Timetabling Problem with Fuzzy Constraints: A Self-Learning Genetic Algorithm

A Timetabling Problem is an NP-hard combinatorial optimization problem which lacks analytical solution methods. During the last two decades several algorithms have been proposed, most of which are based on heuristics like evolutionary computation methods. Here, to solve this problem we design a specific genetic algorithm with fuzzy constraints. Our method incorporates a self-learning genetic algorithm with indirect representation based on event priorities and heuristic local search operators. By using fuzzy sets we measure the violation of soft constraints in the fitness function in order to include inherent uncertainty and vagueness involved in data. The proposed method satisfies all of the hard constraints of the problem and achieves a significantly better score in satisfying the soft constraints. The algorithm is computationally tractable as it is demonstrated on a small, realistic example for which an optimal solution is already known due to exhaustive calculation. The structure of the algorithm enables parallel computations which are necessary for solving large problems.