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 eac h iteration of the solution procedure, the algorithm finds (weak) nond ominated solutions to the relaxed MOILP problem. Only at certain itera tions, if the DM so desires, an additional mixed integer programming p roblem is solved to find an integer (weak) nondominated solution which is close to the current continuous (weak) nondominated solution to th e relaxed MOILP problem. In the proposed algorithm, DM has to provide only the reference point at each iteration. No special software is req uired to implement the proposed algorithm. The algorithm is illustrate d with an example.