Probability-Driven Simulated Annealing for Optimizing Digital FIR Filters

In this paper, we propose to mimic some well-known methods of control theory to automatically fix the parameters of a multi-objective Simulated Annealing (SA) method. Our objective is to allow a decision maker to efficiently use advanced operation research techniques without a deep knowledge of this domain. Classical SA controls the probability of acceptance using an a priori temperature scheduling (Temperature Driven SA, or TD-SA). In this paper, we simply propose to control the temperature using an a priori probability of acceptance scheduling (Probability Driven SA, or PD-SA). As an example, we present an application of signal processing and particularly the design of digital Finite Impulse Response (FIR) filters for very high speed applications. The optimization process of a FIR filter generally trades-off two metrics. The first metric is the quality of its spectral response (measured as a distance between the ideal filter and the real one). The second metric is the hardware cost of the filter. Thus, a Pareto-based approach obtained by a multi-objective simulated annealing is well suited for the decision maker. In this context, TD-SA and PD-SA method are compared. They show no significant differences in terms of performance. But, while TD-SA requires numerous attempts to set an efficient temperature scheduling, PD-SA leads directly to a good solution.