A visual interactive method for solving the multiple criteria problem

This paper proposes a new method for solving multiple criteria mathematical programming problems. The method does not rely on explicit knowledge of the properties of the utility function. However, if the utility function is assumed to be pseudoconcave and differentiable when the procedure terminates, sufficient conditions for optimality can be established. The method has some features in common with the well-known GDF method of Geoffrion, Dyer and Feinberg (1972). However, our method operates solely in terms of efficient solutions contrary to the GDF method. Moreover, the original procedure of the GDF method for solving the direction-finding problem has been abandoned, since it has turned out that it is not very workable in practice. Instead, the idea of using reference goals or aspiration levels, originated by Wierzbicki, is utilized for determining a direction of improvement. The step-size problem is dealt with in a manner analogous to the GDF method. Computer graphics are used as an aid in solving the step-size problem. The method is easy to implement and convenient to use. Any standard LP package with a parametric optimization routine can be used. In addition, a graphical display device is required.