A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm

We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many applications the efficiency of parallel algorithms of the second and third level starts to drop down after some critical parallelisation degree is reached. This weakness of the two-level template is addressed by introduction of one additional parallelisation level. As an alternative to the basic solver some new or modified algorithms are considered on this level. The idea of the proposed methodology is to increase the parallelisation degree by using less efficient algorithms in comparison with the basic solver. As an example we investigate two modified Nelder-Mead methods. For the selected application, a few partial differential equations are solved numerically on the second level, and on the third level the parallel Wang's algorithm is used to solve systems of linear equations with tridiagonal matrices. A greedy workload balancing heuristic is proposed, which is oriented to the case of a large number of available processors. The complexity estimates of the computational tasks are model-based, i.e. they use empirical computational data

Investigation of Electrochemical Processes in Solid Oxide Fuel Cells by Modified Levenberg–Marquardt Algorithm: A New Automatic Update Limit Strategy

Identification of ongoing processes in solid oxide fuel cells (SOFC) enables both optimizing the operating environment and prolonging the lifetime of SOFC. The Levenberg–Marquardt algorithm (LMA) is commonly used in the characterization of unknown electrochemical processes within SOFC by extracting equivalent electrical circuit (EEC) parameter values from electrochemical impedance spectroscopy (EIS) data. LMA is an iteration optimization algorithm regularly applied to solve complex nonlinear least square (CNLS) problems. The LMA convergence can be boosted by the application of an ordinary limit strategy, which avoids the occurrence of off-limit values during the fit. However, to additionally improve LMA descent properties and to discard the problem of a poor initial parameters choice, it is necessary to modify the ordinary limit strategy. In this work, we designed a new automatic update (i.e., adaptive) limit strategy whose purpose is to reduce the impact of a poor initial parameter choice. Consequently, the adaptive limit strategy was embedded in a newly developed EIS fitting engine. To demonstrate that the new adaptive (vs. ordinary) limit strategy is superior, we used it to solve several CNLS problems. The applicability of the adaptive limit strategy was also validated by analyzing experimental EIS data collected by using industrial-scale SOFCs

A three-level parallelisation scheme and application to the Nelder-Mead algorithm

We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many applications the efficiency of parallel algorithms of these two levels starts to drop down after some critical parallelisation degree is reached. This weakness of the twolevel template is addressed by introduction of one additional parallelisation level. As an alternative to the basic solver some new or modified algorithms are considered on this level. The idea of the proposed methodology is to increase the parallelisation degree by using possibly less efficient algorithms in comparison with the basic solver. As an example we investigate two modified Nelder-Mead methods. For the selected application, a Schro¨dinger equation is solved numerically on the second level, and on the third level the parallel Wang’s algorithm is used to solve systems of linear equations with tridiagonal matrices. A greedy workload balancing heuristic is proposed, which is oriented to the case of a large number of available processors. The complexity estimates of the computational tasks are model-based, i.e. they use empirical computational data

Hybrid Statistical and Engineering Optimization Architectures in Early Multidisciplinary Designs of Resilience and Expensive Black-box Complex Systems

Practical engineering design problems are generally multi-disciplinary with limited budget and high risk in terms of life loss, economic resources, etc. In the early phase of such problems, selection of true efficient designs is desired while minimizing overall design cost by avoiding expensive search processes. However, the task is difficult for a simple optimization framework due to the formulation complexity, high function evaluation cost, uncertain design parameters etc. Thus, the overall research goal is to develop complex, hybrid optimization architectures for solving early design problems considering the trade-off among model complexity, performance and cost. We start by comparing multiple architectures, and investigated a nested bi-level architecture for early resilience design with discrete design space and with a trade-off among multiple objectives at different risk level scenarios. The work then focused on increased problem complexity with black-box functions in a mechanical design classification problem with discontinuous design space using a sequential Bayesian Optimization (BO) architecture to locate an unknown creep-fatigue failure constraint boundary. The work then extends a weighted Tchebycheff black-box multi-objective BO (MO-BO) architecture for mechanical design with a trade-off between design risk and cost, with model calibration through regression analysis of unknown parameters. Finally, we investigate an iterative regression model selection procedure, nested into the proposed MO-BO, to enhance design flexibility, estimation and overall performance. This work can be applicable to any domains of complex or/and expensive black-box system design problems