Showing papers on "Surrogate model published in 2003"

Evolutionary Optimization of Computationally Expensive Problems via Surrogate Modeling

Abstract: We present a parallel evolutionary optimization algorithm that leverages surrogate models for solving computationally expensive design problems with general constraints, on a limited computational budget. The essential backbone of our framework is an evolutionary algorithm coupled with a feasible sequential quadratic programming solver in the spirit of Lamarckian learning. We employ a trust-region approach for interleaving use of exact modelsfortheobjectiveandconstraintfunctionswithcomputationallycheapsurrogatemodelsduringlocalsearch. In contrastto earlier work, we construct local surrogatemodels using radial basis functionsmotivated by theprinciple of transductive inference. Further, the present approach retains the intrinsic parallelism of evolutionary algorithms and can hence be readily implemented on grid computing infrastructures. Experimental results are presented for some benchmark test functions and an aerodynamic wing design problem to demonstrate that our algorithm converges to good designs on a limited computational budget.

Bayesian Surrogates Applied to Conceptual Stages of the Engineering Design Process

Abstract: During the conceptual design stages, designers often have incomplete knowledge about the interactions among design parameters. We are developing a methodology that will enable designers to create models with levels of detail and accuracy that correspond to the current state of the design process. Thus, designers can create a rough surrogate model when only a few data points are available and then refine the model as the design progresses and more information becomes available. These surrogates represent the system response when limited information is available and when few realizations of experiments or numerical simulations are possible. This paper presents a covariance-based approach for building multistage surrogates in the conceptual design stages when bounds for the response are not available a priori. We test the methodology using a one-dimensional analytical function and a heat transfer problem with an analytical solution, in order to obtain error measurements. We then illustrate the use of the methodology in a thermal design problem for wearable computers. The surrogate model enables the designer to understand the relationships among the design parameters.

Tutorial on Surrogate Constraint Approaches for Optimization in Graphs

Abstract: Surrogate constraint methods have been embedded in a variety of mathematical programming applications over the past thirty years, yet their potential uses and underlying principles remain incompletely understood by a large segment of the optimization community. In a number of significant domains of combinatorial optimization, researchers have produced solution strategies without recognizing that they can be derived as special instances of surrogate constraint methods. Once the connection to surrogate constraint ideas is exposed, additional ways to exploit this framework become visible, frequently offering opportunities for improvement. We provide a tutorial on surrogate constraint approaches for optimization in graphs, illustrating the key ideas by reference to independent set and graph coloring problems, including constructions for weighted independent sets which have applications to associated covering and weighted maximum clique problems. In these settings, the surrogate constraints can be generated relative to well-known packing and covering formulations that are convenient for exposing key notions. The surrogate constraint approaches yield widely used heuristics for identifying independent sets as simple special cases, and also afford previously unidentified heuristics that have greater power in these settings. Our tutorial also shows how the use of surrogate constraints can be placed within the context of vocabulary building strategies for independent set and coloring problems, providing a framework for applying surrogate constraints that can be used in other applications. At a higher level, we show how to make use of surrogate constraint information, together with specialized algorithms for solving associated sub-problems, to obtain stronger objective function bounds and improved choice rules for heuristic or exact methods. The theorems that support these developments yield further strategies for exploiting surrogate constraint relaxations, both in graph optimization and integer programming generally.

Using support vector machines in optimization for black-box objective functions

Abstract: In many practical engineering design problems, the form of objective functions is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective functions is obtained be real/computational experiments such as structural analysis, fluid mechanic analysis, thermodynamic analysis, and so on. Usually, these experiments are considerable expensive. In order to make the number of these experiments as few as possible, optimization is performed in parallel with predicting the form of objective functions. Response surface methods (RSM) are well known along this approach. This paper suggests to apply support vector machines (SVM) for predicting the objective functions. One of the most important tasks in this approach is to allocate sample moderately in order to make the umber of experiments as small as possible. It will be shown that the information of support vector can be used effectively to this aim. The effectiveness of our suggested method is shown through numerical examples.

Imparting Desired Attributes by Optimization in Structural Design

Abstract: Commonly available optimization methods typically produce a single optimal design as a Constrained minimum of a particular objective function. However, in engineering design practice it is quite often important to explore as much of the design space as possible with respect to many attributes to find out what behaviors are possible and not possible within the initially adopted design concept. The paper shows that the very simple method of the sum of objectives is useful for such exploration. By geometrical argument it is demonstrated that if every weighting coefficient is allowed to change its magnitude and its sign then the method returns a set of designs that are all feasible, diverse in their attributes, and include the Pareto and non-Pareto solutions, at least for convex cases. Numerical examples in the paper include a case of an aircraft wing structural box with thousands of degrees of freedom and constraints, and over 100 design variables, whose attributes are structural mass, volume, displacement, and frequency. The method is inherently suitable for parallel, coarse-grained implementation that enables exploration of the design space in the elapsed time of a single structural optimization.

Incorporating Information From Replications Into Bayesian Surrogate Models

Abstract: In some design domains, particularly rapidly evolving domains such as tissue engineering, analytical representations of the system do not exist. In these domains, the design process can be facilitated by the development of surrogate models that provide an understanding of the interactions of parameters and their influence on system performance, even though the models do not explain the underlying phenomena. Often, physical experiments are the only method for obtaining information about such systems. In particular, in bioengineering design domains, experiments are expensive and must be replicated to account for biological variability. Surrogate models can reduce the number of experiments needed and increase the value of the information gained through experimentation. In this paper, we present a framework for incorporating information from replications (repeated experiments) into Bayesian surrogate models. Within this framework, we develop uncertainty measurements for the prediction of the surrogate model. We illustrate the framework with two test cases using analytical functions. We then present a biomedical example used in the design of scaffold materials for the regeneration of bone tissue to show the use of Bayesian surrogates in exploratory design.© 2003 ASME

Adaptive sampling for optimization under uncertainty

Abstract: The problems of interest are where the objective function must be evaluated using sampling techniques. The sampled function values are used to build an approximation to the response surface over the product space of uncertainties and design variables. This approximation is successively used in the integration over the space of uncertainties and in the optimization (minimization) over the space of design variables. A surrogate-based trust region method is used to determine a succession of design points for optimization

Shape Optimization of a Membrane Wing for Micro Air Vehicles

Abstract: §† Micro air vehicles with a maximal dimension of 15cm require original design concept due to their low Reynolds number flight regime. It has been empirically observed that a flexible membrane wing can improve the aerodynamic performance of the vehicles. To help advance our knowledge in this area, we investigate shape optimization of a membrane wing. A direct membrane wing optimization employing a coupled Navier-Stokes and flexible structure analysis is computationally expensive. Therefore, we use a rigid wing as a surrogate model. We employ a moving grid technique to facilitate automatic grid generation. Our objective is to maximize the lift-to-drag ratio under aerodynamic and geometry constraints. The optimized design exhibits reduced camber from root to tip. Overall, the aerodynamic improvement is primarily derived from the inner 70% of the wing. The optimized platform is checked for performance of the membrane wings and found to improve the performance by about the same margin. Furthermore, both optimized membrane and rigid wings improve the liftto-drag ratios mainly by reducing the form drag. However, the membrane wing demonstrates less variation in lift-to-drag ratio as the angles of attack vary.

Establishment of a foundation for predictive design analysis within the engineering design process

Abstract: In today’s highly competitive market place it is of great importance for companies to deliver reliable products while decreasing the development time and costs. The time to market is a driving force for many companies, and throughout the engineering design process as well as the manufacturing process, the focus is on finding timesaving actions. However, the search for timesaving actions will most certainly result in a loss in product reliability if it is not combined with improved techniques and tools used by members of the engineering design team in order to maintain an acceptable level of reliability. One of the areas within engineering design that is adopting new techniques and methodologies is the design analysis activity that has conventionally been performed by specialists, but has to some extent shifted to also be performed, where applicable, by design engineers. Further, design analysis has traditionally been utilized as a verification tool at the latter engineering design phases and also for failure mode analysis with the objective to investigate failed designs or produce results about whether or not it will withstand applied loading conditions. Today both the research community and industry perceive the value added when design analysis is used in early engineering design phases to predict the performance of the product to be. Statistically planned and Stochastic (alternatively called in literature probabilistic) Finite Element Analysis (FEA) are addressed frequently in this area of research, and different mathematical methodologies have been discussed to provide this value-added information within design analysis. Fractional factorial designed experiments, Response Surface Methodologies (RSM) and Monte Carlo Simulations (MCS) are among the most commonly discussed approaches. One of the vital issues here is the shift from the deterministic design analysis approach, in which accounting for variations is done through safety factors that are overly conservative, to a Statistical or Stochastic design analysis approach where variables are defined in terms of their characteristics: the nature of the distribution of values, a typical value, and also, in stochastic approaches, a measure of the variability. A presentation of Predictive Design Analysis (PDA) is made in this paper, which incorporates Statistical and Stochastic approaches to perform design analysis at different phases of the engineering design process. The PDA methodology addresses abounding uncertainties i.e. material properties, magnitude and direction of loading, part geometry as well as the issues regarding sensitivity to variables acting on the product in service, all of which result in performance that is considerably different from the ideal. (Less)