Multi-Scale Evolution Strategy

Abstract

The choice of evolutionary computing to support industrial multiobjective design has two strong motivations, i.e. global search and robustness (Di Barba 2009). Even if convergence towards global optimum has been proven only in an asymptotic way, on a heuristic basis it can be stated that algorithms inspired by evolutionary computing are always able to find an improvement of an existing design. Moreover, they are robust because they work independently of: Type of analysis problem (static, transient, time-harmonics) Nature of design variables (real-valued, integer-valued) Properties of objective functions and constraints (e.g. non-smoothness, non-convexity, non-linearity).

Nevertheless, from the industrial point of view, the time available to complete a design should be considered as a fixed quantity. More and more the never-ending tendency to keep R&D costs low calls for virtual experiments, so stimulating the development of cost-effective procedures of automated optimal design. This remark implies some consequences in terms of speed requirements. In fact, the optimisation procedure should be implemented with highest efficiency, including the link to the finite element software. Moreover, the designer should be given the freedom to choose the compromise he/she needs between accuracy and computing time. A practical consequence is the implementation of non-standard stopping criteria, like user-defined runtime, i.e. an arbitrary time window after which the optimisation stops and the current design, possibly improving the prototype design (starting point of the optimisation), is taken as a result. Conversely, user-defined improvement can be implemented as a stopping criterion; in that case, the runtime is not controlled, but – if the procedure converges – the result fulfils the level of improvement required by the designer.