Distributed multilevel optimization for complex structures

Optimization problems concerning complex structures with many design variables may entail an unacceptable computational cost. This problem can be reduced considerably with a multilevel approach: A structure consisting of several components is optimized as a whole (global) as well as on the component level. In this paper, an optimization method is discussed with applications in the assessment of the impact of new design considerations in the development of a structure. A strategy based on fully stressed design is applied for optimization problems in linear statics. A global model is used to calculate the interactions (e.g., loads) for each of the components. These components are then optimized using the prescribed interactions, followed by a new global calculation to update the interactions. Mixed discrete and continuous design variables as well as different design configurations are possible. An application of this strategy is presented in the form of the full optimization of a vertical tail plane center box of a generic large passenger aircraft. In linear dynamics, the parametrization of the component interactions is problematic due to the frequency dependence. Hence, a modified method is presented in which the speed of component mode synthesis is used to avoid this parametrization. This method is applied to a simple test case that originates from noise control. \u

A global-local optimization method for problems in structural dynamics

The optimization of complex structures involving many design variables and constraints can be performed using a multi-level approach: a structure consisting of several components is optimized as a whole (global) and on the component level (local). Earlier work [1], [2], [3], described a multilevel technique developed for the optimization the Airbus A380 vertical tail plane. In this application, a global model is used to calculate the loads on each of the components. These components are then optimized using the prescribed loads, followed by a new global calculation to update the loads. The component optimization strategy is based on Neural Networks (NN) and Genetic Algorithms (GA). This paper describes a strategy that makes this global-local optimization method possible for problems in structural dynamics. It is established that a parametrization of the component interactions (e.g. component loads) is problematic due to frequency dependence. Hence, a modified method is proposed in which the speed of Component Mode Synthesis (CMS) is used to avoid this parametrization. The effectiveness of this method is demonstrated in a test case concerning the placement of sensor and actuator locations in Active Structural Acoustic Control (ASAC). Special attention is paid to the behavior of the optimization strategy

Engineering applications of heuristic multilevel optimization methods

Some engineering applications of heuristic multilevel optimization methods are presented and the discussion focuses on the dependency matrix that indicates the relationship between problem functions and variables. Coordination of the subproblem optimizations is shown to be typically achieved through the use of exact or approximate sensitivity analysis. Areas for further development are identified

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Probabilistic Multilevel Clustering via Composite Transportation Distance

We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilevel datasets. Finally, we present experimental results with both synthetic and real data to demonstrate the efficiency and scalability of the proposed approach.Comment: 25 pages, 3 figure

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coarsening stage of multilevel hypergraph partitioning solvers. The algebraic distance is a vertex distance measure that extends hyperedge weights for capturing the local connectivity of vertices which is critical for hypergraph coarsening schemes. The practical effectiveness of the proposed measure and corresponding coarsening scheme is demonstrated through extensive computational experiments on a diverse set of problems. Finally, we propose a benchmark of hypergraph partitioning problems to compare the quality of other solvers

Global supply chains of high value low volume products

Imperial Users onl