SMALL APPROXIMATE PARETO SETS FOR BIOBJECTIVE SHORTEST PATHS AND OTHER PROBLEMS

We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy epsilon the Pareto curve of a multiobjective optimization problem. We show that for a broad class of biobjective problems ( containing many important widely studied problems such as shortest paths, spanning tree, matching, and many others), we can compute in polynomial time an epsilon-Pareto set that contains at most twice as many solutions as the minimum set. Furthermore we show that the factor of 2 is tight for these problems; i.e., it is NP-hard to do better. We present upper and lower bounds for three or more objectives, as well as for the dual problem of computing a specified number k of solutions which provide a good approximation to the Pareto curve.