Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging - Replaces CentER DP 2010-62

This article uses a sequentialized experimental design to select simulation input com- binations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the clas- sic "expected improvement" (EI) in "efficient global optimization" (EGO) through the introduction of an unbiased estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are com- pared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer.Simulation;Optimization;Kriging;Bootstrap

Identification of quasi-optimal regions in the design space using surrogate modeling

The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to find optimal performance characteristics of expensive simulations (forward analysis: from input to optimal output). However, often the practitioner knows a priori the desired performance and is interested in finding the associated input parameters (reverse analysis: from desired output to input). A popular method to solve such reverse (inverse) problems is to minimize the error between the simulated performance and the desired goal. However, there might be multiple quasi-optimal solutions to the problem. In this paper, the authors propose a novel method to efficiently solve inverse problems and to sample Quasi-Optimal Regions (QORs) in the input (design) space more densely. The development of this technique, based on the probability of improvement criterion and kriging models, is driven by a real-life problem from bio-mechanics, i.e., determining the elasticity of the (rabbit) tympanic membrane, a membrane that converts acoustic sound wave into vibrations of the middle ear ossicular bones

Universal Prediction Distribution for Surrogate Models

International audienceThe use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are generally based on Gaussian assumptions. The main advantage of probabilistic approach is that it provides a measure of uncertainty associated with the surrogate model in the whole space. This uncertainty is an efficient tool to construct strategies for various problems such as prediction enhancement, optimization or inversion.In this paper, we propose a universal method to define a measure of uncertainty suitable for any surrogate model either deterministic or probabilistic. It relies on Cross-Validation (CV) sub-models predictions. This empirical distribution may be computed in much more general frames than the Gaussian one. So that it is called the Universal Prediction distribution (UP distribution).It allows the definition of many sampling criteria. We give and study adaptive sampling techniques for global refinement and an extension of the so-called Efficient Global Optimization (EGO) algorithm. We also discuss the use of the UP distribution for inversion problems. The performances of these new algorithms are studied both on toys models and on an engineering design problem

Constrained Optimization in Simulation:A Novel Approach

This paper presents a novel heuristic for constrained optimization of random computer simula-tion models, in which one of the simulation outputs is selected as the objective to be minimized while the other outputs need to satisfy prespecified target values. Besides the simulation out-puts, the simulation inputs must meet prespecified constraints including the constraint that the inputs be integer. The proposed heuristic combines (i) experimental design to specify the simu-lation input combinations, (ii) Kriging (also called spatial correlation modeling) to analyze the global simulation input/output data that result from this experimental design, and (iii) integer nonlinear programming to estimate the optimal solution from the Kriging metamodels. The heuristic is applied to an (s, S) inventory system and a realistic call-center simulation model, and compared with the popular commercial heuristic OptQuest embedded in the ARENA ver-sions 11 and 12. These two applications show that the novel heuristic outperforms OptQuest in terms of search speed (it moves faster towards high-quality solutions) and consistency of the solution quality

Multi-fidelity strategies for lean burn combustor design

In combustor design and development, the use of unsteady computational fluid dynamics (CFD) simulations of transient combustor aero-thermo-dynamics to provide an insight into the complex reacting flow-field is expensive in terms of computational time. A large number of such high-fidelity reactive CFD analyses of the objective and constraint functions are normally required in combustor design and optimisation process. Hence, traditional design strategies utilizing only high-fidelity CFD analyses are often ruled out, given the complexity in obtaining accurate flow predictions and limits on available computational resources and time. This necessitates a careful design of fast, reliable and efficient design strategies. Surrogate modeling design strategies, including Kriging models, are currently being used to balance the challenges of accuracy and computational resource to accelerate the combustor design process. However, its feasibility still largely relies on the total number of design variables, objective and constraint functions, as only high-fidelity CFD analyses are used to construct the surrogate model.This thesis explores these issues in combustor design by aiming to minimize the total number of high fidelity CFD runs and to accelerate the process of finding a good design earlier in the design process. Initially, various multi-fidelity design strategies employing a co-Kriging surrogate modeling approach were developed and assessed for performance and confidence against a traditional Kriging based design strategy, within a fixed computational budget. Later, a time-parallel combustor CFD simulation methodology is proposed, based on temporal domain decomposition, and further developed into a novel time-parallel co-Kriging based multi-fidelity design strategy requiring only a single CFD simulation to be setup for various fidelities. The performance and confidence assessment of the newly developed multi-fidelity strategies shows that they are, in general, competitive against the traditional Kriging based design strategy, and evidence exists of finding a good design early in the design optimisation proces