NEW DEVELOPMENTS IN GLOBAL DYNAMIC OPTIMISATION

SALHI, D.; DAROUX, M.; LATIFI, R.

Abstract

It is well known that dynamic optimisation problems encountered in Chemical Engineering may present many local optima since only necessary conditions for optimality are used. This is due to the non convexity of the large majority of Chemical Engineering process models and it is not guaranteed to reach the global optimum for a non convex problem. The resulting solutions are therefore suboptimal and may have direct important consequences on safety, economical and environmental aspects of processes. The development of global optimisation methods is therefore of utmost importance. In this paper, the objective is to present some recent results obtained in global dynamic optimisation of processes. Thus, a two-dimensional dynamic model is considered and the objective is to determine the optimal values of two parameters involved in the model which fit some experimental measurements. The performance index is then defined as the sum of least squares between experimental measurements and model predictions. The constraints are mainly the dynamic model with the associated initial conditions and the variables and parameters bounds. In a first step, the original dynamic optimisation problem is transformed into an NLP problem using orthogonal collocation method. The resulting optimisation problem is then successfully solved by means of a branch-and-bound (BB) method. Moreover, branch-and-reduce and alpha-BB methods are used and compared. In a second step, convex under estimators for dynamic systems with low dimension is developed. It was shown that when the dynamic model is quasi monotone the method systematically leads to the global optimum. However for non quasi monotone systems further developments are needed.

Coresponding author e-mail: Djalal[dot]Salhi[at]ensic[dot]inpl-nancy[dot]fr

Session: Dynamic and Global Optimisation of Processes (Invited Session, M. Fikar)