An interactive algorithm for solving multiple objective integer linear programming problems

We propose a reference direction based interactive algorithm to solve multiple objective integer linear programming (MOILP) problems. At each iteration of the solution procedure, the algorithm finds (weak) nondominated solutions to the relaxed MOILP problem. Only at certain iterations, if the DM so desires, an additional mixed integer programming problem is solved to find an integer (weak) nondominated solution which is close to the current continuous (weak) nondominated solution to the relaxed MOILP problem. In the proposed algorithm, DM has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.