Weak convergence of particle swarm optimization

Particle swarm optimization algorithm is a stochastic meta-heuristic solving global optimization problems appreciated for its efficacity and simplicity. It consists in a swarm of particles interacting among themselves and searching the global optimum. The trajectory of the particles has been well-studied in a deterministic case and more recently in a stochastic context. Assuming the convergence of PSO, we proposed here two CLT for the particles corresponding to two kinds of convergence behavior. These results can lead to build confidence intervals around the local minimum found by the swarm or to the evaluation of the risk. A simulation study confirms these properties

Particle swarm algorithm with adaptive constraint handling and integrated surrogate model for the management of petroleum fields

This paper deals with the development of effective techniques to automatically obtain the optimum management of petroleum fields aiming to increase the oil production during a given concession period of exploration. The optimization formulations of such a problem turn out to be highly multimodal, and may involve constraints. In this paper, we develop a robust particle swarm algorithm coupled with a novel adaptive constraint-handling technique to search for the global optimum of these formulations. However, this is a population-based method, which therefore requires a high number of evaluations of an objective function. Since the performance evaluation of a given management scheme requires a computationally expensive high-fidelity simulation, it is not practicable to use it directly to guide the search. In order to overcome this drawback, a Kriging surrogate model is used, which is trained offline via evaluations of a High-Fidelity simulator on a number of sample points. The optimizer then seeks the optimum of the surrogate model