LEARNING AUTOMATA WITH CONTINUOUS INPUTS AND THEIR APPLICATION FOR MULTIMODAL FUNCTIONS OPTIMIZATION

This paper deals with the design and the analysis of a new reinforceme nt scheme for learning automata and its application for multimodal fun ctions optimization. This reinforcement scheme generalizes the well kn own Bush-Mosteller scheme with decreasing gain for learning automata w ith continuous inputs. The theoretical analysis is based on martingale theory. The conditions associated with the convergence of this scheme to the optimal pure strategy are stated, and the order of convergence rate is estimated. The variation domains of the variables of the func tion to be optimized are discretized into subsets which are associated to the outputs of the learning automaton. The values of the function on these subsets are used to construct the continuous automation input s. Simulation results show the feasibility and the good performance of this optimization technique.