Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

Müller, Juliane; Day, Marcus S.

doi:10.1287/ijoc.2018.0864

Cited by 30 publications

(21 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the generated engine architectures, 33% converged during the initial DOE whereas this increased to 92% for the last iteration. Similar to the simple problem, this demonstrates that the problem is subject to hidden constraints [44], and that NSGA-II is able to deal with these effectively.…”

Section: Realistic Multi-objective Architecting Problemmentioning

confidence: 77%

“…Approximately 49% of the generated engine architectures converged during the initial DOE, whereas this increased to 92% for the last iteration. This can be seen as the presence of hidden constraints [44]: constraints that are not known a-priori, and are considered violated whenever the simulation did not converge to a meaningful result. Hidden constraints are present in many simulation-based optimization problems, and can be challenging to deal with for the optimizer.…”

Section: B Simple Single-objective Architecting Problemmentioning

confidence: 99%

“…Hidden constraints are present in many simulation-based optimization problems, and can be challenging to deal with for the optimizer. NSGA-II is robust with respect to hidden constraints, as there the so-called extreme barrier approach [44] is applied: invalid results are assigned the value +∞, to guide the selection and non-dominated sorting steps towards valid results. It can be seen that turbojets have higher TSFC and lower weight and lower diameter compared to turbofan engines, which is expected.…”

Section: B Simple Single-objective Architecting Problemmentioning

confidence: 99%

See 2 more Smart Citations

System Architecture Optimization: An Open Source Multidisciplinary Aircraft Jet Engine Architecting Problem

Bussemaker

Smedt

Rocca

et al. 2021

Aiaa Aviation 2021 Forum

View full text Add to dashboard Cite

Decisions regarding the system architecture are important and taken early in the design process, however suffer from large design spaces and expert bias. Systematic design space exploration techniques, like optimization, can be applied to system architecting. Realistic engineering benchmark problems are needed to enable development of optimization algorithms that can successfully solve these black-box, hierarchical, mixed-discrete, multi-objective architecture optimization problems. Such benchmark problems support the development of more capable optimization algorithms, more suitable methods for modeling system architecture design space, and educating engineers and other stakeholders on system architecture optimization in general. In this paper, an engine architecting benchmark problem is presented that exhibits all this behavior and is based on the open-source simulation tools pyCycle and OpenMDAO. Next to thermodynamic cycle analysis, the proposed benchmark problem includes modules for the estimation of engine weight, length, diameter, noise and NOx emissions. The problem is defined using modular interfaces, allowing to tune the complexity of the problem, by varying the number of design variables, objectives and constraints. The benchmark problem is validated by comparing to pyCycle example cases and existing engine performance data, and demonstrated using both a simple and a realistic problem formulation, solved using the multiobjective NSGA-II algorithm. It is shown that realistic results can be obtained, even though the design space is subject to hidden constraints due to the engine evaluation not converging for all design points.

show abstract

Section: Realistic Multi-objective Architecting Problemmentioning

confidence: 77%

Section: B Simple Single-objective Architecting Problemmentioning

confidence: 99%

Section: B Simple Single-objective Architecting Problemmentioning

confidence: 99%

See 1 more Smart Citation

System Architecture Optimization: An Open Source Multidisciplinary Aircraft Jet Engine Architecting Problem

Bussemaker

Smedt

Rocca

et al. 2021

Aiaa Aviation 2021 Forum

View full text Add to dashboard Cite

show abstract

“…(2000), Carter et al. (2001), Conn, Scheinberg and Toint (2001), Huyer and Neumaier (2008), Lee, Gramacy, Linkletter and Gray (2011), Chen and Kelley (2016), Porcelli and Toint (2017) and Müller and Day (2019).…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

Derivative-free optimization methods

2019

View full text Add to dashboard Cite

Dedicated to the memory of Andrew R. Conn for his inspiring enthusiasm and his many contributions to the renaissance of derivative-free optimization methods. AbstractIn many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

show abstract

“…We consider the problem of global optimization of a high dimensional, black box, possibly non-linear non-convex, function. A black box function can only be evaluated at selected locations, and no gradient information is returned upon evaluation [1,2]. Such optimization problems are attracting interest in engineering (AI-controlled systems, certification of embedded systems), as well as scientific (scientific machine learning for emulation of highly complex physical phenomena) applications [3,4].…”

Section: Introductionmentioning

confidence: 99%

Scaling Bayesian Optimization With Game Theory

Mathesen,

Pedrielli,

Smith

2021

Preprint

View full text Add to dashboard Cite

We introduce the algorithm Bayesian Optimization with Fictitious Play (BOFiP) for the optimization of high dimensional black box functions. BOFiP decomposes the original, high dimensional, space into several sub-spaces defined by non-overlapping sets of dimensions. These sets are randomly generated at the start of the algorithm, and they form a partition of the dimensions of the original space. BOFiP can search the original space through a strategic learning mechanism that alternates Bayesian optimization, to search within sub-spaces, and information exchange among sub-spaces, to update the sub-space function evaluation. The basic idea is to achieve increased efficiency by distributing the high dimensional optimization across low dimensional sub-spaces. In particular, each sub-space is interpreted as a player within an equal interest game. At each iteration, Bayesian optimization produces approximate best replies that allow the update of the players belief distribution. The belief update and Bayesian optimization continue to alternate until a stopping condition is met. High dimensional problems are often encountered in real applications, and several contributions in the Bayesian optimization literature have highlighted the difficulty in scaling to high dimensions due to the computational complexity associated to the estimation of the model hyperparameters. Such complexity is exponential in the problem dimension, resulting in substantial loss of performance for most techniques with the increase of the input dimensionality. We compare BOFiP to several state-of-the-art approaches in the field of high dimensional black box optimization. The numerical experiments show the performance over three benchmark objective functions from 20 up to 1000 dimensions. A neural network architecture design problem is tested with 42 up to 911 nodes in 6 up to 92 layers, respectively, resulting into networks with 500 up to 10,000 weights. These sets of experiments empirically show that BOFiP outperforms its competitors, showing consistent performance across different problems and increasing problem dimensionality.

show abstract

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

Cited by 30 publications

References 41 publications

System Architecture Optimization: An Open Source Multidisciplinary Aircraft Jet Engine Architecting Problem

System Architecture Optimization: An Open Source Multidisciplinary Aircraft Jet Engine Architecting Problem

Derivative-free optimization methods

Scaling Bayesian Optimization With Game Theory

Contact Info

Product

Resources

About