Approximating the Convex Edgeworth-Pareto Hull in Integer Multi-objective Problems with Monotone Criteria
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 10, pp 1686-1699
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.