Multi-Objective Global Pattern Search: Effective numerical optimisation in structural dynamics

Abstract

With this work, a novel derivative-free multi-objective optimisation approach for solving engineering problems is presented. State-of-the-art algorithms usually require numerical experimentation in order to tune the algorithm’s multiple parameters to a specific optimisation problem. This issue is effectively tackled by the presented deterministic method which has only a single parameter. The most popular multi-objective optimisation algorithms are based on pseudo-random numbers and need several parameters to adjust the associated probability distributions. Deterministic methods can overcome this issue but have not attracted much research interest in the past decades and are thus seldom applied in practice. The proposed multi-objective algorithm is an extension of the previously introduced deterministic single-objective Global Pattern Search algorithm. It achieves a thorough recovery of the Pareto frontier by tracking a predefined number of non-dominated samples during the optimisation run. To assess the numerical efficiency of the proposed method, it is compared to the well-established NSGA2 algorithm. Convergence is demonstrated and the numerical performance of the proposed optimiser is discussed on the basis of several analytic test functions. Finally, the optimiser is applied to two structural dynamics problems: transfer function estimation and finite element model updating.

The introduced algorithm performs well on test functions and robustly converges on the considered practical engineering problems. Hence, this deterministic algorithm can be a viable and beneficial alternative to random-number-based approaches in multi-objective engineering optimisation.