RBF-metamodel driven multi-objective optimization and its applications

Metamodeling of simulation results with radial basis functions (RBF) is an efficient method for the continuous representation of objectives in parametric optimization. In the multi-objective case a detection of non-convex Pareto fronts is especially difficult, which is a point where many simple algorithms fail. In this paper we consider different formulations of the multi-objective optimization problem: as a sequential linear program (SLP), as a sequential quadratic program (SQP) and as a generic nonlinear program (NLP). We compare their efficiency and apply them in three realistic test cases. In the first application we consider a bi-objective optimization problem from non-invasive tumor therapy planning, where the typical goal is to maximize the level of tumor destruction and to minimize the influence to healthy organs. The second application case is safety assessment in automotive design. Here the crash intrusion in the driver and passenger compartment is minimized together with the total mass of the vehicle. The third application comes from the simulation of gas transport networks, where the goal is to fulfil the contract values, such as incoming pressure and outgoing flow delivery, providing the best energetic efficiency of the transport.