Modified interactive Chebyshev algorithm (MICA) for convex multiobjective programming

In this paper, we describe an interactive procedural algorithm for convex multiobjective programming based upon the Tchebycheff method, Wierzbicki's reference point approach, and the procedure of Michalowski and Szapiro. At each iteration, the decision maker (DM) has the option of expressing his or her objective-function aspirations in the form of a reference criterion vector. Also, the DM has the option of expressing minimally acceptable values for each of the objectives in the form of a reservation vector. Based upon this information, a certain region is defined for examination. In addition, a special set of weights is constructed. Then with the weights, the algorithm of this paper is able to generate a group of efficient solutions that provides for an overall view of the current iteration's certain region. By modification of the reference and reservation vectors, one can "steer" the algorithm at each iteration. From a theoretical point of view, we prove that none of the efficient solutions obtained using this scheme impair any reservation value for convex problems. The behavior of the algorithm is illustrated by means of graphical representations and an illustrative numerical example.