Opsearch, Vol. 35, No. 2, 1998 0030-3887/95 $ 2.00 + 0.00 © Operational Research Society of India Solving Discrete Multiobjective Optimization Problems Based on Approximation Alfonso Mateos, Sixto Rios-Insua and Gregorio Nevado Department of Artifical Intelligence, School of Computer Science Technical University of Madrid, Campus de Montegancedo Boadilla dei Monte, 28660 Madrid, Spain Abstract We consider the descrete multiobjective decision making problem under partial information given through a vector value function. We propose adecision aid procedure based on an approximation to the efficient set and its interactive reduction. Finally, an example iIIustrates the method. 1. INTRODUCTION In multiobjective decision making the set of efficient solutions plays an important role in the solution process. Its main property is that from a sulution in this set, it is not possible to move feasible so as to increase one of the objectives without necessarily decreasing at least one of the others. However, the generation of such set may be involved in linear problems and very difficult in nonlinear ones. In the case of discrete problems this is easier, but we note that the set of efficient solutions might be far too be for practical purposes. Hence, the generation of the efficient set is not usually considered the resolution of a multiobjective problem because this set might have many elements and is not generally totally ordered. Thus, there is a need for more clever strategies to generate a set of representative efficient solutions or an approximation that gives a fair representation of the whole efficient set. Although there are several methods to aid adecision maker (DM) to generate the efficient set or a representative subset (see, e.g., [1], [5]. [6]. [11]. [14]. [15], [16]. [17]. [18].) under different approaches, there is not a definitive solution to this problem. We consider in this paper a value-based procedure (e.g., [2]. [3], [7]) with partial information on the DM's preferences, which uses an approximation concept, [8], [9] and intends, on one hand, to make easier the generation process of a representative set of the whole efficient set and, on the other its interactive reduction to reach a final solution. Throughout the paper we employ the following notation: For two scalars a and b, a b denotes a > b or a = b. For two vectors