Stochastic Multi-objective Optimization on a Budget: Application to multi-pass wire drawing with quantified uncertainties

  title={Stochastic Multi-objective Optimization on a Budget: Application to multi-pass wire drawing with quantified uncertainties},
  author={Piyush Pandita and Ilias Bilionis and Jitesh H. Panchal and B. P. Gautham and Amol Joshi and Pramod Zagade},
  journal={arXiv: Optimization and Control},
Design optimization of engineering systems with multiple competing objectives is a painstakingly tedious process especially when the objective functions are expensive-to-evaluate computer codes with parametric uncertainties. The effectiveness of the state-of-the-art techniques is greatly diminished because they require a large number of objective evaluations, which makes them impractical for problems of the above kind. Bayesian global optimization (BGO), has managed to deal with these… 

Figures from this paper

Evolutionary Multi-Objective Optimization Under Uncertainty Through Adaptive Kriging in Augmented Input Space

A surrogate model-based computationally efficient optimization scheme for design problems with multiple, probabilistic objectives estimated through stochastic simulation, established by replacing the originally used epsilon-constraint optimizer with a multi-objective evolutionary algorithm (MOEA).

Industrial Applications of Intelligent Adaptive Sampling Methods for Multi-Objective Optimization

This chapter covers a time-tested technology specifically tailored to limited-data scenarios called Bayesian hybrid modeling (GEBHM) developed and maintained at General Electric (GE) research and the impact of GEBHM/GE-IDACE on multiple real-world engineering applications including additive manufacturing, combustion testing, and computational fluid dynamic design modeling.

Deriving Information Acquisition Criteria For Sequentially Inferring The Expected Value Of A Black-Box Function

This paper derives an expression for the expected KL divergence to sequentially infer the expected QoI of the black-box function, and demonstrates the methodology on a steel wire manufacturing problem.

A New Multi-Objective Bayesian Optimization Formulation With the Acquisition Function for Convergence and Diversity

A novel acquisition function is proposed to determine the next sample point, which helps improve the diversity and convergence of the Pareto solutions.

Multifidelity Model Calibration in Structural Dynamics Using Stochastic Variational Inference on Manifolds

A stochastic variational inference algorithm is employed that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference.

Bayesian Optimal Design of Experiments For Inferring The Statistical Expectation Of A Black-Box Function

The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response.

Bayesian Networks for Inverse Inference in Manufacturing Bayesian Networks

This paper investigates the application of conditional linear Gaussian Bayesian networks to address the inverse problem with multi-pass wire drawing process as a case study and proposes an approach to systematically find all solutions and rank them according to their likelihood.

Bayesian model calibration and optimization of surfactant-polymer flooding

A systematic approach for Bayesian history matching and uncertainty quantification in the model calibration stage of SP flooding using coreflood experimental data is presented and a variant of Bayesian global optimization (BGO), a class of algorithms capable of optimizing black-box, gradient-free, computationally expensive functions, is employed.



Extending Expected Improvement for High-dimensional Stochastic Optimization of Expensive Black-Box Functions

This work extends the expected improvement IAF to the case of design optimization under uncertainty wherein the EI policy is reformulated to filter out parametric and measurement uncertainties and employs a fully Bayesian interpretation of Gaussian processes by constructing a particle approximation of the posterior of its hyperparameters using adaptive Markov chain Monte Carlo.

Improvement criteria for constraint handling and multiobjective optimization

This thesis investigates efficient improvement criteria to address constrained problems and multiobjective problems, leading to the development of an improvement criterion that better balances improvement of the objective and all the constraint approximations.

Efficient Global Optimization of Expensive Black-Box Functions

This paper introduces the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering and shows how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule.

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

A Bayesian Approach to Constrained Multi-objective Optimization

This paper makes use of an extended domination rule taking both constraints and objectives into account under a unified multi-objective framework and proposes a generalization of the expected improvement sampling criterion adapted to the problem.

ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems

Results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used.

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

The proposed method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point and has excellent consistency and efficiency in finding global optimal solutions.

The computation of the expected improvement in dominated hypervolume of Pareto front approximations

A Monte Carlo method is reported that provides a direct computation procedure for the integral expression of the hypervolume measure and will be useful to enhance both accuracy and speed of computation for this important measure.

Survey of multi-objective optimization methods for engineering

A survey of current continuous nonlinear multi-objective optimization concepts and methods finds that no single approach is superior and depends on the type of information provided in the problem, the user's preferences, the solution requirements, and the availability of software.

Statistical Improvement Criteria for Use in Multiobjective Design Optimization

The work presented combines design of experiment methods with kriging (Gaussian process) models to enable the parallel evolution of multiobjective Pareto sets through the use of updating schemes based on new extensions of the expected improvement criterion commonly applied in single-objective searches.