A Genetic Algorithm to Solve the Timetable Problem

The paper presents an application of an adapted genetic algorithm to a real world instance of the timetable problem. The results of its application are described. We also compare our results with simulated annealing and tabu search. Abstract In this paper we present the results of an investigation of the possibilities offered by genetic algorithms to solve the timetable problem. This problem has been chosen since it is representative of the class of multi-constrained, NP-hard, combinatorial optimization problems with real-world application. First we present our model, including the definition of a hierarchical structure for the objective function and the generalized genetic operators which can be applied to matrices representing timetables. Then we report about the outcomes of the utilization of the implemented system to the specific case of the generation of a school timetable. We compare two versions of the genetic algorithm (GA), with and without local search, both to a handmade timetable and to two other approaches based on simulated annealing and tabu search. Our results show that GA with local search and tabu search with relaxation both outperform simulated annealing and handmade timetables. Evolutionary algorithms [14] constitute a class of computational paradigms useful for function optimization inspired from the study of natural processes. They use a population of possible solutions, which are concurrently subject to modifications aimed at the determination of the optimal solution. A particularly efficient instantiation of evolutionary algorithms is represented by the genetic algorithm (GA) [22] , in which the natural analogy is population genetics. In the GA every possible solution is represented by a "digital individual" and after the generation of an initial set of feasible solutions (a population), individuals are randomly mated allowing the recombination of genetic material. The resulting individuals can then be mutated with a specific mutation probability. The new population so obtained undergoes a process of natural selection which favors the survival of the fittest individuals (the best solutions), and provides the basis for a new evolutionary cycle. The fitness of the individuals is made explicit by means of a function, called the fitness function (f.f.), which is related with the objective function to optimize. The f.f. quantifies how good a solution is for the problem faced. In GAs individuals are sometimes called chromosomes, and positions in the chromosome are called genes. The value a gene actually takes is called an allele (or allelic value). Allelic values may vary on …