Surrogate-Assisted Optimization for Augmentation of Finite Element Techniques

The application of finite element techniques for the analysis and optimization of complex thermo-mechanical structures typically involves highly nonlinear models for material characterization, tribological contact, large deformation, damage, etc. These nonlinearities usually call for a higher-order Spatio-temporal discretization, including a large number of elements and time-steps in order to provide good convergence and sufficiently accurate simulation results. This inevitably leads to many expensive simulations in terms of cost and time if an optimization or adaption of model parameters has to be done. In this work, a FEM simulation modeling approach is proposed, which uses radial basis function interpolations (RBF) as efficient surrogate models to save FEM simulations. Also, a surrogate-assisted optimization algorithm [3] is utilized to find the parameter setting, which would lead to maximum damage in a simple tensile testing scenario involving a notched specimen with as few FEM simulations as possible. The relatively high accuracy of the utilized surrogate models showcases promising results and indicates the potential of surrogate models in saving time-expensive simulations

SACOBRA with Online Whitening for Solving Optimization Problems with High Conditioning

Real-world optimization problems often have expensive objective functions in terms of cost and time. It is desirable to find near-optimal solutions with very few function evaluations. Surrogate-assisted optimizers tend to reduce the required number of function evaluations by replacing the real function with an efficient mathematical model built on few evaluated points. Problems with a high condition number are a challenge for many surrogate-assisted optimizers including SACOBRA. To address such problems we propose a new online whitening operating in the black-box optimization paradigm. We show on a set of high-conditioning functions that online whitening tackles SACOBRA's early stagnation issue and reduces the optimization error by a factor between 10 to 1e12 as compared to the plain SACOBRA, though it imposes many extra function evaluations. Covariance matrix adaptation evolution strategy (CMA-ES) has for very high numbers of function evaluations even lower errors, whereas SACOBRA performs better in the expensive setting (less than 1e03 function evaluations). If we count all parallelizable function evaluations (population evaluation in CMA-ES, online whitening in our approach) as one iteration, then both algorithms have comparable strength even on the long run. This holds for problems with dimension D Algorithms and the Foundations of Software technolog

Self-adjusting parameter control for surrogate-assisted constrained optimization under limited budgets

Algorithms and the Foundations of Software technolog

Robust optimal design of FOPID controller for five bar linkage robot in a cyber-physical system: a new simulation-optimization approach

This paper aims to further increase the reliability of optimal results by setting the simulation conditions to be as close as possible to the real or actual operation to create a Cyber-Physical System (CPS) view for the installation of the Fractional-Order PID (FOPID) controller. For this purpose, we consider two different sources of variability in such a CPS control model. The first source refers to the changeability of a target of the control model (multiple setpoints) because of environmental noise factors and the second source refers to an anomaly in sensors that is raised in a feedback loop. We develop a new approach to optimize two objective functions under uncertainty including signal energy control and response error control while obtaining the robustness among the source of variability with the lowest computational cost. A new hybrid surrogate-metaheuristic approach is developed using Particle Swarm Optimization (PSO) to update the Gaussian Process (GP) surrogate for a sequential improvement of the robust optimal result. The application of efficient global optimization is extended to estimate surrogate prediction error with less computational cost using a jackknife leave-one-out estimator. This paper examines the challenges of such a robust multi-objective optimization for FOPID control of a five-bar linkage robot manipulator. The results show the applicability and effectiveness of our proposed method in obtaining robustness and reliability in a CPS control system by tackling required computational efforts

Development of an optimization framework for solving engineering design problems.

The integration of optimization methodologies with computational simulations plays a profound role in the product design. Such integration, however, faces multiple challenges arising from computation-intensive simulations, unknown function properties (i.e., black-box functions), complex constraints, and high-dimensionality of problems. To address these challenges, metamodel-based methods which apply metamodels as a cheaper alternative to costly analysis tools prove to be a practical way in design optimization and have gained continuous development. In this thesis, an intrinsically linear function (ILF) assisted and trust region based optimization method (IATRO) is proposed first for solving low-dimensional constrained black-box problems. Then, the economical sampling strategy (ESS), modified trust region strategy and self-adaptive normalization strategy (SANS) are developed to enhance the overall optimization capability. Moreover, as the radial basis function (RBF) interpolation is found to better approximate both objective and constraint functions than ILF, a RBF-assisted optimization framework is established by the combination of the balanced trust region strategy (BTRS), global intelligence selection strategy (GIS) and early termination strategy (ETS). Following that, the fast computation strategy (FCS) and successive refinement strategy (SRS) are proposed for solving large-scale constrained black-box problems and the final optimization framework is called as RATRLO (radial basis function assisted and trust region based large-scale optimization framework). By testing a set of well-known benchmark problems including 22 G-problems, 4 engineering design problems and 1 high-dimensional automotive problem, RATRLO shows remarkable advantages in achieving high-quality results with very few function evaluations and slight parameter tuning. Compared with various state-of-the-art algorithms, RATRLO can be considered one of the best global optimizers for solving constrained optimization problems. Further more, RATRLO provides a valuable insight into the development of algorithms for efficient large-scale optimization