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

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

Advances and applications in high-dimensional heuristic optimization

“Applicable to most real-world decision scenarios, multiobjective optimization is an area of multicriteria decision-making that seeks to simultaneously optimize two or more conflicting objectives. In contrast to single-objective scenarios, nontrivial multiobjective optimization problems are characterized by a set of Pareto optimal solutions wherein no solution unanimously optimizes all objectives. Evolutionary algorithms have emerged as a standard approach to determine a set of these Pareto optimal solutions, from which a decision-maker can select a vetted alternative. While easy to implement and having demonstrated great efficacy, these evolutionary approaches have been criticized for their runtime complexity when dealing with many alternatives or a high number of objectives, effectively limiting the range of scenarios to which they may be applied. This research introduces mechanisms to improve the runtime complexity of many multiobjective evolutionary algorithms, achieving state-of-the-art performance, as compared to many prominent methods from the literature. Further, the investigations here presented demonstrate the capability of multiobjective evolutionary algorithms in a complex, large-scale optimization scenario. Showcasing the approach’s ability to intelligently generate well-performing solutions to a meaningful optimization problem. These investigations advance the concept of multiobjective evolutionary algorithms by addressing a key limitation and demonstrating their efficacy in a challenging real-world scenario. Through enhanced computational efficiency and exhibited specialized application, the utility of this powerful heuristic strategy is made more robust and evident”--Abstract, page iv