Application of Satisfiability algorithms to time-table problems Fahima NADER, Mouloud KOUDIL, Karima BENATCHBA, Lotfi ADMANE, Said GHAROUT and Nacer HAMANI Institut National de formation en Informatique, BP 68M, 16270, Oued Smar, Algérie. Abstract: - Decision Support Systems (DSS) are a constantly growing area. More and more domains of the daily life take advantage of the available tools (medicine, trade, meteorology…). However, such tools are confronted to a particular problem: the great number of characteristics that qualify data samples. They are more or less victims of the abundance of information. Sat domain benefits from the appearance of powerful solvers that can process huge amounts of data in short times. This paper presents an approach for translating timetable problems (which are a particular case of DSS), into a Boolean formula, which is then provided to an environment that allows experimenting different heuristics in order to extract solutions that satisfy a maximum number of clauses (Max-Sat problem). Finally, the best solutions are back-translated into the original problem in order to find an adequate schedule that satisfies the characteristics and constraints of the timetable problem. Key-Words: - Decision Support Systems, Satisfiability, Optimization, Ant Colony Systems. 1. Introduction The Decision Support System (DSS) concept was born at the USA during the seventies, to help managers in the decision process. DSSs have been developed to solve decision systems that have been few or badly structured [1], and that have at least one of the following characteristics: decider preferences are essential; the criteria for making a decision are numerous, they raise a or the problem evolves rapidly [2]. There exist a great number of DSS methods, based on fundamentally different principles. From a mathematical point of view, the main difficulty that occurs in DSS is the problem formulation [3]. From an organizational point of view, the main problem is the identification of the actors and their relation [4]. These two aspects are complementary, since on one hand, the choice of a DSS method requires a deep knowledge of the decision context, and on the other hand, the materialization of the result is conditioned by the opportunity of the chosen approach [5]. [6] tackled the search for an optimum. He explains that the existence of an optimal solution is conditioned by three constraints: exclusivity, exhaustivity and transitivity of the actions. However, the decider preferences are often fuzzy, incompletely formulated and non-transitive. Besides, they tend to evolve during the decision process. [7] showed the limits of this type of methods in the resolution of timetable problems, which is the problem our works deal with. This paper presents an approach for translating timetable problems, expressed as sets of positive and negative examples, into Boolean formulas composed of CNF (Conjunctive Normal Form) clauses. The Sat problem obtained is then provided to an environment that allows experimenting different heuristics and sets of parameters in order to extract solutions that satisfy a maximum number of clauses (Max-Sat problem). The best solutions are back-translated into cases that are applied to the data sets in order to extract the pertinent information solving the original learning problem. Section 2 gives an overview about timetable problem. The third one introduces the Sat/Max-Sat problem. Section 4 references the translation method used to transform a set of examples into a CNF formula. Section 5 presents the environment used to solve Sat problems, as well as the heuristic used in these works. The sixth section gives some results obtained on a benchmark. 2. Timetable problem Timetable problem was defined by [8] as the follows: “Timetabling is the allocation, subject to constraints, of given resources to objects being placed in space time, in such a way as to satisfy as nearly as possible a set of desirable objectives”. This problem is strongly constrained. These constraints are classified in two sets: the imperative (hard) constraints and the desirable (soft) constraints [7].