Support vector regression based metamodeling for seismic reliability analysis of structures

The present study deals with support vector regression-based metamodeling approach for efficient seismic reliability analysis of structure. Various metamodeling approaches e.g. response surface method, Kriging interpolation, artificial neural network, etc. are usually adopted to overcome computational challenge of simulation based seismic reliability analysis. However, the approximation capability of such empirical risk minimization principal-based metamodeling approach is largely affected by number of training samples. The support vector regression based on the principle of structural risk minimization has revealed improved response approximation ability using small sample learning. The approach is explored here for improved estimate of seismic reliability of structure in the framework of Monte Carlo Simulation technique. The parameters necessary to construct the metamodel are obtained by a simple effective search algorithm by solving an optimization sub-problem to minimize the mean square error obtained by cross-validation method. The simulation technique is readily applied by random selection of metamodel to implicitly consider record to record variations of earthquake. Without additional computational burden, the approach avoids a prior distribution assumption about approximated structural response unlike commonly used dual response surface method. The effectiveness of the proposed approach compared to the usual polynomial response surface and neural network based metamodels is numerically demonstrated.     

A time-space Kriging-based sequential metamodeling approach for multi-objective crashworthiness optimization

A time-space Kriging-based sequential metamodeling approach is proposed for multi-objective crashworthiness optimization (MOCO) in this paper. By defining the novel time-space design criteria, the constructed metamodels for the optimization objectives include the characteristic mechanical responses with respect to both the structural space domain and crash time domain, compared to standard metrics with the extremum of the time history of the entire structure. The adaptive addition of new samples is performed to gradually improve the approximation accuracy during the optimization with the guidance of an adaptive weighted sum method. The effectiveness of the proposed method is demonstrated by investigating a multi-cell thin-walled crashworthiness design problem. Finally, its effectiveness in practical engineering is validated by the crashworthiness design for a vehicle under full-overlap frontal crash loadcase.     

Nonscalarized multiobjective global optimization

A new approach to multiobjective optimization is presented which is made possible due to our ability to obtain full global optimal solutions. A distinctive feature of this approach is that a vector cost function is nonscalarized. The method provides a means for the solution of vector optimization problems with nonreconcilable objectives.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A3492.     

Quantile regression metamodeling: Toward improved responsiveness in the high-tech electronics manufacturing industry

Both technology and market demands within the high-tech electronics manufacturing industry change rapidly. Accurate and efficient estimation of cycle-time (CT) distribution remains a critical driver of on-time delivery and associated customer satisfaction metrics in these complex manufacturing systems. Simulation models are often used to emulate these systems in order to estimate parameters of the CT distribution. However, execution time of such simulation models can be excessively long limiting the number of simulation runs that can be executed for quantifying the impact of potential future operational changes. One solution is the use of simulation metamodeling which is to build a closed-form mathematical expression to approximate the input–output relationship implied by the simulation model based on simulation experiments run at selected design points in advance. Metamodels can be easily evaluated in a spreadsheet environment “on demand” to answer what-if questions without needing to run lengthy simulations. The majority of previous simulation metamodeling approaches have focused on estimating mean CT as a function of a single input variable (i.e., throughput). In this paper, we demonstrate the feasibility of a quantile regression based metamodeling approach. This method allows estimation of CT quantiles as a function of multiple input variables (e.g., throughput, product mix, and various distributional parameters of time-between-failures, repair time, setup time, loading and unloading times). Empirical results are provided to demonstrate the efficacy of the approach in a realistic simulation model representative of a semiconductor manufacturing system.     

Dimension reduction in multiobjective optimization

In multiobjective optimization there is often the problem of the existence of a large number of objectives. For more than two objectives there is a difficulty with the representation and visualization of the solutions in the objective space. Therefore, it is not clear for the decision maker the trade-off between the different alternative solutions. Thus, this creates enormous difficulties when choosing a solution from the Pareto-optimal set and constitutes a central question in the process of decision making. Based on statistical methods as Principle Component Analysis and Cluster Analysis, the problem of reduction of the number of objectives is addressed. Several test examples with different number of objectives have been studied in order to evaluate the process of decision making through these methods. Preliminary results indicate that this statistical approach can be a valuable tool on decision making in multiobjective optimization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new multi-objective discrete robust optimization algorithm for engineering design

This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.     

Analysis of event-based, single-server nonstationary simulation responses using classical time-series models

In this article, we present a metamodeling methodology for analyzing event-based, single-server nonstationary simulation responses that is based on the use of classical ARIMA (or SARIMA) time-series models. Some analytical results are derived for a Markovian queue and are used to evaluate the proposed methodology. The use of the corresponding procedure is illustrated on a traffic example from the simulation literature. Some conclusions are drawn and recommendations for further work are stated.     

An integrated simulation-optimization framework for the operational planning of seaport container terminals

In this article the operational planning of seaport container terminals is considered by defining a suitable integrated framework in which simulation and optimization interact. The proposed tool is a simulation environment (implemented by using the Arena software) representing the dynamics of a container terminal. When the system faces some particular conditions (critical events), an optimization procedure integrated in the simulation tool is called. This means that the simulation is paused, an optimization problem is solved and the relative solution is an input for the simulation environment where some system parameters are modified (generally, the handling rates of some resources are changed). For this reason, in the present article we consider two modelling and planning levels about container terminals. The simulation framework, based on an appropriate discrete-event model, represents the dynamic behaviour of the terminal, thus it needs to be quite detailed and it is used as an operational planning tool. On the other hand, the optimization approach is devised in order to define some system parameters such as the resource handling rates; in this sense, it can be considered as a tool for tactical planning. The optimization procedure is based on an aggregate representation of the terminal where the dynamics is modelled by means of discrete-time equations.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

Better Optimization of Nonlinear Uncertain Systems (BONUS) for Vehicle Structural Design

With the continuous improvement of computational performance, vehicle structural design has been addressed using computational methods, resulting in more efficient development of new vehicles. Most simulation-based optimization approaches generate deterministic optimal designs without considering variability effects in modeling, simulation, and/or manufacturing. One of the main reasons for this omission is due to the fact that the computing time of a single crash analysis for vehicle structural design still requires significant computing time using a state-of-the-art computer. This calls for the development and implementation of an efficient optimization under uncertainty method. In this paper, a new integrated stochastic optimization method, which combines the advantages of metamodeling techniques and Better Optimization of Nonlinear Uncertain Systems (BONUS), is developed for vehicle side impact design. Nonlinear metamodels are built by using a stepwise regression method to replace the expensive computational model and BONUS is employed to obtain optimal designs under uncertainty. A benchmark problem for vehicle safety design is used to demonstrate the method. The main goal of this case study is to maintain or enhance the vehicle side impact test performance while minimizing the vehicle weight under various uncertainties.     

Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

Simulation metamodeling with dynamic Bayesian networks

This paper presents a novel approach to simulation metamodeling using dynamic Bayesian networks (DBNs) in the context of discrete event simulation. A DBN is a probabilistic model that represents the joint distribution of a sequence of random variables and enables the efficient calculation of their marginal and conditional distributions. In this paper, the construction of a DBN based on simulation data and its utilization in simulation analyses are presented. The DBN metamodel allows the study of the time evolution of simulation by tracking the probability distribution of the simulation state over the duration of the simulation. This feature is unprecedented among existing simulation metamodels. The DBN metamodel also enables effective what-if analysis which reveals the conditional evolution of the simulation. In such an analysis, the simulation state at a given time is fixed and the probability distributions representing the state at other time instants are updated. Simulation parameters can be included in the DBN metamodel as external random variables. Then, the DBN offers a way to study the effects of parameter values and their uncertainty on the evolution of the simulation. The accuracy of the analyses allowed by DBNs is studied by constructing appropriate confidence intervals. These analyses could be conducted based on raw simulation data but the use of DBNs reduces the duration of repetitive analyses and is expedited by available Bayesian network software. The construction and analysis capabilities of DBN metamodels are illustrated with two example simulation studies.     

A metamodel-assisted evolutionary algorithm for expensive optimization

Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems.     

A metamodel-assisted evolutionary algorithm for expensive optimization

Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems.     

不确定条件下工程项目的多目标模糊均衡优化

在工程项目多目标优化问题研究基础上,研究不确定环境下工程项目多目标均衡优化问题.利用模糊数表示费用变化率和质量变化率,考虑模糊集的不同可能性水平,建立工程项目多目标模糊均衡优化模型,给出模型的求解方法和步骤,得到不同可能性水平下多目标优化问题的最优折衷解变化范围.优化方法使决策者能够根据决策风险的大小进行最优目标值的确定.     

Neural network metamodeling for cycle time-throughput profiles in manufacturing

This paper proposed a neural network (NN) metamodeling method to generate the cycle time (CT)–throughput (TH) profiles for single/multi-product manufacturing environments. Such CT–TH profiles illustrate the trade-off relationship between CT and TH, the two critical performance measures, and hence provide a comprehensive performance evaluation of a manufacturing system. The proposed methods distinct from the existing NN metamodeling work in three major aspects: First, instead of treating an NN as a black box, the geometry of NN is examined and utilized; second, a progressive model-fitting strategy is developed to obtain the simplest-structured NN that is adequate to capture the CT–TH relationship; third, an experiment design method, particularly suitable to NN modeling, is developed to sequentially collect simulation data for the efficient estimation of the NN models.     

Unilateral Crack Identification: A Filter-Driven, Iterative, Boundary Element Approach

An identification problem for parametric variational inequalities and linear com-plementarity problems is solved here by means of iterative filter techniques. A concrete application in engineering mechanics, the unilateral crack identification problem, is solved. The elastic contact problem is formulated by boundary element-linear complementarity techniques. By means of numerical results and comparison with previous approaches based on optimization and neural networks it is shown that this method is advantageous. In view of the difficulty of the considered bilevel optimization problem, this approach may be of interest for other applications as well.     

Discrete-event simulation: from the pioneers to the present,what next?

Discrete-event simulation is one of the most popular modelling techniques. It has developed significantly since the inception of computer simulation in the 1950s, most of this in line with developments in computing. The progress of simulation from its early days is charted with a particular focus on recent history. Specific developments in the past 15 years include visual interactive modelling, simulation optimization, virtual reality, integration with other software, simulation in the service sector, distributed simulation and the use of the worldwide web. The future is then speculated upon. Potential changes in model development, model use, the domain of application for simulation and integration with other simulation approaches are all discussed. The desirability of continuing to follow developments in computing, without significant developments in the wider methodology of simulation, is questioned.     

Multi-objective OLSR for proactive routing in MANET with delay,energy, and link lifetime predictions

In this paper, we develop a multi-objective approach for proactive routing in a Mobile Ad Hoc Network (MANET). We consider three routing objectives: minimizing average end-to-end delay, maximizing network energy lifetime, and maximizing packet delivery ratio. Accordingly, we develop three routing metrics: mean queuing delay on each node, energy cost on each node, and link stability on each link. For the proposed multi-objective approach, we develop efficient prediction methods: (a) predicting queuing delay and energy consumption using double exponential smoothing, and (b) predicting residual link lifetime using a heuristic of the distributions of the link lifetimes in MANET. Extensive simulation (by using ns2) is performed for the comparison of this multi-objective OLSR with existing OLSRs. The results show that the multi-objective OLSR is effective in finding optimal routing by tradeoffs among proposed objectives.     

A dynamic approach to multiple-objective resource allocation problem

A new approach using dynamic programming is developed for solving the multiple-objective resource allocation problem. There are two key issues being addressed in this approach. The first one is to develop a methodology of fuzzy evaluation and fuzzy optimization for multiple-objective systems. The procedure of getting the marginal evaluation for each objective and aggregating them synthetically into a global evaluation is presented in this paper. The second one is to design a dynamic optimization algorithm by incorporating the method of fuzzy evaluation and fuzzy optimization with the conventional dynamic programming technique. A characteristic feature of the approach presented is that various objectives are synthetically considered by the fuzzy systematic technique instead of the frequently employed weighted-average method. Numeric examples are also given to clarify the developed approach and to demonstrate its effectiveness.