Generating search directions in multiobjective linear programming using the analytic hierarchy process

The algorithm presented in this paper describes an interactive approach for generating search directions in multiobjective linear programming problems (MOLP). The approach is based on using the AHP to assign priorities to vertices adjacent to those that are in the basis, as generated by the simplex method. Using these priorities, an approximate gradient is found that is used to weigh the objective functions during the next iteration. The novel feature of the algorithm is that the decision-maker (DM) is not required to provide interactive inputs to implicit preference questions concerning his objectives, but instead considers explicit evaluation of adjacent possible improvements to generate the next step in his most preferred direction.