Methods of approximating Pareto set faces in a linear multiple-criteria problem (Q1281230)

A problem of a linear multicriteria optimization is considered. A logical convolution \[ \Phi (x, \lambda)= \min_{i; \lambda_{i}>0} \{ f_{i}(x) / \lambda_{i} \}, \] where the functions \(f_{i}\) \((i=1,2,\ldots, m)\) are maximazing criteria and \(\lambda\) is a parameter from a unit simplex \(S^{n}=\{ \lambda\in\mathbb{R}^{n}: \lambda_{i}\geq 0, \sum_{i} \lambda_{i}=1 \}\) for approximating faces of the Pareto set is proposed. It is possible to find out any effective point, maximizing this convolution in x. A method which permits to decrease a number one-criteria tasks to solve is given for this convolution. Two algorithms based on this method are constructed. They were tested on a three-criteria problem of lattice optimization.