A non‐dominance‐based online stopping criterion for multi‐objective evolutionary algorithms

A non‐dominance criterion‐based metric that tracks the growth of an archive of non‐dominated solutions over a few generations is proposed to generate a convergence curve for multi‐objective evolutionary algorithms (MOEAs). It was observed that, similar to single‐objective optimization problems, there were significant advances toward the Pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured. This convergence curve was used to terminate the MOEA search to obtain a good trade‐off between the computational cost and the quality of the solutions. Two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric. Copyright © 2010 John Wiley & Sons, Ltd.     

Reliability‐based robust design optimization: A multi‐objective framework using hybrid quality loss function

In this globally competitive business environment, design engineers are constantly striving to establish new and effective tools and techniques to ensure a robust and reliable product design. Robust design (RD) and reliability‐based design approaches have shown the potential to deal with variability in the life cycle of a product. This paper explores the possibilities of combining both approaches into a single model and proposes a hybrid quality loss function‐based multi‐objective optimization model. The model is unique because it uses a hybrid form of quality loss‐based objective function that is defined in terms of desirable as well as undesirable deviations to obtain efficient design points with minimum quality loss. The proposed approach attempts to optimize the product design by addressing quality loss, variability, and life‐cycle issues simultaneously by combining both reliability‐based and RD approaches into a single model with various customer aspirations. The application of the approach is demonstrated using a leaf spring design example. Copyright © 2009 John Wiley & Sons, Ltd.     

Co‐evolutionary algorithm for structural damage identification using minimal physical testing

The problem of damage identification using minimum test data is studied in this work. Data sparsity in damage identification applications commonly results in inverse problems that are mathematically ill‐posed (e.g. non‐unique solutions). Although solution non‐uniqueness may be addressed by performing multiple tests on a structure, it is not trivial to decide which tests to carry out given that actual physical testing is costly. This problem is addressed in this work through a new co‐evolutionary algorithm that interactively searches for damage scenarios and optimum physical tests. The algorithm is composed of two stages: the estimation phase, which searches for damage scenarios that can predict current physical tests, and the exploration phase, which searches for tests that increase the level of information about the damaged system. The feasibility of the methodology is demonstrated using numerical examples. Copyright © 2006 John Wiley & Sons, Ltd.     

Convergence speed in multi‐objective metaheuristics: Efficiency criteria and empirical study

Solving optimization problems using a reduced number of objective function evaluations is an open issue in the design of multi‐objective optimization metaheuristics. The usual approach to analyze the behavior of such techniques is to choose a benchmark of known problems, to perform a predetermined number of function evaluations, and then, apply a set of performance indicators in order to assess the quality of the solutions obtained. However, this sort of methodology does not provide any insights of the efficiency of each algorithm. Here, efficiency is defined as the effort required by a multi‐objective metaheuristic to obtain a set of non‐dominated solutions that is satisfactory to the user, according to some pre‐defined criterion. Indeed, the type of solutions of interest to the user may vary depending on the specific characteristics of the problem being solved. In this paper, the convergence speed of seven state‐of‐the‐art multi‐objective metaheuristics is analyzed, according to three pre‐defined efficiency criteria. Our empirical study shows that SMPSO (based on a particle swarm optimizer) is found to be the best overall algorithm on the test problems adopted when considering the three efficiency criteria. Copyright © 2010 John Wiley & Sons, Ltd.     

A structural damage identification method based on genetic algorithm and vibrational data

The problem of damage identification in framed structures using vibrational data is considered. The identification problem is modelled as an optimization task and the use of measured natural frequencies as well as modeshape information in the construction of objective functions is discussed. In a first attempt, a standard genetic algorithm is shown to be ineffective in obtaining the correct damage distribution in test problems. Using domain knowledge, modifications are introduced in the coding process, in the initial population generation, in the fitness function, and in the genetic operators, leading to a promising tool to solve this class of problems. Synthetic problems, with the addition of noise in the simulated measured data associated with the damaged structure, are analysed in order to assess the capability of the proposed technique. Copyright © 2006 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.     

A multi‐objective optimization using distribution characteristics of reference data for reverse engineering

As different industries produce similar products, engineers tend to analyze the products of competitors and adopt the excellent merits in their current products. This process is called reverse engineering. There can be multiple target characteristics in reverse engineering. In many cases, the improved design from reverse engineering usually keeps the data distribution characteristics of the competitors unless the developed product is a fully new creative design. The distribution should be considered in reverse engineering. Therefore, the reverse engineering process can be modeled as multi‐objective optimization considering data distribution. Recently, Taguchi developed the Mahalanobis Taguchi system (MTS) technique to minimize the Mahalanobis distance (MD), which is defined by a multi‐objective function with data distribution. However, the MTS technique has the limit that the new design is not better than the mean values of the competitors. In this research, a function named as the skewed Mahalanobis distance (SMD) is proposed to overcome the drawbacks of the MTS technique. SMD is a new distance scale defined by multiplying the skewed value of a design point to MD. SMD is used instead of MD and the method is named the SMD method. The SMD method can always give a unique Pareto optimum solution. To verify the efficiency of the SMD method, a non‐convex mathematical example, a cantilever beam, and a practical automobile suspension system are optimized. Copyright © 2010 John Wiley & Sons, Ltd.     

Large strain phase‐field‐based multi‐material topology optimization

A multi‐material topology optimization scheme is presented. The formulation includes an arbitrary number of phases with different mechanical properties. To ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions, an obstacle potential function, which introduces infinity penalty for negative densities, is utilized. The problem is formulated for nonlinear deformations, and the objective of the optimization is the end displacement. The boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method. To illustrate the possibilities of the method, it is applied to a simple boundary value problem where optimal designs using multiple phases are considered. Copyright © 2015 John Wiley & Sons, Ltd.     

A new approach to solving problems of multi‐state system reliability optimization

Usually engineers try to achieve the required reliability level with minimal cost. The problem of total investment cost minimization, subject to reliability constraints, is well known as the reliability optimization problem. When applied to multi‐state systems (MSS), the system has many performance levels, and reliability is considered as a measure of the ability of the system to meet the demand (required performance). In this case, the outage effect will be essentially different for units with different performance rate. Therefore, the performance of system components, as well as the demand, should be taken into account. In this paper, we present a technique for solving a family of MSS reliability optimization problems, such as structure optimization, optimal expansion, maintenance optimization and optimal multistage modernization. This technique combines a universal generating function (UGF) method used for fast reliability estimation of MSS and a genetic algorithm (GA) used as an optimization engine. The UGF method provides the ability to estimate relatively quickly different MSS reliability indices for series‐parallel and bridge structures. It can be applied to MSS with different physical nature of system performance measure. The GA is a robust, universal optimization tool that uses only estimates of solution quality to determine the direction of search. Copyright © 2001 John Wiley & Sons, Ltd.     

Studies of multi‐start clustering for global optimization

Global/multi‐modal optimization problems arise in many engineering applications. Owing to the existence of multiple minima, it is a challenge to solve the multi‐modal optimization problem and to identify the global minimum especially if efficiency is a concern. In this paper, variants of the multi‐start with clustering strategy are developed and studied for identifying multiple local minima in nonlinear global optimization problems. The study considers the sampling procedure, the use of Hessian information in forming clusters, the technique for cluster analysis and the local search procedure. Variations of multi‐start with clustering are applied to 15 multi‐modal problems. A comparative study focuses on the overall search effectiveness in terms of the number of local searches performed, local minima found and required function evaluations. The performance of these multi‐start clustering algorithms ranges from very efficient to very robust. Copyright © 2002 John Wiley & Sons, Ltd.     

Knowledge‐based algorithms in fixed‐grid GA shape optimization

Shape optimization through a genetic algorithm (GA) using discrete boundary steps and the fixed‐grid (FG) finite‐element analysis (FEA) concept was recently introduced by the authors. In this paper, algorithms based on knowledge specific to the FG method with the GA‐based shape optimization (FGGA) method are introduced that greatly increase its computational efficiency. These knowledge‐based algorithms exploit the information inherent in the system at any given instance in the evolution such as string structure and fitness gradient to self‐adapt the string length, population size and step magnitude. Other non‐adaptive algorithms such as string grouping and deterministic local searches are also introduced to reduce the number of FEA calls. These algorithms were applied to two examples and their effects quantified. The examples show that these algorithms are highly effective in reducing the number of FEA calls required hence significantly improving the computational efficiency of the FGGA shape optimization method. Copyright © 2003 John Wiley & Sons, Ltd.     

Efficient generation of pareto‐optimal topologies for compliance optimization

In multi‐objective optimization, a design is defined to beit pareto‐optimal if no other design exists that is better with respect to one objective, and as good with respect to other objectives. In this paper, we first show that if a topology is pareto‐optimal, then it must satisfy certain properties associated with the topological sensitivity field, i.e. no further comparison is necessary. This, in turn, leads to a deterministic, i.e. non‐stochastic, method for efficiently generating pareto‐optimal topologies using the classic fixed‐point iteration scheme. The proposed method is illustrated, and compared against SIMP‐based methods, through numerical examples. In this paper, the proposed method of generating pareto‐optimal topologies is limited to bi‐objective optimization, namely compliance–volume and compliance–compliance. The future work will focus on extending the method to non‐compliance and higher dimensional pareto optimization. Copyright © 2011 John Wiley & Sons, Ltd.     

A multi‐start threshold accepting algorithm for multiple objective continuous optimization problems

A multi‐start threshold accepting algorithm with an adaptive memory (MS‐TA) is proposed to solve multiple objective continuous optimization problems. The aim of this paper is to find efficiently multiple Pareto‐optimal solutions. Comparisons are carried out with multiple objective taboo search algorithm and genetic algorithm. Experiments on literature problems show that the proposed algorithm is more effective. The presented multi‐start adaptive algorithm improves the best‐known results by a significant margin. Copyright © 2010 John Wiley & Sons, Ltd.     

基于多传感器信息融合的结构损伤识别研究

针对结构健康监测系统中的传感器数量多、数据信息复杂的特点，从模式识别和局部控制、全局参与的思想出发，提出了多传感器信息融合方法对结构损伤进行识别。首先应用小波包变换对结构振动测试数据进行特征提取，通过不同传感器特征向量的合成完成数据层融合；然后建立三个耦合神经网络分别实现结构损伤的确认、定位及定量，并完成决策层的信息融合；最后进行了36个损伤工况的结构模型实验研究，验证了所提出的方法是可行的和有效的。从实验验证的结果来看，对损伤率在7．5％以上的结构，损伤识别精度较高；对于损伤确认和损伤定位，识别精度较高，而对于损伤程度识别有一定偏差。     

基于不变环境振动的结构损伤识别方法

建立了受随机外力激励作用的损伤识别理论模型和计算方法 ,提出一种在线结构损伤识别方法。讨论一个15层框架结构 ,数值仿真结果表明 ,该方法具有较高的辨别率和计算精度。它能够使用在桥梁和建筑的健康监测中。     

基于证据理论的结构损伤识别研究

基于多源损伤信息可以有效解决由多种不确定性所导致的损伤误判问题。将证据理论作为理论基础，研究基于多源信息的损伤识别方法。为了充分体现不同证据在重要性、可靠性方面的差异，在考虑实际损伤识别过程的基础上，提出了基于先验和后验可靠性联合校正的证据合成方法。损伤识别试验研究表明，所提出的证据合成方法优于经典的D—S合成法则；相对于传统的基于单一损伤信息的损伤识别而言，基于多源损伤信息能够有效降低损伤误判的可能性，获得准确性、鲁棒性更好的损伤识别结果。     

An approach to multi‐start clustering for global optimization with non‐linear constraints

This paper describes a multi‐start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of non‐linear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi‐start with clustering found in the literature have focused on unconstrained problems with little attention to non‐linear constrained problems. In this study, variations of multi‐start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) sub‐problem used in cluster formation. The strategies are evaluated by solving 18 non‐linear mathematical problems and six engineering design problems. Numerical results show that the solution of a one‐step QP sub‐problem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi‐start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required. Copyright © 2002 John Wiley & Sons, Ltd.     

An isogeometric approach to topology optimization of multi‐material and functionally graded structures

A new isogeometric density‐based approach for the topology optimization of multi‐material structures is presented. In this method, the density fields of multiple material phases are represented using the isogeometric non‐uniform rational B‐spline‐based parameterization leading to exact modeling of the geometry, removing numerical artifacts and full analytical computation of sensitivities in a cost‐effective manner. An extension of the perimeter control technique is introduced where restrictions are imposed on the perimeters of density fields of all phases. Consequently, not only can one control the complexity of the optimal design but also the minimal lengths scales of all material phases. This leads to optimal designs with significantly enhanced manufacturability and comparable performance. Unlike the common element‐wise or nodal‐based density representations, owing to higher order continuity of density fields in this method, their gradients required for perimeter control restrictions are calculated exactly without additional computational cost. The problem is formulated with constraints on either (1) volume fractions of different material phases or (2) the total mass of the structure. The proposed method is applied for the minimal compliance design of two‐dimensional structures consisting of multiple distinct materials as well as functionally graded ones. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved multi‐level Newton solvers for fully coupled multi‐physics problems

An algorithm is suggested to improve the efficiency of the multi‐level Newton method that is used to solve multi‐physics problems. It accounts for full coupling between the subsystems by using the direct differentiation method rather than error prone finite difference calculations and retains the advantage of greater flexibility over the tightly coupled approaches. Performance of the algorithm is demonstrated by solving a fluid–structure interaction problem. Copyright © 2003 John Wiley & Sons, Ltd.