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Register a new userSurrogate-Based Simulation Optimization
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Added by
Xiaowei Zhang
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation optimization is concerned with developing efficient sampling schemes -- subject to a computational budget -- to solve such optimization problems. To mitigate the computational burden, surrogates are often constructed using simulation outputs to approximate the response surface of the simulation model. In this tutorial, we provide an up-to-date overview of surrogate-based methods for simulation optimization with continuous decision variables. Typical surrogates, including linear basis function models and Gaussian processes, are introduced. Surrogates can be used either as a local approximation or a global approximation. Depending on the choice, one may develop algorithms that converge to either a local optimum or a global optimum. Representative examples are presented for each category. Recent advances in large-scale computation for Gaussian processes are also discussed.
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Gradient-free optimization methods, such as surrogate based optimization (SBO) methods, and genetic (GAs), or evolutionary (EAs) algorithms have gained popularity in the field of constrained optimization of expensive black-box functions. However, constraint-handling methods, by both classes of solvers, do not usually guarantee strictly feasible candidates during optimization. This can become an issue in applied engineering problems where design variables must remain feasible for simulations to not fail. We propose a constraint-handling method for computationally inexpensive constraint functions which guarantees strictly feasible candidates when using a surrogate-based optimizer. We compare our method to other SBO, GA/EA and gradient-based algorithms on two (relatively simple and relatively hard) analytical test functions, and an applied fully-resolved Computational Fluid Dynamics (CFD) problem concerned with optimization of an undulatory swimming of a fish-like body, and show that the proposed algorithm shows favorable results while guaranteeing feasible candidates.
Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate-based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. It was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.
A probabilistic performance-oriented control design optimization approach is introduced for flight systems. Aiming at estimating rare-event probabilities accurately and efficiently, subset simulation is combined with surrogate modeling techniques to improve efficiency. At each level of subset simulation, the samples that are close to the failure domain are employed to construct a surrogate model. The existing surrogate is then refined progressively. In return, seed and sample candidates are screened by the updated surrogate, thus saving a large number of calls to the true model and reducing the computational expense. Afterwards, control parameters are optimized under rare-event chance constraints to directly guarantee system performance. Simulations are conducted on an aircraft longitudinal model subject to parametric uncertainties to demonstrate the efficiency and accuracy of this method.
We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call z-identifiability, reduces to ordinary identifiability when Z = empty and, like the latter, can be given syntactic characterization using the do-calculus [Pearl, 1995; 2000]. We provide a graphical necessary and sufficient condition for z-identifiability for arbitrary sets X,Z, and Y (the outcomes). We further develop a complete algorithm for computing the causal effect of X on Y using information provided by experiments on Z. Finally, we use our results to prove completeness of do-calculus relative to z-identifiability, a result that does not follow from completeness relative to ordinary identifiability.
In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated in a subdivison algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.
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