Simulation-Optimization via Kriging and Bootstrapping:A Survey (Revision of CentER DP 2011-064)

Abstract: This article surveys optimization of simulated systems. The simulation may be either deterministic or random. The survey reflects the author’s extensive experience with simulation-optimization through Kriging (or Gaussian process) metamodels. The analysis of these metamodels may use parametric bootstrapping for deterministic simulation or distribution-free bootstrapping (or resampling) for random simulation. The survey covers: (1) Simulation-optimization through "efficient global optimization" (EGO) using "expected improvement" (EI); this EI uses the Kriging predictor variance, which can be estimated through parametric bootstrapping accounting for estimation of the Kriging parameters. (2) Optimization with constraints for multiple random simulation outputs and deterministic inputs through mathematical programming applied to Kriging metamodels validated through distribution-free bootstrapping. (3) Taguchian robust optimization for uncertain environments, using mathematical programming— applied to Kriging metamodels— and distribution- free bootstrapping to estimate the variability of the Kriging metamodels and the resulting robust solution. (4) Bootstrapping for improving convexity or preserving monotonicity of the Kriging metamodel.

Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (> 2s ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure

Metamodel variability analysis combining bootstrapping and validation techniques

Research on metamodel-based optimization has received considerably increasing interest in recent years, and has found successful applications in solving computationally expensive problems. The joint use of computer simulation experiments and metamodels introduces a source of uncertainty that we refer to as metamodel variability. To analyze and quantify this variability, we apply bootstrapping to residuals derived as prediction errors computed from cross-validation. The proposed method can be used with different types of metamodels, especially when limited knowledge on parameters’ distribution is available or when a limited computational budget is allowed. Our preliminary experiments based on the robust version of the EOQ model show encouraging results

Design of Experiments: An Overview

Design Of Experiments (DOE) is needed for experiments with real-life systems, and with either deterministic or random simulation models. This contribution discusses the different types of DOE for these three domains, but focusses on random simulation. DOE may have two goals: sensitivity analysis including factor screening and optimization. This contribution starts with classic DOE including 2k-p and Central Composite designs. Next, it discusses factor screening through Sequential Bifurcation. Then it discusses Kriging including Latin Hyper cube Sampling and sequential designs. It ends with optimization through Generalized Response Surface Methodology and Kriging combined with Mathematical Programming, including Taguchian robust optimization.simulation;sensitivity analysis;optimization;factor screening;Kriging;RSM;Taguchi

Coordination of Coupled Black Box Simulations in the Construction of Metamodels

This paper introduces methods to coordinate black box simulations in the construction of metamodels for situations in which we have to deal with coupled black boxes.We de.ne three coordination methods: parallel simulation, sequential simulation and sequential modeling.To compare these three methods we focus on .ve aspects: throughput time, .exibility, simulated product designs, coordination complexityand the use of prior information.Special attention is given to the throughput time aspect.For this aspect we derive mathematical formulas and we give relations between the throughput times of the three coordination methods.At the end of this paper we summarize the results and give recommendations on the choice of a suitable coordination method.simulation;simulation models;coordination;black box;metamodels

A numerical approach to robust in-line control of roll forming processes

The quality of roll formed products is known to be highly sensitive and dependent on the process parameters and thus the unavoidable variations of these parameters during mass production. To maintain a constant high product quality, a new roll former with an adjustable final roll forming stand is developed at Deakin University enabling the continuous compensation for possible shape defects. In this work, a numerical approach to robust in-line control of the roll forming of a V-section profile is presented, combining the aspects of robust process design and in-line compensation methods. A numerical study is performed to determine the relationship between controllable process settings and uncontrollable variation of incoming material properties with respect to the common product defects longitudinal bow and springback. The computationally expensive non-linear FE simulations used in this study are subsequently replaced by metamod-els based on efficient Single Response Surfaces. Using these metamodels, the optimal setting for the adjustable stand is determined with robust optimization techniques and the effect on product quality analyzed. It is shown that the subsequent adjustment of the final roll stand position leads to a significantly improved product quality by preventing product defects and minimizing the deteriorating effects of scattering variables

A Robust Optimisation Strategy for Metal Forming Processes

Robustness, reliability, optimisation and Finite Element simulations are of major importance to improve product\ud quality and reduce costs in the metal forming industry. In this paper, we propose a robust optimisation strategy for metal\ud forming processes. The importance of including robustness during optimisation is demonstrated by applying the robust\ud optimisation strategy to an analytical test function and an industrial hydroforming process, and comparing it to deterministic\ud optimisation methods. Applying the robust optimisation strategy significantly reduces the scrap rate for both the analytical\ud test function and the hydroforming proces