Approximating the Nondominated Frontiers of Multi-Objective Combinatorial Optimization Problems

Finding, all nondominated vectors for multi-objective combinatorial optimization (MOCO) problems is computationally very hard in general. We approximate the nondominated Frontiers of MOCO problems by fitting smooth hypersurfaces. For a given problem, we lit the hypersurface using a single nondominated reference vector. We experiment with different types of MOCO problems and demonstrate that in all cases the fitted hypersurfaces approximate all nondominated vectors well. We discuss that such an approximation is useful to find the neighborhood of preferred regions of the nondominated vectors with very little computational effort. Further computational effort can then be spent in the identified region to find the actual nondominated vectors the decision maker will prefer. (C) 2009 Wiley Periodical, Inc. Naval Research Logistics 56: 191-198, 2009