An Interior Multiple Objective Primal-dual Linear Programming Algorithm Using Efficient Anchoring Points

We present an interior Multiple Objective Linear Programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of the constraints polytope by following its vertices, the path-following primal-dual algorithm moves through the interior of the polytope. Interior algorithms lend themselves to modifications capable of addressing MOLP problems in a way that is quite different from current solution approaches. In addition, moving through the interior of the polytope results in a solution approach that is less sensitive to problem size than simplex-based MOLP algorithms. The modification of the interior single-objective algorithm to MOLP problems, as presented here, is accomplished by combining the step direction vectors generated by applying the single-objective algorithm to each of the cost vectors into a combined direction vector along which we step from the current iterate to the next iterate.