Local Approximation of Pareto Surface

designer is solving an optimization problem, which involves different disciplines and where all design criteria have to be optimized simultaneously. Mathematically this problem can be reduced to a vector optimization problem. The solution of this problem is not unique and is represented by a Pareto surface in the space of the objective functions. Once a Pareto solution is obtained, it may be very useful for the decision-maker to be able to perform a quick local approximation in the vicinity of this Pareto solution in order to explore its sensitivity. In this paper, a method for obtaining linear and quadratic local approximations of the Pareto surface is derived. The concept of a local quick 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 few examples are considered.