Approximating the convex Edgeworth–Pareto hull in integer multi-objective problems with monotone criteria

A method for the iterative polyhedral approximation of the convex Edgeworth–Pareto hull is proposed and examined experimentally. This method is designed for integer multi-objective problems with monotone objective functions and constraints given by a computational module. It is based on a synthesis of the ideas of the branch-and-bound method and the methods for the polyhedral approximation of convex bodies. A sequence of interior and exterior polyhedral sets is constructed so as to approximate the Edgeworth–Pareto hull to the desired accuracy. The results of the theoretical and experimental analyses of the proposed method are presented.