# PolySCIP

PolySCIP - a solver for multi-criteria optimization problems. PolySCIP is a new solver for multi-criteria integer as well as multi-criteria linear programs handling an arbitrary number of objectives. It is available as an official part of the non-commercial constraint integer programming framework SCIP. It utilizes a lifted weight space approach to compute the set of supported extreme non-dominated (SEN) points and unbounded non-dominated rays, respectively. The algorithmic approach can be summarized as follows: At the beginning an arbitrary SEN point is computed (or it is determined that there is none) and a weight space polyhedron created. In every next iteration a vertex of the weight space polyhedron is selected whose entries yield a single-objective optimization problem via a combination of the original objectives. If the optimization of this single-objective problem leads to a new SEN point, the weight space polyhedron is updated. Otherwise another vertex of the weight space polyhedron is investigated. The algorithm finishes if all vertices of the weight space polyhedron have been investigated and no update steps of the polyhedron are necessary anymore. The file format of PolySCIP is based on the widely used MPS format and allows a simple generation of multi-criteria models via an algebraic modelling language.