Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Yufei Wu ◽  
Teng Long ◽  
Renhe Shi ◽  
G. Gary Wang
Keyword(s):  
Design Optimization ◽  
Sampling Method ◽  
Sequential Sampling ◽  
Computational Cost ◽  
Optimization Methods ◽  
Black Box ◽  
High Dimensional ◽  
Beam Design ◽  
Convergence Performance ◽  
Coordinate Perturbation

Abstract This article presents a novel mode-pursuing sampling method using discriminative coordinate perturbation (MPS-DCP) to further improve the convergence performance of solving high-dimensional, expensive, and black-box (HEB) problems. In MPS-DCP, a discriminative coordinate perturbation strategy is integrated into the original mode-pursuing sampling (MPS) framework for sequential sampling. During optimization, the importance of variables is defined by approximated global sensitivities, while the perturbation probabilities of variables are dynamically adjusted according to the number of optimization stalling iterations. Expensive points considering both optimality and space-filling property are selected from cheap points generated by perturbing the current best point, which balances between global exploration and local exploitation. The convergence property of MPS-DCP is theoretically analyzed. The performance of MPS-DCP is tested on several numerical benchmarks and compared with state-of-the-art metamodel-based design optimization methods for HEB problems. The results indicate that MPS-DCP generally outperforms the competitive methods regarding convergence and robustness performances. Finally, the proposed MPS-DCP is applied to a stepped cantilever beam design optimization problem and an all-electric satellite multidisciplinary design optimization (MDO) problem. The results demonstrate that MPS-DCP can find better feasible optima with the same or less computational cost than the competitive methods, which demonstrates its effectiveness and practicality in solving real-world engineering problems.

scholarly journals Metamodel-based multidisciplinary design optimization methods for aerospace system

Astrodynamics ◽  
2021 ◽  
Vol 5 (3) ◽  
pp. 185-215
Author(s):  
Renhe Shi ◽  
Teng Long ◽  
Nianhui Ye ◽  
Yufei Wu ◽  
Zhao Wei ◽  
...  
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Computational Cost ◽  
Optimization Methods ◽  
Problem Formulation ◽  
Black Box ◽  
Optimization Techniques ◽  
Multidisciplinary Optimization ◽  
Multidisciplinary Design ◽  
Aerospace Systems

AbstractThe design of complex aerospace systems is a multidisciplinary design optimization (MDO) problem involving the interaction of multiple disciplines. However, because of the necessity of evaluating expensive black-box simulations, the enormous computational cost of solving MDO problems in aerospace systems has also become a problem in practice. To resolve this, metamodel-based design optimization techniques have been applied to MDO. With these methods, system models can be rapidly predicted using approximate metamodels to improve the optimization efficiency. This paper presents an overall survey of metamodel-based MDO for aerospace systems. From the perspective of aerospace system design, this paper introduces the fundamental methodology and technology of metamodel-based MDO, including aerospace system MDO problem formulation, metamodeling techniques, state-of-the-art metamodel-based multidisciplinary optimization strategies, and expensive black-box constraint-handling mechanisms. Moreover, various aerospace system examples are presented to illustrate the application of metamodel-based MDOs to practical engineering. The conclusions derived from this work are summarized in the final section of the paper. The survey results are expected to serve as guide and reference for designers involved in metamodel-based MDO in the field of aerospace engineering.

High-Dimensional Reliability-Based Design Optimization Involving Highly Nonlinear Constraints and Computationally Expensive Simulations

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Meng Li ◽  
Mohammadkazem Sadoughi ◽  
Chao Hu ◽  
Zhen Hu ◽  
Amin Toghi Eshghi ◽  
...  
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Sequential Sampling ◽  
Computational Cost ◽  
High Dimensional ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Modeling Strategy ◽  
Design Cost

Reliability-based design optimization (RBDO) aims at optimizing the design of an engineered system to minimize the design cost while satisfying reliability requirements. However, it is challenging to perform RBDO under high-dimensional uncertainty due to the often prohibitive computational burden. In this paper, we address this challenge by leveraging a recently developed method for reliability analysis under high-dimensional uncertainty. The method is termed high-dimensional reliability analysis (HDRA). The HDRA method optimally combines the strengths of univariate dimension reduction (UDR) and kriging-based reliability analysis to achieve satisfactory accuracy with an affordable computational cost for HDRA problems. In this paper, we improve the computational efficiency of high-dimensional RBDO by pursuing two new strategies: (i) a two-stage surrogate modeling strategy is adopted to first locate a highly probable region of the optimum design and then locally refine the accuracy of the surrogates in this region; and (ii) newly selected samples are updated for all the constraints during the sequential sampling process in HDRA. The results of two mathematical examples and one real-world engineering example suggest that the proposed HDRA-based RBDO (RBDO-HDRA) method is capable of solving high-dimensional RBDO problems with higher accuracy and comparable efficiency than the UDR-based RBDO (RBDO-UDR) and ordinary kriging-based RBDO (RBDO-kriging) methods.

scholarly journals Genetic evolution vs. function approximation: Benchmarking algorithms for architectural design optimization

2018 ◽  
Vol 6 (3) ◽  
pp. 414-428 ◽  
Author(s):  
Thomas Wortmann
Keyword(s):  
Genetic Algorithms ◽  
Design Optimization ◽  
Architectural Design ◽  
Parametric Design ◽  
Fitness Landscape ◽  
Optimization Methods ◽  
Black Box ◽  
Direct Search ◽  
Model Based ◽  
Simulation Based

Abstract This article presents benchmark results from seven simulation-based problems from structural, building energy, and daylight optimization. Growing applications of parametric design and performance simulations in architecture, engineering, and construction allow the harnessing of simulation-based, or black-box, optimization in the search for less resource- and/or energy consuming designs. In architectural design optimization (ADO) practice and research, the most commonly applied black-box algorithms are genetic algorithms or other metaheuristics, to the neglect of more current, global direct search or model-based, methods. Model-based methods construct a surrogate model (i.e., an approximation of a fitness landscape) that they refine during the optimization process. This benchmark compares metaheuristic, direct search, and model-based methods, and concludes that, for the given evaluation budget and problems, the model-based method (RBFOpt) is the most efficient and robust, while the tested genetic algorithms perform poorly. As such, this article challenges the popularity of genetic algorithms in ADO, as well as the practice of using them for one-to-one comparisons to justify algorithmic innovations. Highlights Benchmarks optimization algorithms on structural, energy, and daylighting problems. Benchmarks metaheuristic, direct search, and model-based optimization methods. Challenges the popularity of genetic algorithms in architectural design optimization. Presents model-based methods as a more efficient and reliable alternative.

Metamodel-based design optimization employing a novel sequential sampling strategy

2017 ◽  
Vol 34 (8) ◽  
pp. 2547-2564 ◽  
Author(s):  
Leshi Shu ◽  
Ping Jiang ◽  
Li Wan ◽  
Qi Zhou ◽  
Xinyu Shao ◽  
...  
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Sequential Sampling ◽  
Computational Cost ◽  
Sampling Strategy ◽  
Local Optimum ◽  
Optimization Approach ◽  
Great Ability ◽  
Content Type ◽  
Sample Points

Purpose Metamodels are widely used to replace simulation models in engineering design optimization to reduce the computational cost. The purpose of this paper is to develop a novel sequential sampling strategy (weighted accumulative error sampling, WAES) to obtain accurate metamodels and apply it to improve the quality of global optimization. Design/methodology/approach A sequential single objective formulation is constructed to adaptively select new sample points. In this formulation, the optimization objective is to select a sample point with the maximum weighted accumulative predicted error obtained by analyzing data from previous iterations, and a space-filling criterion is introduced and treated as a constraint to avoid generating clustered sample points. Based on the proposed sequential sampling strategy, a two-step global optimization approach is developed. Findings The proposed WAES approach and the global optimization approach are tested in several cases. A comparison has been made between the proposed approach and other existing approaches. Results illustrate that WAES approach performs the best in improving metamodel accuracy and the two-step global optimization approach has a great ability to avoid local optimum. Originality/value The proposed WAES approach overcomes the shortcomings of some existing approaches. Besides, the two-step global optimization approach can be used for improving the optimization results.

Response Surface Method Using Sequential Sampling for Reliability-Based Design Optimization

2009 ◽  
Author(s):  
Liang Zhao ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
Liu Du
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Response Surface Method ◽  
Sampling Method ◽  
Prediction Interval ◽  
Sequential Sampling ◽  
Kriging Method ◽  
Point Of Interest ◽  
Surface Method ◽  
Current Point

Traditional RBDO requires the sensitivity for both the most probable point (MPP) search in inverse reliability analysis and design optimization. However, the sensitivity is often unavailable or difficult to compute in complex multi-physics or multidisciplinary engineering applications. Hence, the response surface method (RSM) is often used to calculate both function evaluations and sensitivity effectively. Researchers have been developing the RSM for decades, and yet are still searching for an approach with an efficient sampling method for fast convergence while meeting the accuracy criteria. This paper proposes a new adaptive sequential sampling method to be integrated with the Kriging method for RBDO. By using the bandwidth of the prediction interval from the Kriging method, a new sampling strategy and a new local response surface accuracy criteria are proposed. In this sequential sampling method, the response surface is initiated using very few samples. An additional sampling point will then be determined by finding the point that has the largest absolute ratio between the bandwidth of the prediction interval and the predicted response within a neighboring area of current point of interest. The insertion of additional sampling will continue until the accuracy criterion of the response surface in the neighborhood of the current point of interest is achieved. Case studies show this proposed adaptive sequential sampling technique yields better result in terms of convergence speed compared with other sampling methods, such as the Latin hypercube sampling and the grid sampling, when the same sample size is used. Both a highly nonlinear mathematical example and a vehicle durability engineering example show that the proposed RSM yields accurate RBDO results that are comparable to the sensitivity-based RBDO results, as well as significant savings in computational time for function evaluation and sensitivity computation.

Learning manipulation skills from a single demonstration

2017 ◽  
Vol 37 (1) ◽  
pp. 137-154 ◽  
Author(s):  
Peter Englert ◽  
Marc Toussaint
Keyword(s):  
State Of The Art ◽  
Optimization Methods ◽  
Black Box ◽  
Bayesian Optimization ◽  
High Dimensional ◽  
Control Methods ◽  
Benchmark Experiment ◽  
Real Robot ◽  
Optimal Control Methods ◽  
Single Demonstration

We consider the scenario where a robot is demonstrated a manipulation skill once and should then use only a few trials on its own to learn to reproduce, optimize, and generalize that same skill. A manipulation skill is generally a high-dimensional policy. To achieve the desired sample efficiency, we need to exploit the inherent structure in this problem. With our approach, we propose to decompose the problem into analytically known objectives, such as motion smoothness, and black-box objectives, such as trial success or reward, depending on the interaction with the environment. The decomposition allows us to leverage and combine (i) constrained optimization methods to address analytic objectives, (ii) constrained Bayesian optimization to explore black-box objectives, and (iii) inverse optimal control methods to eventually extract a generalizable skill representation. The algorithm is evaluated on a synthetic benchmark experiment and compared with state-of-the-art learning methods. We also demonstrate the performance on real-robot experiments with a PR2.

A Kriging Metamodel Assisted Multi-Objective Genetic Algorithm for Design Optimization

2006 ◽  
Author(s):  
Mian Li ◽  
Genzi Li ◽  
Shapour Azarm
Keyword(s):  
Genetic Algorithm ◽  
Design Optimization ◽  
Pareto Frontier ◽  
Computational Cost ◽  
Optimization Methods ◽  
Optimization Approach ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Main Challenge ◽  
Engineering Design Problems

The high computational cost of population based optimization methods, such as multi-objective genetic algorithms, has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise methods that can significantly reduce the number of computationally intensive simulation (objective/constraint functions) calls. We present a new multi-objective design optimization approach in that kriging-based metamodeling is embedded within a multi-objective genetic algorithm. The approach is called Kriging assisted Multi-Objective Genetic Algorithm, or K-MOGA. The key difference between K-MOGA and a conventional MOGA is that in K-MOGA some of the design points or individuals are evaluated by kriging metamodels, which are computationally inexpensive, instead of the simulation. The decision as to whether the simulation or their kriging metamodels to be used for evaluating an individual is based on checking a simple condition. That is, it is determined whether by using the kriging metamodels for an individual the non-dominated set in the current generation is changed. If this set is changed, then the simulation is used for evaluating the individual; otherwise, the corresponding kriging metamodels are used. Seven numerical and engineering examples with different degrees of difficulty are used to illustrate applicability of the proposed K-MOGA. The results show that on the average, K-MOGA converges to the Pareto frontier with about 50% fewer number of simulation calls compared to a conventional MOGA.

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