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

A new interior MOLP algorithm based on the path-following primal dual algorithm was presented. The algorithms is based on using the single-objective primal dual algorithm to generate interior search directions that are than used to derive an approximation to an implicitly-known utility function. Projecting the approximated gradient provides the interior search direction along which we move from the current iterate to the next one. Future research should address the issue of devising interaction schemes that allow following an interior 'win-win' trajectory. Such trajectories have the potential benefit of allowing the DM to easily comprehend the evolution of the solution process by following the increase in levels of all objectives. This is a major advantage of using interior methods as opposed to using simplex-based method that require trading off efficient solution in order to move from one iterate to the next. In addition, further efforts should be directed at the role of anchor points in the process and that of selecting and scaling the step size factor used in the process. [16].