Local pareto analyser for preliminary design.

In the design process of complex systems, the designer has to solve an optimisation problem, which involves coupled disciplines and where all design criteria have to be optimised (traded-off) simultaneously. This problem is known as vector optimisation. Many numerical methods exist for obtaining solutions but in general, the solution is not unique. In such a case, the solution set is represented by a Pareto surface in the space of the objective functions. Regarding industrial applications, the multi-disciplinary optimisation problem is usually very time-consuming and the Pareto set rarely can be described analytically. The description of a Pareto surface is often reduced to a set of points lying onto the surface. Therefore, in the real design the set of Pareto solution is never exhaustively explored. Once a Pareto point is obtained, it may be very useful for the decision-maker to be able to perform a quick local approximation in order to obtain other approximate optimal solutions. In this paper, a local Pareto analyser is proposed. This concept is based on a local sensitivity analysis, which provides the relation between variations of the different objective functions under constraints. A method for obtaining a linear and quadratic local approximation of the Pareto surface is then derived. Application of the local Pareto analyser concept is demonstrated through the study of a few test cases.