A Simple and Effective Methodology to Perform Multi-Objective Bayesian Optimization: An Application in the Design of Sandwich Composite Armors for Blast Mitigation

2021 ◽  
Author(s):  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Bayesian Optimization ◽  
Sandwich Composite ◽  
Blast Mitigation ◽  
Multi Objective

A Simple and Effective Methodology to Perform Multi-Objective Bayesian Optimization: An Application in the Design of Sandwich Composite Armors for Blast Mitigation

2020 ◽  
Author(s):  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Finite Element ◽  
Surrogate Model ◽  
Test Problem ◽  
Pareto Front ◽  
Computational Cost ◽  
Bayesian Optimization ◽  
Sandwich Composite ◽  
Blast Mitigation ◽  
Multi Objective ◽  
Probabilistic Information

Abstract Bayesian optimization is a versatile numerical method to solve global optimization problems of high complexity at a reduced computational cost. The efficiency of Bayesian optimization relies on two key elements: a surrogate model and an acquisition function. The surrogate model is generated on a Gaussian process statistical framework and provides probabilistic information of the prediction. The acquisition function, which guides the optimization, uses the surrogate probabilistic information to balance the exploration and the exploitation of the design space. In the case of multi-objective problems, current implementations use acquisition functions such as the multi-objective expected improvement (MEI). The evaluation of MEI requires a surrogate model for each objective function. In order to expand the Pareto front, such implementations perform a multi-variate integral over an intricate hypervolume, which require high computational cost. The objective of this work is to introduce an efficient multi-objective Bayesian optimization method that avoids the need for multi-variate integration. The proposed approach employs the working principle of multi-objective traditional methods, e.g., weighted sum and min-max methods, which transform the multi-objective problem into a single-objective problem through a functional mapping of the objective functions. Since only one surrogate is trained, this approach has a low computational cost. The effectiveness of the proposed approach is demonstrated with the solution of four problems: (1) an unconstrained version of the Binh and Korn test problem (convex Pareto front), (2) the Fonseca and Fleming test problem (non-convex Pareto front), (3) a three-objective test problem and (4) the design optimization of a sandwich composite armor for blast mitigation. The optimization algorithm is implemented in MATLAB and the finite element simulations are performed in the explicit, nonlinear finite element analysis code LS-DYNA. The results are comparable (or superior) to the results of the MEI acquisition function.

scholarly journals MOBOpt — multi-objective Bayesian optimization

SoftwareX ◽  
2020 ◽  
Vol 12 ◽  
pp. 100520 ◽  
Author(s):  
Paulo Paneque Galuzio ◽  
Emerson Hochsteiner de Vasconcelos Segundo ◽  
Leandro dos Santos Coelho ◽  
Viviana Cocco Mariani
Keyword(s):  
Bayesian Optimization ◽  
Multi Objective

Multi-Objective Optimal Design of Sandwich Composite Laminates Using Simulated Annealing and FEM

2008 ◽  
Author(s):  
A. Sarhadi ◽  
M. Tahani ◽  
F. Kolahan ◽  
M. Sarhadi
Keyword(s):  
Simulated Annealing ◽  
Optimal Design ◽  
Composite Laminates ◽  
Composite Structures ◽  
Simulated Annealing Algorithm ◽  
Core Layer ◽  
Sandwich Composite ◽  
Surface Layers ◽  
Multi Objective ◽  
Aspect Ratios

Multi-objective optimal design of sandwich composite laminates consisting of high stiffness and expensive surface layers and low-stiffness and inexpensive core layer is addressed in this paper. The object is to determine ply angles and number of surface layers and core thickness in such way that natural frequency is maximized with minimal material cost and weight. A simulated annealing algorithm with finite element method is used for simultaneous cost and weight minimization and frequency maximization. The proposed procedure is applied to Graphite-Epoxy/Glass-Epoxy and Graphite-epoxy/Aluminum sandwich laminates and results are obtained for various boundary conditions and aspect ratios. Results show that this technique is useful in designing of effective, competitive and light composite structures.

scholarly journals Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization

2020 ◽  
Vol 34 (06) ◽  
pp. 10044-10052 ◽  
Author(s):  
Syrine Belakaria ◽  
Aryan Deshwal ◽  
Nitthilan Kannappan Jayakodi ◽  
Janardhan Rao Doppa
Keyword(s):  
Optimization Problem ◽  
State Of The Art ◽  
Selection Method ◽  
Bayesian Optimization ◽  
Benchmark Problems ◽  
Multi Objective ◽  
Blackbox Optimization ◽  
Expensive Function ◽  
Area Overhead ◽  
Measure Of Uncertainty

We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions while minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel uncertainty-aware search framework referred to as USeMO to efficiently select the sequence of inputs for evaluation to solve this problem. The selection method of USeMO consists of solving a cheap MO optimization problem via surrogate models of the true functions to identify the most promising candidates and picking the best candidate based on a measure of uncertainty. We also provide theoretical analysis to characterize the efficacy of our approach. Our experiments on several synthetic and six diverse real-world benchmark problems show that USeMO consistently outperforms the state-of-the-art algorithms.

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