An approach to determine unsupported non-dominated solutions in bicriteria integer linear programs

In this paper, we introduce a method for finding both supported and unsupported non-dominated solutions of a bicriteria integer linear program (BCILP). One-phase and two-phase implementations of the method are described, and their interactive versions are outlined. The one-phase method and the second phase of the other are based on the minimization of weighted Chebyshev distances to well-chosen reference points. The dynamic change of reference point proposed here makes this method particularly suitable for interactive approaches. Computational experiments on random instances of three classes of BCILP are reported and discussed. The implementation of the proposed method as a method to approximate the set of non-dominated solutions is described and evaluated in computational terms.