On Sampling Methods for Costly Multi-Objective Black-Box Optimization

2016 ◽  
pp. 273-296 ◽  
Author(s):  
Ingrida Steponavičė ◽  
Mojdeh Shirazi-Manesh ◽  
Rob J. Hyndman ◽  
Kate Smith-Miles ◽  
Laura Villanova
Keyword(s):  
Sampling Methods ◽  
Black Box ◽  
Multi Objective

Multiobjective Optimization for High Dimensional Expensively Constrained Black-Box Problems

2021 ◽  
pp. 1-59
Author(s):  
George Cheng ◽  
G. Gary Wang ◽  
Yeong-Maw Hwang
Keyword(s):  
Multiobjective Optimization ◽  
Trust Region ◽  
Adaptive Strategy ◽  
Black Box ◽  
Superior Performance ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Semiconductor Substrate ◽  
Multi Objective ◽  
Computationally Expensive

Abstract Multi-objective optimization (MOO) problems with computationally expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches for MOO are often not suitable for high-dimensional problems and often do not support expensive constraints. In this work, the Situational Adaptive Kreisselmeier and Steinhauser (SAKS) method was combined with a new multi-objective trust region optimizer (MTRO) strategy to form the SAKS-MTRO method for MOO problems with expensive black-box constraint functions. The SAKS method is an approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The MTRO strategy uses a combination of objective decomposition and K-means clustering to handle MOO problems. SAKS-MTRO was benchmarked against four popular multi-objective optimizers and demonstrated superior performance on average. SAKS-MTRO was also applied to optimize the design of a semiconductor substrate and the design of an industrial recessed impeller.

Expected-Improvement-Based Methods for Adaptive Sampling in Multi-Objective Optimization Problems

2016 ◽  
Author(s):  
Jesper Kristensen ◽  
You Ling ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Convex Hull ◽  
Design Optimization ◽  
Adaptive Sampling ◽  
Pareto Front ◽  
Performance Metrics ◽  
Sampling Methods ◽  
Optimization Problems ◽  
Expected Improvement ◽  
Multi Objective Optimization ◽  
Multi Objective

Adaptive sampling methods have been used to build accurate meta-models across large design spaces from which engineers can explore data trends, investigate optimal designs, study the sensitivity of objectives on the modeling design features, etc. For global design optimization applications, adaptive sampling methods need to be extended to sample more efficiently near the optimal domains of the design space (i.e., the Pareto front/frontier in multi-objective optimization). Expected Improvement (EI) methods have been shown to be efficient to solve design optimization problems using meta-models by incorporating prediction uncertainty. In this paper, a set of state-of-the-art methods (hypervolume EI method and centroid EI method) are presented and implemented for selecting sampling points for multi-objective optimizations. The classical hypervolume EI method uses hyperrectangles to represent the Pareto front, which shows undesirable behavior at the tails of the Pareto front. This issue is addressed utilizing the concepts from physical programming to shape the Pareto front. The modified hypervolume EI method can be extended to increase local Pareto front accuracy in any area identified by an engineer, and this method can be applied to Pareto frontiers of any shape. A novel hypervolume EI method is also developed that does not rely on the assumption of hyperrectangles, but instead assumes the Pareto frontier can be represented by a convex hull. The method exploits fast methods for convex hull construction and numerical integration, and results in a Pareto front shape that is desired in many practical applications. Various performance metrics are defined in order to quantitatively compare and discuss all methods applied to a particular 2D optimization problem from the literature. The modified hypervolume EI methods lead to dramatic resource savings while improving the predictive capabilities near the optimal objective values.

Prediction of Pareto Dominance Using an Attribute Tendency Model for Expensive Multi-Objective Optimization

2019 ◽  
Vol 29 (02) ◽  
pp. 2050021
Author(s):  
Wenbin Li ◽  
Junqiang Jiang ◽  
Xi Chen ◽  
Guanqi Guo ◽  
Jianjun He
Keyword(s):  
Surrogate Model ◽  
Prediction Method ◽  
Optimization Methods ◽  
Black Box ◽  
Benchmark Problems ◽  
Pareto Dominance ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Attributes ◽  
Coarse Model

This paper proposes a novel surrogate-assisted multi-objective evolutionary algorithm, MOEA-ATCM, to solve expensive or black-box multi-objective problems with small evaluation budgets. The proposed approach encompasses a state-of-the-art MOEA based on a nondominated sorting genetic algorithm assisted by multi-fidelity optimization methods. A high-fidelity attribute tendency (AT) surrogate model was used to construct a linear decision space by introducing the knowledge of the objective space. A coarse model (CM) based on the AT model and correlation analyses of the objective functions and decision attributes were used to predict the Pareto dominance for candidates in the new decision space constructed by the AT model. Two major roles of MOEA-ATCM were identified: (1) the development of a new multi-fidelity surrogate-model-based method to predict Pareto dominance in a decision space that was then applied to MOEA, which does not need to dynamically update surrogate models in the optimization process and (2) the development of a Pareto dominance prediction method to obtain good nondominated solutions of expensive or black box problems with relatively few objective function evaluations. The advantages of MOEA-ATCM were verified by mathematical benchmark problems and a real-world multi-objective parameter optimization problem.

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

2020 ◽  
Author(s):  
Jesper Kristensen ◽  
Waad Subber ◽  
Yiming Zhang ◽  
Sayan Ghosh ◽  
Natarajan Chennimalai Kumar ◽  
...  
Keyword(s):  
Adaptive Sampling ◽  
Sampling Methods ◽  
Industrial Applications ◽  
Multi Objective Optimization ◽  
Multi Objective

An efficient general black-box adversarial attack approach based on multi-objective optimization for high dimensional images

2021 ◽  
Vol 95 ◽  
pp. 107402
Author(s):  
Chunkai Zhang ◽  
Xin Guo ◽  
Yepeng Deng ◽  
Xuan Wang ◽  
Peiyi Han ◽  
...  
Keyword(s):  
Black Box ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Adversarial Attack

An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems

2016 ◽  
Vol 67 (1-2) ◽  
pp. 399-423 ◽  
Author(s):  
Haoxiang Jie ◽  
Yizhong Wu ◽  
Jianjun Zhao ◽  
Jianwan Ding ◽  
Liangliang
Keyword(s):  
Pso Algorithm ◽  
Black Box ◽  
Multi Objective ◽  
Kriging Metamodel
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