Expensive multi-objective optimization of electromagnetic mixing in a liquid metal

This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet … Read more

Representation of the Pareto front for heterogeneous multi-objective optimization

Optimization problems with multiple objectives which are expensive, i.e. where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance analytically given, this can be used in … Read more

Numerical Results for the Multi-objective Trust Region Algorithm MHT

A set of 78 test examples is presented for the trust region method MHT described in J. Thomann, G. Eichfelder, A trust region algorithm for heterogeneous multi-objective optimization, 2018 (available as preprint: http://optimization-online.org/DB_HTML/2018/03/6495.html) . It is designed for multi-objective heterogeneous optimization problems where one of the objective functions is an expensive black-box function, for example … Read more

A Trust Region Algorithm for Heterogeneous Multiobjective Optimization

This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically … Read more