A method for nonlinear optimization with discrete design variables

The use of computer experiments and surrogate approximations (metamodels) introduces a source of uncertainty in simulation-based design that we term model interpolation uncertainty. Most existing approaches for treating interpolation uncertainty in computer experiments have been developed for deterministic optimization and are not applicable to design under uncertainty in which randomness is present in noise and/or design variables. Because the random noise and/or design variables are also inputs to the metamodel, the effects of metamodel interpolation uncertainty are not nearly as transparent as in deterministic optimization. In this work, a methodology is developed within a Bayesian framework for quantifying the impact of interpolation uncertainty on the robust design objective, under consideration of uncertain noise variables. By viewing the true response surface as a realization of a random process, as is common in kriging and other Bayesian analyses of computer experiments, we derive a closed-form analytical expression for a Bayesian prediction interval on the robust design objective function. This provides a simple, intuitively appealing tool for distinguishing the best design alternative and conducting more efficient computer experiments. We illustrate the proposed methodology with two robust design examples—a simple container design and an automotive engine piston design with more nonlinear response behavior and mixed continuous-discrete design variables.

Download Full-text

Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

Mathematical Problems in Engineering ◽

10.1155/2017/1457297 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Yue Wu ◽

Qingpeng Li ◽

Qingjie Hu ◽

Andrew Borgart

Keyword(s):

Topology Optimization ◽

Firefly Algorithm ◽

Optimization Problems ◽

Optimization Method ◽

Structural Topology ◽

Discrete Variables ◽

And Topology ◽

Design Variables ◽

Improved Firefly Algorithm ◽

Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

Download Full-text

An adaptive elitist differential evolution for optimization of truss structures with discrete design variables

Computers & Structures ◽

10.1016/j.compstruc.2015.11.014 ◽

2016 ◽

Vol 165 ◽

pp. 59-75 ◽

Cited By ~ 80

Author(s):

V. Ho-Huu ◽

T. Nguyen-Thoi ◽

T. Vo-Duy ◽

T. Nguyen-Trang

Keyword(s):

Differential Evolution ◽

Truss Structures ◽

Design Variables ◽

Discrete Design Variables

Download Full-text

Model Bias Characterization Considering Discrete and Continuous Design Variables

Volume 2B: 42nd Design Automation Conference ◽

10.1115/detc2016-60109 ◽

2016 ◽

Author(s):

Xiangxue Zhao ◽

Zhimin Xi ◽

Hongyi Xu ◽

Ren-Jye Yang

Keyword(s):

Regression Model ◽

Potential Model ◽

Training Data ◽

Data Sets ◽

Model Errors ◽

Model Bias ◽

Modeling Approach ◽

Operation Conditions ◽

Design Variables ◽

Discrete Design Variables

Model bias can be normally modeled as a regression model to predict potential model errors in the design space with sufficient training data sets. Typically, only continuous design variables are considered since the regression model is mainly designed for response approximation in a continuous space. In reality, many engineering problems have discrete design variables mixed with continuous design variables. Although the regression model of the model bias can still approximate the model errors in various design/operation conditions, accuracy of the bias model degrades quickly with the increase of the discrete design variables. This paper proposes an effective model bias modeling strategy to better approximate the potential model errors in the design/operation space. The essential idea is to firstly determine an optimal base model from all combination models derived from discrete design variables, then allocate majority of the bias training samples to this base model, and build relationships between the base model and other combination models. Two engineering examples are used to demonstrate that the proposed approach possesses better bias modeling accuracy compared to the traditional regression modeling approach. Furthermore, it is shown that bias modeling combined with the baseline simulation model can possess higher model accuracy compared to the direct meta-modeling approach using the same amount of training data sets.

Download Full-text