An algorithm for optimizing over the efficient set of a bicriterion linear programming

In this paper a face optimization algorithm is developed for solving the problme (P) of optimizing a linear function over the set of efficient solutions of a bicriterion linear program. It is shown that problem (P) can arise in a variety of practical situations. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. The algorithm for solving problem (P) is guaranteed to find an exact optimal or almost exact optimal solution for the problem in a finite number of iterations. The algorithm can be easily implemented using only the linear programming method.