Finding the global optimum on a large, multimodal, complex, and discontinuous (or nondifferentiable) landscape is usually very hard, even using the evolutionary approach. However, some of these complex landscapes can be approximated and smoothened without changing the nature of the problem, i.e., without modifying the global optimum and its location. The approximated and smoothened landscape is often much easier to search than the original one. In this paper, we propose a new algorithm using landscape approximation and hybrid evolutionary and local search. We also list several algorithm design principles. Following the basic algorithm, an example algorithm is given from our previous work of the combination of landscape approximation and local search (LALS). Furthermore, we develop a novel evolutionary algorithm with n-dimensional approximation (EANA), which shares the same rules as the basic algorithm, but remedies some of the drawbacks found in the LALS. Comparisons with evo...

Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is time-consuming. Simulations on two bench-mark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time. 1

This paper presents results for a 31 variable helicopter rotor design example. Results are given for several numerical methods. This is a brief description of a portion of the Boeing/IBM/Rice University collaboration whose purpose is to develop effective numerical methods for managing the use of approximation concepts or response surface methodology in design optimization.

this paper |produces a user-speci ed number of suggested evaluation points in each step; |proceeds by successive partitioning of the box (branch) and building local quadratic models ( t); |combines local and global search and allows the user to determine which of both should be emphasized; |handles local search from the best point with the aid of trust regions; |allows for hidden constraints and assigns to such points a function value based on the function values of nearby feasible points

. The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial di#erential equations, e.g. fluid flows. It can also be used to develop reduced order control models. The essential is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model. We present an approach where the suitable reduced order model is derived successively and give global convergence results. Keywords: proper orthogonal decomposition, flow control, reduced order modeling, trust region methods, global convergence 1. Introduction. We present a robust reduced order method for the control of complex time-dependent physical processes governed by partial di#erential equations (PDE). Such a control problem often is hard to solve because of the high order system that describes the state (a large number of (finite element) basis elements for every point in the time d...

A powerful new space-mapping (SM) optimization algorithm is presented in this paper. It draws upon recent developments in both surrogate model-based optimization and modeling of microwave devices. SM optimization is formulated as a general optimization problem of a surrogate model. This model is a convex combination of a mapped coarse model and a linearized fine model. It exploits, in a novel way, a linear frequency-sensitive mapping. During the optimization iterates, the coarse and fine models are simulated at different sets of frequencies. This approach is shown to be especially powerful if a significant response shift exists. The algorithm is illustrated through the design of a capacitively loaded 10 : 1 impedance transformer and a double-folded stub filter. A high-temperature superconducting filter is also designed using decoupled frequency and SMs.

Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where high-fidelity analysis models are used, each function evaluation may require a Computational Structural Mechanics (CSM), Computational Fluid Dynamics (CFD) or Computational Electro-Magnetics (CEM) simulation costing minutes to hours of supercomputer time. Since EAs typically require thousands of function evaluations to locate a near optimal solution, the use of EAs often becomes computationally prohibitive for this class of problems. In this paper, we present frameworks that employ surrogate models for solving computationally expensive optimization problems on a limited computational budget. In particular, the key factors responsible for the success of these frameworks are discussed. Experimental results obtained on benchmark test functions and real-world complex design problems are presented.

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Shape optimization is applied to time-dependent trailing-edge flow in order to minimize aerodynamic noise. Optimization is performed using the surrogate management framework (SMF), a non-gradient based pattern search method chosen for its e#ciency and rigorous convergence properties. Using SMF, design space exploration is performed not with the expensive actual function but with an inexpensive surrogate function. The use of a polling step in the SMF guarantees that the algorithm generates a convergent subsequence of mesh points, each iterate of which is a local minimizer of the cost function on a mesh in the parameter space. Results are presented for an unsteady laminar flow past an acoustically compact airfoil. Constraints on lift and drag are handled within SMF by applying the filter pattern search method of Audet and Dennis, within which a penalty function is used to form and optimize a surrogate function.

One of the most significant problems in the application of standard optimization methods to real-world engineering design problems is that the computation of the objective function often takes so much computer time (sometimes hours) that traditional optimization techniques are not practical. A solution that has long been used in this situation has been to approximate the objective function with something much cheaper to compute, called a "model" (or surrogate), and optimize the model instead of the actual objective function. This simple approach succeeds some of the time, but sometimes it fails because there is not sufficient a priori knowledge to build an adequate model. One way to address this problem is to build the model with whatever a priori knowledge is available, and during the optimization process sample the true objective at selected points and use the results to monitor the progress of the optimization and to adapt the model in the region of interest. We call this approach "model management". This thesis will build on the fundamental ideas and theory of pattern search optimization methods to develop a rigorous methodology for model management. A general framework for model management algorithms will iv be presented along with a convergence analysis. A software implementation of the framework, which allows for the reuse of existing modeling and optimization software, has been developed and results for several test problems will be presented. The model management methodology and potential applications in aerospace engineering are the subject of an ongoing collaboration between researchers at Boeing, IBM, Rice and College of William & Mary.