Topology optimization to design spacial thrusters
Prof Frederic Messine
15 Enero 2020
Lugar: SALA DE GRADOS (1.010). Edificio CIENCIAS JURIDICAS - (D). Fecha: 15/01/20 Hora: 10:00In this talk, I will present the problem to design magnetic circuits for some spatial thrusters. The associated topology optimization problem is a binary non linear one where the objective function is computed via numerical methods (black-box). Generally, heuristic methods such as genetic algorithms or particular swarm methods are used to solve the problem. Another way is to relax the binary problem into a continuous one and to penalize it in order to obtain binary solutions. The main issue is about the computation of the gradient in order to make possible efficient uses of descent local optimization methods. Some thruster designs will be presented and discussed showing the interest of this approach.
On a possible use of optimality conditions in interval Branch and Bound methods
Prof Boglárka G.Tóth
15 Enero 2020
Lugar: SALA DE GRADOS (1.010). Edificio CIENCIAS JURIDICAS - (D). Fecha: 15/01/20 Hora: 10:00Interval Branch and Bound methods (IBB) are used when rigorous solutions are needed for Nonlinear Programming (NLP) problems. Nowadays, various implementations of IBB exist, although many of them do not use the Karush-Kuhn-Tucker (KKT) or Fritz-John (FJ) optimality conditions for eliminating non-optimal boxes. When it is used, it is used only in the general form, where an interval linear system of equations needs to be solved. This is rather time-consuming, and in many cases it has a negative outcome: the tested box cannot be removed because with the overestimation on the inclusion of the gradients one can find that the optimality conditions may fulfill. In order to save unnecessary computations, the common rule is to apply such tests only when the box is ``small enough". However, depending on the problem at hand ``small enough" might be difficult to predict.
The idea in this research is to investigate the use of the optimality conditions from a geometrical point of view and to minimize the computational effort when the optimality conditions cannot be used to discard the given box. In this way, there is no need to predict when to apply the test on optimality conditions and so it may become more efficient. In this talk, we describe a method that checks if the conic hull of the enclosure of the gradients of the active constraints is not full, so the test can have a positive outcome.