Using efficient feasible directions in interactive multiple objective linear programming

In this paper the authors show how to incorporate efficient feasible directions into interactive line search algorithms for multiple objective linear programming problems. The resulting new line search is guaranteed to generate points that lie in the efficient set. In addition, the new line search automatically corrects possible errors in judgment that the decision maker may inadvertently commit in giving some of the decision marker’s responses. These two improvements are achieved without sacrificing the key property of typical interactive line search algorithms, namely that they yield a new point at each iteration more preferred by the decision maker than the current point. The only additional computational requirement of the new line search is the solution of a single linear programming problem at each iteration. For these reasons, we advocate the incorporation of efficient feasible directions into interactive line search algorithms for multiple objective linear programs in the manner shown in this paper.