A Fuzzy Valuation-Based Local Search Framework for Combinatorial Problems 1 ARMANDO BLANCO armando@ugr.es Depto. de Ciencias de la Computacio ´n e I.A, E.T.S. Ing. Informa ´tica, 18071 - Granada, Spain DAVID A. PELTA 2 dpelta@ugr.es Depto. de Ciencias de la Computacio ´n e I.A, E.T.S. Ing. Informa ´tica, 18071 - Granada, Spain JOSE ´ -L. VERDEGAY 3 verdegay@ugr.es Depto. de Ciencias de la Computacio ´n e I.A, E.T.S. Ing. Informa ´tica, 18071 - Granada, Spain Abstract. A novel local search method is presented. One of the new elements of this Fuzzy Adaptive Neighborhood Search (FANS ) algorithm is a fuzzy valuation, which is used to measure the degree to which the solutions that are considered at the decision stages accomplish a certain qualitative property. FANS is analyzed from two perspectives: first, it is shown how FANS may be adapted to behave like other traditional local search techniques by means of suitable definitions for the fuzzy valuation component. Second, comparisons are made to show the potential of the method as a general purpose optimization tool, when none or minimal knowledge of the problem being solved is available. Both aspects make FANS a valuable tool regarding further developments within the context of decision support systems involving heuristic algorithms. 1. Introduction The design, construction and search for exact algorithms solving real life problems are, as a whole, key objectives of Computer Science. Although this kind of problems generally has a high level of difficulty, they need to be solved because of their importance. Both facts, difficulty and importance, together with increasing computer power, encourage the development of heuristics which, even though it may lead to non-optimal solutions, can solve the problem at hand based on the decision makers’ satisfaction. In this way the decision maker may prefer to obtain satisfying solutions according to his wishes than optimal ones. Consequently, in order to face a problem in terms of satisfaction, and not only optimization, heuristic methods must search for solutions not only providing good values for the objective function, but also having additional characteristics predefined by the decisor. In general, those characteristics will be of a subjective nature and therefore they could be well modelized by fuzzy sets. From our point of view, the last decades have witnessed a flow of information from classical fields, such as Operational Research or Control Theory, to the area of Fuzzy Sets and Systems, which have provided very fruitful results. Now, terms like ‘‘fuzzy mathematical programming’’, ‘‘fuzzy control’’, ‘‘fuzzy rule based systems’’, etc. sound familiar to a wider audience (IFSA99 (1999), Delgado et al (1994)). However, it has not Fuzzy Optimization and Decision Making, 1, 177 – 193, 2002 # 2002 Kluwer Academic Publishers. Printed in The Netherlands.