A Bayesian approach to constrained single- and multi-objective optimization

Feliot, Paul; Bect, Julien; Vázquez, Emmanuel

doi:10.1007/s10898-016-0427-3

Cited by 122 publications

(74 citation statements)

References 62 publications

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“…We next show the hypervolume indicator (HVI) [12] function for the whole set of the Spatial benchmarks as a function of the initial number of warm-up samples (for sake of space we omit the smallest benchmark, BlackScholes). For every benchmark, we show 5 repetitions of the experiments and report variability via a line plot with 80% confidence interval.…”

Section: E Hypervolume Indicatormentioning

confidence: 99%

Practical Design Space Exploration

Nardi

Koeplinger

Olukotun

2019

2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS

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Multi-objective optimization is a crucial matter in computer systems design space exploration because real-world applications often rely on a trade-off between several objectives. Derivatives are usually not available or impractical to compute and the feasibility of an experiment can not always be determined in advance. These problems are particularly difficult when the feasible region is relatively small, and it may be prohibitive to even find a feasible experiment, let alone an optimal one.We introduce a new methodology and corresponding software framework, HyperMapper 2.0, which handles multi-objective optimization, unknown feasibility constraints, and categorical/ordinal variables. This new methodology also supports injection of the user prior knowledge in the search when available. All of these features are common requirements in computer systems but rarely exposed in existing design space exploration systems. The proposed methodology follows a white-box model which is simple to understand and interpret (unlike, for example, neural networks) and can be used by the user to better understand the results of the automatic search.We apply and evaluate the new methodology to the automatic static tuning of hardware accelerators within the recently introduced Spatial programming language, with minimization of design run-time and compute logic under the constraint of the design fitting in a target field-programmable gate array chip. Our results show that HyperMapper 2.0 provides better Pareto fronts compared to state-of-the-art baselines, with better or competitive hypervolume indicator and with 8x improvement in sampling budget for most of the benchmarks explored.

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Section: E Hypervolume Indicatormentioning

confidence: 99%

Practical Design Space Exploration

Nardi

Koeplinger

Olukotun

2019

2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS

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“…18,19,20,21,22 This includes utilities based on feasible improvement, 16,23,24 penalty method, 25 Lagrangian formulation, 26 or information gain. 27,28,29 For instance, the expected improvement with constraint (EIC) 16 is a natural extension of the expected improvement (EI) utility.…”

Section: B Constrained Bayesian Optimizationmentioning

confidence: 99%

Advances in Bayesian Optimization with Applications in Aerospace Engineering

Poloczek

Frazier

Lam

et al. 2018

2018 AIAA Non-Deterministic Approaches Conference

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Optimization requires the quantities of interest that define objective functions and constraints to be evaluated a large number of times. In aerospace engineering, these quantities of interest can be expensive to compute (e.g., numerically solving a set of partial di↵erential equations), leading to a challenging optimization problem. Bayesian optimization (BO) is a class of algorithms for the global optimization of expensive-to-evaluate functions. BO leverages all past evaluations available to construct a surrogate model. This surrogate model is then used to select the next design to evaluate. This paper reviews two recent advances in BO that tackle the challenges of optimizing expensive functions and thus can enrich the optimization toolbox of the aerospace engineer. The first method addresses optimization problems subject to inequality constraints where a finite budget of evaluations is available, a common situation when dealing with expensive models (e.g., a limited time to conduct the optimization study or limited access to a supercomputer). This challenge is addressed via a lookahead BO algorithm that plans the sequence of designs to evaluate in order to maximize the improvement achieved, not only at the next iteration, but once the total budget is consumed. The second method demonstrates how sensitivity information, such as gradients computed with adjoint methods, can be incorporated into a BO algorithm. This algorithm exploits sensitivity information in two ways: first, to enhance the surrogate model, and second, to improve the selection of the next design to evaluate by accounting for future gradient evaluations. The benefits of the two methods are demonstrated on aerospace examples.

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“…In addition, ECMO [42] uses a Probability of Feasibility (PoF) criterion to handle constraints. Another recent example is the Bayesian Multi-Objective Optimization (BMOO) algorithm (Féliot et al [43]), that uses a Bayesian expected hypervolume improvement sampling criterion. Hence, the proposed MOCS-RS framework along with promising numerical results provides a significant addition to the class of algorithms for constrained multi-objective black-box optimization.…”

Section: Literature Reviewmentioning

confidence: 99%

Multi-objective constrained black-box optimization using radial basis function surrogates

Regis

2016

Journal of Computational Science

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A Bayesian approach to constrained single- and multi-objective optimization

Cited by 122 publications

References 62 publications

Practical Design Space Exploration

Practical Design Space Exploration

Advances in Bayesian Optimization with Applications in Aerospace Engineering

Multi-objective constrained black-box optimization using radial basis function surrogates

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