An interior multiobjective primal-dual linear programming algorithm based on approximated gradients and efficient anchoring points

A new algorithm for addressing multiple objective linear programming (MOLP) problems is presented. The proposed algorithm modifies the path-following primal-dual algorithm to MOLP problems. The algorithm requires interaction with a Decision Maker (DM) to obtain locally-relevant preference information for the interior directions generated at each step of the iterative process. This preference information is used to derive an approximation to the gradient of an implicitly-known utility function and its projection provides a direction vector along which the paper moves to the next iterate. In addition, it generates boundary points that provide both a mean to enhance the progress of the algorithm, and a set of candidate solutions at which to terminate the algorithm.