Most real engineering problems require the simultaneous optimisation of multiple criteria, some conflicting with each other, so that different conflicting objectives can be met simultaneously. The solution to these problems, known as multi-criteria or multi-objective optimisation problems, has been traditionally achieved by combining multiple objectives in a single cost function. This combination of objectives is usually a weighted sum of each of the objectives to be achieved. The choice of these weightings is manifestly arbitrary, and difficult to establish a priori. Thus, the solutions obtained reflect this arbitrariness and are generally sensitive to the values assigned to the weightings.
One area of interest relevant to process control is the search for a set of drivers to meet different design specifications (generally the solution is not unique), as well as a set of tools to explore all the designs that can be chosen. In process control, an open research area is the selection of an optimal operating point, while bearing in mind various criteria and constraints: performance, safety, as well as environmental and economic factors (Acedo 2003).
The purpose of this project is to research a novel technique of multi-objective optimisation called ‘physical programming’ (Messac 2001, 2000, 1996a) and adapt the technique to the resolution of two problems: the optimisation of setpoint settings in multivariable predictive control, and the tuning of parameters in this type of controller. Currently, the optimisation of setpoints is usually performed solely on economic criteria. The tuning of the multiple parameters of predictive controllers usually requires an iterative process, especially if the specifications required are numerous and opposing (this approach also requires the use of simulation – and this usually leads to a suboptimal design).
The aim is to transform both problems (the setpoint optimisation and the tuning of predictive controllers) into multi-objective optimisation problems where the designer clearly expresses a preference for each of the criteria to be optimised independently of the rest. The physical programming method introduces a number of developments in the formulation of the optimisation problem in an attempt to incorporate the knowledge that the designer has on the physical variables that define the problem (or the desired values for the specifications to be met by the solution), so as to guide the process or optimisation algorithm to a correct selection of the solution. Since the physical programming implementation process contains an optimisation algorithm of a general nonlinear function and is subject to constraints, precautions should be taken to ensure that physical programming is sufficiently robust to avoid being trapped in local minima. Evolutionary algorithms that have proven their worth for solving global optimisation problems are used in this project. These algorithms obtain solutions that are as close as possible to the preferences of the designer.