COMPLETE EFFICIENCY AND THE INITIALIZATION OF ALGORITHMS FOR MULTIPLE OBJECTIVE PROGRAMMING

Complete efficiency in multiple objective programming may be more common than has been thought, especially for problems whose feasible regions have no interior. In view of this, we present methods for testing for complete efficiency in multiple objective programming, with special attention to the linear case. These tests do not require the feasible region to have a nonempty interior. For typical linear problems, including those with compact feasible regions, the test not only checks for complete efficiency, but also generates both an initial efficient and an initial extreme point efficient solution for use in vector maximum or interactive algorithms.