A human‐like numerical technique for design of engineering systems

Because of the necessity for considering various creative and engineering design criteria, optimal design of an engineering system results in a highly‐constrained multi‐objective optimization problem. Major numerical approaches to such optimal design are to force the problem into a single objective function by introducing unjustifiable additional parameters and solve it using a single‐objective optimization method. Due to its difference from human design in process, the resulting design often becomes completely different from that by a human designer. This paper presents a novel numerical design approach, which resembles the human design process. Similar to the human design process, the approach consists of two steps: (1) search for the solution space of the highly‐constrained multi‐objective optimization problem and (2) derivation of a final design solution from the solution space. Multi‐objective gradient‐based method with Lagrangian multipliers (MOGM‐LM) and centre‐of‐gravity method (CoGM) are further proposed as numerical methods for each step. The proposed approach was first applied to problems with test functions where the exact solutions are known, and results demonstrate that the proposed approach can find robust solutions, which cannot be found by conventional numerical design approaches. The approach was then applied to two practical design problems. Successful design in both the examples concludes that the proposed approach can be used for various design problems that involve both the creative and engineering design criteria. Copyright © 2005 John Wiley & Sons, Ltd.     

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

基于演化算法的带频率约束的桁架结构形状和尺寸优化

具有频率约束的桁架结构形状和尺寸优化设计是一个难度大的非线性动力优化问题。形状和尺寸变量的耦合通常导致收敛困难,而频率约束则使得动力灵敏度分析困难,传统的优化准则法和数学规划法难于求解。将单纯形算法、子空间变维技术、均匀变异有机融入郭涛算法,提出一种混合演化算法,避开繁琐的动力灵敏度分析,简单、有效地求解这类桁架形状和尺寸优化问题。典型的桁架算例验证了算法的有效性和可靠性。     

A new harmony search algorithm for solving mixed–discrete engineering optimization problems

In general design optimization problems, it is usually assumed that the design variables are continuous. However, many practical problems in engineering design require considering the design variables as integer or discrete values. The presence of discrete and integer variables along with continuous variables adds to the complexity of the optimization problem. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This article presents a mixed–discrete harmony search approach for solving these nonlinear optimization problems which contain integer, discrete and continuous variables. Some engineering design examples are also presented to demonstrate the effectiveness of the proposed method.     

Single- and multiobjective optimization problems in robust parameter design

This paper reviews the evolution of off-line quality engineering methods with respect to one or more quality criteria, and presents some recent results. The fundamental premises that justify the use of robust product/process design are established with an illustrative example. The use of designed experiments to model quality criteria and their optimization is briefly reviewed. The fact that most design-for-quality problems involve multiple quality criteria motivates the development of multiobjective optimization techniques for robust parameter design. Two situations are considered: one in which response surface models for the quality characteristics can be obtained using regression and considered over a continuous factor space, and one in which the problem scenario and the experiment permit only discrete parameter settings for the design factors. In the former scenario, a multiobjective optimization technique based on the reference-point method is presented; this technique also incorporates an inference mechanism to deal with uncertainty in the response surface models caused by finite, noisy data. In the discrete-factors scenario, an efficient method to reduce computational complexity for a class of models is presented.     

A surrogate assisted parallel multiobjective evolutionary algorithm for robust engineering design

A number of multi-objective evolutionary algorithms have been proposed in recent years and many of them have been used to solve engineering design optimization problems. However, designs need to be robust for real-life implementation, i.e. performance should not degrade substantially under expected variations in the variable values or operating conditions. Solutions of constrained robust design optimization problems should not be too close to the constraint boundaries so that they remain feasible under expected variations. A robust design optimization problem is far more computationally expensive than a design optimization problem as neighbourhood assessments of every solution are required to compute the performance variance and to ensure neighbourhood feasibility. A framework for robust design optimization using a surrogate model for neighbourhood assessments is introduced in this article. The robust design optimization problem is modelled as a multi-objective optimization problem with the aim of simultaneously maximizing performance and minimizing performance variance. A modified constraint-handling scheme is implemented to deal with neighbourhood feasibility. A radial basis function (RBF) network is used as a surrogate model and the accuracy of this model is maintained via periodic retraining. In addition to using surrogates to reduce computational time, the algorithm has been implemented on multiple processors using a master–slave topology. The preliminary results of two constrained robust design optimization problems indicate that substantial savings in the actual number of function evaluations are possible while maintaining an acceptable level of solution quality.     

Optimality criteria-based topology optimization of a bi-material model for acoustic–structural coupled systems

This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.     

A MODIFIED DEMPSTER-SHAFER THEORY FOR MULTICRITERIA OPTIMIZATION

Abstract

A new methodology, based on a modified Dempster-Shafer (DS) theory, is proposed for solving multicriteria design optimization problems. It is well known that considerable amount of computational information is acquired during the iterative process of optimization. Based on the computational information generated in each iteration, an evidence-based approach is presented for solving a multiobjective optimization problem. The method handles the multiple design criteria, which are often conflicting and non-commensurable, by constructing belief structures that can quantitatively evaluate the effectiveness of each design in the range 0 to 1. An overall satisfaction function is then defined for converting the original multicriteria design problem into a single-criterion problem so that standard single-objective programming techniques can be employed for the solution. The design of a mechanism in the presence of seven design criteria and eighteen design variables is considered to illustrate the computational details of the approach. This work represents the first attempt made in the literature at applying DS theory for numerical engineering optimization.     

An uncertain optimization method for overall ballistics based on stochastic programming and a neural network surrogate model

A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on classical interior ballistics, projectile initial disturbance calculation model, exterior ballistics and firing dispersion calculation model. Secondly, the random characteristics of uncertainties are simulated using a hybrid probabilistic and interval model. Then, a nonlinear stochastic programming method is put forward by integrating a back-propagation neural network with the Monte Carlo method. Thus, the uncertain optimization problem is transformed into a deterministic multi-objective optimization problem by employing the mean value, the standard deviation, the probability and the expected loss function, and then the sorting and optimizing of design vectors are realized by the non-dominated sorting genetic algorithm-II. Finally, two numerical examples in practical engineering are presented to demonstrate the effectiveness and robustness of the proposed method.     

Multi-objective optimization based on meta-modeling by using support vector regression

Practical engineering design problems have a black-box objective function whose forms are not explicitly known in terms of design variables. In those problems, it is very important to make the number of function evaluations as few as possible in finding an optimal solution. So, in this paper, we propose a multi-objective optimization method based on meta-modeling predicting a form of each objective function by using support vector regression. In addition, we discuss a way how to select additional experimental data for sequentially revising a form of objective function. Finally, we illustrate the effectiveness of the proposed method through some numerical examples.     

Logistic 组稀疏回归模型的 Bayes 建模及变分推断

在工程应用中,如数据挖掘、成本预测以及风险预测等,Logistic 回归是一类十分重要的预测方法．当前,大部分 Logistic 回归方法都是基于优化准则而设计,这类回归方法具有参数调试过程繁琐、模型解释性差、估计子没有置信区间等缺点．本文从 Bayes 概率角度研究 Logistic 组稀疏性回归的建模与推断问题．具体来说,首先利用高斯-方差混合公式提出 Logistic 组稀疏回归的 Bayes 概率模型;其次,通过变分 Bayes 方法设计出一个高效的推断算法．在模拟数据上的实验结果表明,本文所提出的方法具有较好的预测性能．     

Stress-based topology optimization of concrete structures with prestressing reinforcements

Following the extended two-material density penalization scheme, a stress-based topology optimization method for the layout design of prestressed concrete structures is proposed. The Drucker–Prager yield criterion is used to predict the asymmetrical strength failure of concrete. The prestress is considered by making a reasonable assumption on the prestressing orientation in each element and adding an additional load vector to the structural equilibrium function. The proposed optimization model is thus formulated as to minimize the reinforcement material volume under Drucker–Prager yield constraints on elemental concrete local stresses. In order to give a reasonable definition of concrete local stress and prevent the stress singularity phenomenon, the local stress interpolation function and the ? -relaxation technique are adopted. The topology optimization problem is solved using the method of moving asymptotes combined with an active set strategy. Numerical examples are given to show the efficiency of the proposed optimization method in the layout design of prestressed concrete structures.     

Radial basis functions and level set method for structural topology optimization

Level set methods have become an attractive design tool in shape and topology optimization for obtaining lighter and more efficient structures. In this paper, the popular radial basis functions (RBFs) in scattered data fitting and function approximation are incorporated into the conventional level set methods to construct a more efficient approach for structural topology optimization. RBF implicit modelling with multiquadric (MQ) splines is developed to define the implicit level set function with a high level of accuracy and smoothness. A RBF–level set optimization method is proposed to transform the Hamilton–Jacobi partial differential equation (PDE) into a system of ordinary differential equations (ODEs) over the entire design domain by using a collocation formulation of the method of lines. With the mathematical convenience, the original time dependent initial value problem is changed to an interpolation problem for the initial values of the generalized expansion coefficients. A physically meaningful and efficient extension velocity method is presented to avoid possible problems without reinitialization in the level set methods. The proposed method is implemented in the framework of minimum compliance design that has been extensively studied in topology optimization and its efficiency and accuracy over the conventional level set methods are highlighted. Numerical examples show the success of the present RBF–level set method in the accuracy, convergence speed and insensitivity to initial designs in topology optimization of two‐dimensional (2D) structures. It is suggested that the introduction of the radial basis functions to the level set methods can be promising in structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficiency of Jaya algorithm for solving the optimization-based structural damage identification problem based on a hybrid objective function

A Jaya algorithm was recently proposed for solving effectively both constrained and unconstrained optimization problems. In this article, the Jaya algorithm is further extended for solving the optimization-based damage identification problem. In the current optimization problem, the vector of design variables represents the damage extent of elements discretized by the finite element model, and a hybrid objective function is proposed by combining two different objective functions to determine the sites and extent of damage. The first one is based on the multiple damage location assurance criterion and the second one is based on modal flexibility change. The robustness and efficiency of the proposed damage detection method are verified through three specific structures. The obtained results indicate that even under relatively high noise level, the proposed method not only successfully detects and quantifies damage in engineering structures, but also shows better efficiency in terms of computational cost.     

Finding all global optima of engineering design problems with discrete signomial terms

ABSTRACT

Many engineering design problems are frequently modelled as nonlinear programming problems with discrete signomial terms. In general, signomial programs are very difficult to solve for obtaining the globally optimal solution. This study reformulates the engineering design problem with discrete signomial terms as a mixed-integer linear program and finds all alternative global optima. Compared with existing exact methods, the proposed method uses fewer variables and constraints in the reformulated model and therefore efficiently solves the engineering problem to derive all global optima. Illustrative examples from the literature are solved to demonstrate the usefulness and efficiency of the proposed method.     

A target-based normalization technique for materials selection

Ranking and selection of the optimal material is an important stage in the engineering design process. However, most of the methods proposed for ranking in materials selection have tended to focus on cost and benefit criteria, with target values receiving much less attention in spite of their importance in many practical decision-making problems such as selecting materials to best match the properties of human tissue in biomedical engineering applications. In response to this perceived gap, the development of a new normalization technique is considered in this paper that provides an extension of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method and objective weighting in materials selection. There are four example cases included to validate the accuracy of outcomes from the proposed model. It is believed that the proposed decision-making model is suitable for linking to material databases and has the potential to enhance the efficiency of computer-aided materials selection systems.     

Development of a multidisciplinary–multiresponse robust design optimization model

Robust design is an efficient process improvement methodology that combines experimentation with optimization to create systems that are tolerant to uncontrollable variation. Most traditional robust design models, however, consider only a single quality characteristic, yet customers judge products simultaneously on a variety of scales. Additionally, it is often the case that these quality characteristics are not of the same type. To addresses these issues, a new robust design optimization model is proposed to solve design problems involving multiple responses of several different types. In this new approach, noise factors are incorporated into the robust design model using a combined array design, and the results of the experiment are optimized using a new approach that is formulated as a nonlinear goal programming problem. The results obtained from the proposed methodology are compared with those of other robust design methods in order to examine the trade-offs between meeting the objectives associated with different optimization approaches.     

A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so‐called Hamilton–Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re‐initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

A methodological concept for phase change material selection based on multiple criteria decision analysis with and without fuzzy environment

Selection of proper phase change material (PCM) plays an important role towards the development of a latent heat thermal energy storage system. Selection of the phase change material is a difficult and restrained task due to the immense number of different available materials having different characteristics. One has to select such PCM which will give the desired thermal performance at minimum cost. This study deals with two Multiple Attribute Decision-Making (MADM) methods to solve PCM selection problem. These two methods are technique for order preference by similarity to ideal solution (TOPSIS) method and fuzzy TOPSIS method that uses linguistic variable presentation and fuzzy operation. Both the methods use an analytic hierarchy process (AHP) method to determine weights of the criteria. TOPSIS and fuzzy TOPSIS methods are used to obtain final ranking. A problem to evaluate the best choice of PCM used in solar domestic hot water system is considered here to demonstrate the effectiveness and feasibility of the proposed model. Empirical results showed that the proposed methods are viable approaches in solving PCM selection problem. TOPSIS is suitable for the use of precise performance ratings while the fuzzy TOPSIS is a preferred technique when the performance ratings are vague and inaccurate.     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。