Numerical Solution of Dirichlet Boundary Value Problems using Mesh Adaptive Direct Search Optimization

This study gives a different numerical approach for solving second order differential equation with a Dirichlet boundary condition. Mesh Adaptive Direct Search (MADS) algorithm is adopted to train the feed forward neural network used in this approach. As MADS is a derivative-free optimization algorithm, it helps us to reduce the time-consuming workload in the training stage. The results obtained from this approach are also compared with Generalized Pattern Search (GPS) algorithm.

Optimization of fastener pattern in airframe assembly

Purpose The authors consider the problem of optimizing temporary fastener patterns in aircraft assembly. Minimizing the number of fasteners while maintaining final product quality is one of the key enablers for intensifying production in the aerospace industry. The purpose of this study is to formulate the fastener pattern optimization problem and compare different solving approaches on both test benchmarks and rear wing-to-fuselage assembly of an Airbus A350-900. Design/methodology/approach The first considered algorithm is based on a local exhaustive search. It is proved to be efficient and reliable but requires much computational effort. Secondly, the Mesh Adaptive Direct Search (MADS) implemented in NOMAD software (Nonlinear Optimization by Mesh Adaptive Direct Search) is used to apply the powerful mathematical machinery of surrogate modeling and associated optimization strategy. In addition, another popular optimization algorithm called simulated annealing (SA) was implemented. Since a single fastener pattern must be used for the entire aircraft series, cross-validation of obtained results was applied. The available measured initial gaps from 340 different aircraft of the A350-900 series were used. Findings The results indicated that SA cannot be applicable as its random character does not provide repeatable results and requires tens of runs for any optimization analysis. Both local variations (LV) method and MADS have proved to be appropriate as they improved the existing fastener pattern for all available gaps. The modification of the MADS' search step was performed to exploit all the information the authors have about the problem. Originality/value The paper presents deterministic and probabilistic optimization problem formulations and considers three different approaches for their solution. The existing fastener pattern was improved.

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

We introduce the algorithm SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives), an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points. We compare the performance of our algorithm with that of the mesh-based algorithms mesh adaptive direct search (MADS, NOMAD [nonlinear optimization by mesh adaptive direct search] implementation) and implicit filtering and SNOBFIT (stable noisy optimization by branch and fit), which assigns artificial function values to points that violate the hidden constraints. Our numerical experiments for a large set of test problems with 2–30 dimensions and a 31-dimensional real-world application problem arising in combustion simulation show that SHEBO is an efficient solver that outperforms the other methods for many test problems.