Modi ed Interactive Chebyshev Algorithm (MICA) for Convex Multiobjective Programming

In this paper, we describe an interactive procedure algorithm for convex multiobjective programming based upon the Tchebyche 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 de ned 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 e cient solutions that provides for an overall view of the current iteration's certain region. By modi cation 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 e cient solutions obtained using this scheme impair any reservation value for convex problems. The