Robust optimization of a 2D air conditioning duct using kriging

The design of systems involving fluid flows is typically based on computationally intensive Computational Fluid Dynamics (CFD) simulations. Kriging based optimization methods, especially the Efficient Global Optimization (EGO) algorithm, are now often used to solve deterministic optimization problems involving such expensive models. When the design accounts for uncertainties, the optimization is usually based on double loop approaches where the uncertainty propagation (e.g., Monte Carlo simulations, reliability index calculation) is recursively performed inside the optimization iterations. We have proposed in a previous work a single loop kriging based method for minimizing the mean of an objective function: simulations points are calculated in order to simultaneously propagate uncertainties, i.e., estimate the mean objective function, and optimize this mean. In this report this method has been applied to the shape optimization of a 2D air conditioning duct. For comparison purposes, deterministic designs were first obtained by the EGO algorithm. Very high performance designs were obtained, but they are also very sensitive to numerical model parameters such as mesh size, which suggests a bad consistency between the physics and the numerical model. The 2D duct test case has then been reformulated by introducing shape uncertainties. The mean of the duct performance criteria with respect to shape uncertainties has been maximized with the simultaneous optimization and sampling method. The solutions found were not only robust to shape uncertainties but also to the CFD model numerical parameters. These designs show that the method is of practical interest in engineering tasks

Parallel expected improvements for global optimization: summary, bounds and speed-up

Deliverable no. 2.1.1-BThe sequential sampling strategies based on Gaussian processes are widely used for optimization of time consuming simulators. In practice, such computationally demanding problems are solved by increasing number of processing units. This has therefore induced extensions of sampling criteria which consider the framework of parallel calculation. This report further studies expected improvement criteria for parallel and asynchronous computations. A unified parallel asynchronous expected improvement criterion is formulated. Bounds and strategies for comparing criteria values at various design points are discussed. Finally, the impact of the number of available computing units on the performance is empirically investigated

Dealing with asynchronicity in parallel Gaussian Process based global optimization

During the last decade, Kriging-based sequential algorithms like EGO and its variants have become reference optimization methods in computer experiments. Such algorithms rely on the iterative maximization of a sampling criterion, the expected improvement (EI), which takes advantage of Kriging conditional distributions to make an explicit trade-off between promizing and uncertain search space points. We have recently worked on a multipoints EI criterion meant to simultaneously choose several points, which is useful for instance in synchronous parallel computation. Here we propose extensions of these works to asynchronous parallel optimization and focus on a variant of EI, EEI, for the case where some new evaluation(s) have to be done while the reponses of previously simulations are not all known yet. In particular, different issues regarding EEI's maximization are addressed, and a proxy strategy is proposed

Simultaneous Kriging-Based Sampling For Optimization And Uncertainty Propagation

http://uma.ensta-paristech.fr/files/diam/docro/roadef_2011/VERSION-ELECTRONIQUE/roadef2011_submission_447.pdfInternational audienceRobust analysis and optimization is typically based on repeated calls to a deterministic simulator that aim at propagating uncertainties and finding optimal design variables. Without loss of generality a double set of simulation parameters can be assumed: x are deterministic optimization variables, u are random parameters of known probability density function and f (x, u) is the objective function attached to the simulator. Most robust optimization methods involve two imbricated tasks, the u's uncertainty propagation (e.g., Monte Carlo simulations, reliability index calculation) which is recurcively performed inside optimization iterations on the x's. In practice, f is often calculated through a computationally expensive software. This makes the computational cost one of the principal obstacle to optimization in the presence of uncertainties

Simultaneous kriging-based estimation and optimization of mean response

International audienceRobust optimization is typically based on repeated calls to a deterministic simulation program that aim at both propagating uncertainties and finding optimal design variables. Often in practice, the "simulator" is a computationally intensive software which makes the computational cost one of the principal obstacles to optimization in the presence of uncertainties. This article proposes a new efficient method for minimizing the mean of the objective function. The efficiency stems from the sampling criterion which simultaneously optimizes and propagates uncertainty in the model. Without loss of generality, simulation parameters are divided into two sets, the deterministic optimization variables and the random uncertain parameters. A kriging (Gaussian process regression) model of the simulator is built and a mean process is analytically derived from it. The proposed sampling criterion that yields both optimization and uncertain parameters is the one-step ahead minimum variance of the mean process at the maximizer of the expected improvement. The method is compared with Monte Carlo and kriging-based approaches on analytical test functions in two, four and six dimensions

A study of asynchronous budgeted optimization

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Fast integration of multi-point improvements

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Expected Improvements for the Asynchronous Parallel Global Optimization of Expensive Functions: Potentials and Challenges

Revised selected articles from the LION 6 Conference (Paris, Jan. 16-20, 2012), LNCS 7219, 978-3-642-34412-1International audienceSequential sampling strategies based on Gaussian processes are now widely used for the optimization of problems involving costly simulations. But Gaussian processes can also generate parallel optimiza- tion strategies. We focus here on a new, parameter free, parallel expected improvement criterion for asynchronous optimization. An estimation of the criterion, which mixes Monte Carlo sampling and analytical bounds, is proposed. Logarithmic speed-ups are measured on 1 and 9 dimensional functions

Dealing with asynchronicity in kriging-based parallel global optimization

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Dealing with asynchronicity in kriging-based parallel global optimization

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