Modified Algorithm to Compute Pareto-Optimal Vectors

Finding Pareto-minimum vectors among r given vectors, each of dimension m, is a fundamental problem in multiobjective optimization problems or multiple-criteria decision-making problems. Corley and Moon (Ref. 1) have given an algorithm for finding all the Pareto-minimum paths of a multiobjective network optimization problem from the initial node to any other node. It uses another algorithm by Corley and Moon, which actually computes the Pareto-minimum vectors. We observed that the latter algorithm is incorrect. In this note, we correct the algorithm for computing Pareto-minimum vectors and present a modified algorithm.