Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model

A non‐gradient‐based approach for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the non‐gradient‐based topology optimization method in flow problems, this research focuses on two single‐objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and one multi‐objective optimization problem, which combines earlier two single‐objective optimization problems. The shape of flow channels is represented by the level set function. The pressure loss and the heat transfer performance of the channels are evaluated by the Building‐Cube Method code, which is a Cartesian‐mesh CFD solver. The proposed method resulted in an agreement with previous study in the single‐objective problems in its topology and achieved global exploration of non‐dominated solutions in the multi‐objective problems. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd     

Locally weighted regression models for surrogate-assisted design optimization

We consider engineering design optimization problems where the objective and/or constraint functions are evaluated by means of computationally expensive blackboxes. Our practical optimization strategy consists of solving surrogate optimization problems in the search step of the mesh adaptive direct search algorithm. In this paper, we consider locally weighted regression models to build the necessary surrogates, and present three ideas for appropriate and effective use of locally weighted scatterplot smoothing (LOWESS) models for surrogate optimization. First, a method is proposed to reduce the computational cost of LOWESS models. Second, a local scaling coefficient is introduced to adapt LOWESS models to the density of neighboring points while retaining smoothness. Finally, an appropriate order error metric is used to select the optimal shape coefficient of the LOWESS model. Our surrogate-assisted optimization approach utilizes LOWESS models to both generate and rank promising candidates found in the search and poll steps. The “real” blackbox functions that govern the original optimization problem are then evaluated at these ranked candidates with an opportunistic strategy, reducing CPU time significantly. Computational results are reported for four engineering design problems with up to six variables and six constraints. The results demonstrate the effectiveness of the LOWESS models as well as the order error metric for surrogate optimization.     

运营桥梁结构间接系统辨识的模式搜索方法

通过引入模式搜索的下降准则及其算法,部分解决了环境激励下运营桥梁结构间接辨识中可能存在的局部极值与算法收敛的问题,以及工程数据中可能存在的不可导、不连续的问题。引入了带收敛证明的广义模式搜索方法,介绍了模式移动、网格尺寸、表决等概念,通过构造算例来阐述了其搜索机理。对于运营结构的间接辨识,提出了其响应数据可能不可导、甚至不连续,或在一般算法中可能存在局部极值、算法不收敛的问题;基于无导数下降准则的模式搜索,能准确地通过车辆响应来对结构参数、车辆参数进行辨识;通过比较不同噪声水平下算法的迭代过程中的目标函数值、搜索次数、网格尺寸与表决结果,说明了其具备抗强噪声水平干扰的能力;并指出了通过加入罚函数即可向含约束的类似问题推广。     

Genetically assisted optimization of cell layout and material flow path skeleton

A continuous plane manufacturing cell layout and intercell flow path skeleton problem formulation involving rectilinear distances between cell input/output stations is mapped to a genetic search space. Certain properties of such a search space are exploited to design a very efficient method for reduction of a mixed-integer programming problem formulation to an iterative sequence of linear programming problems. This paper reports theoretical and computational insights for efficiently finding good solutions for the above problem formulation, taking advantage of the solution structure and the search stage. The scores of the objective function on a set of test cases indicate better solutions than those previously reported in the literature. The empirical results based on multiple runs also suggest that the method generates final results that are not dependent on the quality of the initial solution; hence the solution search seems to be more global than many of the previous approaches.     

Considerations of accuracy and uncertainty with kriging surrogate models in single-objective electromagnetic design optimisation

The high computational cost of evaluating objective functions in electromagnetic optimum design problems necessitates the use of cost-effective techniques. The paper discusses the use of one popular technique, surrogate modelling, with emphasis placed on the importance of considering both the accuracy of, and uncertainty in, the surrogate model. After a brief review of how such considerations have been made in the single-objective optimisation of electromagnetic devices, their use with kriging surrogate models is investigated. Traditionally, space-filling experimental designs are used to construct the initial kriging model, with the aim of maximising the accuracy of the initial surrogate model, from which the optimisation search will start. Utility functions, which balance the predictions made by this model with its uncertainty, are often used to select the next point to be evaluated. In this paper, the performances of several different utility functions are examined, with experimental designs that yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through a search for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations can be achieved if the iterative optimisation search is started earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimum design are discussed     

Fast Bayesian approach for parameter estimation

This paper presents two techniques, i.e. the proper orthogonal decomposition (POD) and the stochastic collocation method (SCM), for constructing surrogate models to accelerate the Bayesian inference approach for parameter estimation problems associated with partial differential equations. POD is a model reduction technique that derives reduced‐order models using an optimal problem‐adapted basis to effect significant reduction of the problem size and hence computational cost. SCM is an uncertainty propagation technique that approximates the parameterized solution and reduces further forward solves to function evaluations. The utility of the techniques is assessed on the non‐linear inverse problem of probabilistically calibrating scalar Robin coefficients from boundary measurements arising in the quenching process and non‐destructive evaluation. A hierarchical Bayesian model that handles flexibly the regularization parameter and the noise level is employed, and the posterior state space is explored by the Markov chain Monte Carlo. The numerical results indicate that significant computational gains can be realized without sacrificing the accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

A method for simulation based optimization using radial basis functions

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.     

Robust design optimisation via surrogate network model and soft outer array design

Robust design searches for a performance optimum with least sensitivity to variable and parameter variations. Taguchi method applies an inner array for control factors and an outer array for noise factors to estimate the Signal-to-Noise ratio (S/N). However, the cross product arrays impose serious cost concerns for expensive samplings. Also, rigorous control of noise factors to pre-set levels is impractical in industrial applications. This study presents a soft computing-based robust optimisation that merges control and noise factors into a combined experimental design to establish a surrogate using artificial neural network. Genetic algorithm is applied to search in the sub-space of control factors in the surrogate with a soft outer array to estimate the S/N served as the evolution fitness. Performance variations due to the tolerances of control and uncontrollable factors can then be estimated without conducting actual experiments. The verifications of the predicted optima become additional learning samples to refine the surrogate, and the iteration continues until convergence. The robust optimisation of a micro-accelerometer with maximised gain is used as an illustrative example. The proposed algorithm provides a superior robust optimum using a much smaller sample and less controlling cost compared with Taguchi method and a conventional response surface method.     

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered.     

OPTIMAL PRODUCTION PLANNING AND INVENTORY CONTROL*

This paper is concerned with the optimal production planning and inventory control. The first problem is a multiperiod production scheduling problem in which the objective is to minimize the operating cost for a planning period. This cost is composed principally of the sum of the production cost and inventory carrying cost. The second problem considers an inventory system with two decision variables in each planning period. These are the production schedule and work force which are to be determined so as to minimize the operating cost which includes the costs of changing the production rate, of changing the work force and of carrying the inventory. The maximum principle in the discrete form is used to reduce both the first problem which has N decision variables and the second problem which has 2N decision variables respectively to a series of two decision variables problems. The so-called sequential simplex pattern search technique is used to determine the optimal values of these two decision variables. Numerical examples are given to demonstrate the method.