicriteria problems on groups and graphs

Abstract

We relax an integer linear vector optimization problem [[Pbar]]. whose vector of variables ia additionally bounded from above. neglecting the upper and lowcr bounds of the basic variables. The relaxation is transformed into an equivalent muliizriteria prcup knapsack problem and this into a shortest path problem on a vectorially valued graph. The efficient points of the relaxation can be calculated from the solutions ol the corresponding group knapsack or shortesr path problem respectively. We derive a sufficient condition for the fact that the efficiency set of the relaxation contains elements feasible and thus efficient for problem [[Pbar]] Besides. criteria for finding the complete solution of the integer linear vector optimization problem by solving the relaxation are developed.