A comparison of discrete and continuous neural network approaches to solve the class/teacher timetabling problem

This study explores the application of neural network-based heuristics to the class/teacher timetabling problem (CTTP). The paper begins by presenting the problem characteristics in terms of hard and soft constraints and proposing a formulation for the energy function required to map the issue within the artificial neural network model. There follow two distinct approaches to simulating neural network evolution. The first uses a Potts mean-field annealing simulation based on continuous Potts neurons, which has obtained favorable results in various combinatorial optimization problems. Afterwards, a discrete neural network simulation, with discrete winner-takes-all neurons, is proposed. The paper concludes with a comparison of the computational results taken from the application of both heuristics to hard hypothetical and real CTTP instances. The experiment demonstrates that the discrete approach performs better, in terms of solution quality as well as execution time. By extending the comparison, the neural discrete solutions are also compared with those obtained from a multiobjective genetic algorithm, which is already being successfully used for this problem within a timetabling software application.