Multi-objective Mathematical Programming

Although traditional mathematical programming techniques has been remarkably developed for the last half century, they do not necessarily give satisfactory results in practical applications. Because many practical problems often have several objectives conflicting with each other, while traditional mathematical programming techniques can treat only one objective function. The history of multi-objective mathematical programming began almost at the same time as nonlinear programming. In particular, it has been developed very actively since the beginning of 70’s. Now, several effective methods have been being applied to a wide range of real problems. This paper makes an introductory remarks for multi-objective mathematical programming ahead the following papers in this chapter.