Attraction Force Optimization (AFO): A deterministic nature-inspired heuristic for solving optimization problems in stochastic simulation

The paper presents a new optimization heuristic called AFO-Attraction Force Optimization, able to maximize discontinuous, non-differentiable and highly non-linear functions in discrete simulation problems. The algorithm was developed specifically to overcome the limitations of traditional search algorithms in optimization problems performed on discrete-event simulation models used, for example, to study industrial systems and processes. Such applications are characterized by three particular aspects: the response surfaces of the objective function is not known to the experimenter, a few number of independent variables are involved, very high computational time for each single simulation experiment. In this context it is therefore essential to use an optimization algorithm that on one hand tries to explore as effectively as possible the entire domain of investigation but, in the same time, does not require an excessive number of experiments. The article, after a quick overview of the most known optimization techniques, explains the properties of AFO, its strengths and limitations compared to other search algorithms. The operating principle of the heuristic, inspired by the laws of attraction occurring in nature, is discussed in detail in the case of 1, 2 and N-dimensional functions from a theoretical and applicative point of view. The algorithm was then validated using the most common 2-dimensional and N-dimensional benchmark functions. The results are absolutely positive if compared, for the same initial conditions, with the traditional methods up to 10-dimensional vector spaces. A higher number of independent variables is generally not of interest for discrete simulation optimization problems in industrial applications (our research field).