Optimisation d'un procédé de traitement des brasques

The optimization of chemical processes defined by computer simulations does not have an exploitable structure, as required for mathematical programming theory. Classical solving methods do not generally work well; they can only detect local optima, when they succeed. Heuristic algorithms usually exhibit good performances, especially if they are stochastic; unfortunately, there is no proof of the solution's optimality.

Direct search algorithms are designed for problems in which the evaluation of the objective function is costly, or derivatives estimation is hard or impossible (noisy, piecewise or modular functions). These algorithms do not need information provided by derivatives.

The goal of this work is to use a Mesh Adaptive Direct Search algorithm (MADS) in order to optimize a spent potliner treatment process (spent potliners are highly toxic wastes of aluminum production). The chosen algorithm is believed to fulfill practical and theoretical lacks of classical and heuristic methods, respectively.

The mesh adaptive direct search algorithm uses a conceptual mesh (which is never explicitly defined) in the space of the variables with evolutionary dimensions. This mesh tends to be infinitely fine at convergence. An iteration consists of two steps: search and poll. The search step, optional, permits the user to guide the algorithm or to provide supplementary information. The poll step, mandatory, consists of an efficient exploration of neighbors defined with the mesh. This step guarantees mathematical convergence to a solution satisfying necessary optimality conditions.