Showing papers by "John E. Dennis published in 2003"

Optimal aeroacoustic shape design using the surrogate management framework

Abstract: 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 efficiency 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 in the parameter space. Each term of this subsequence is a weak local minimizer of the cost function on the mesh in a sense to be made precise later. We will discuss necessary optimality conditions for the design problem that are satisfied by the limit of this subsequence. 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. Optimal shapes that minimize noise have been identified for the trailing-edge problem in constrained and unconstrained cases. Results show a significant reduction (as much as 80%) in acoustic power with reasonable computational cost using several shape parameters. Physical mechanisms for noise reduction are discussed.

Pattern search algorithms for mixed variable general constrained optimization problems

Abstract: : A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented The Audet-Dennis Generalized Pattern Search (GPS) algorithm for bound constrained mixed variable optimization problems is extended to problems with general nonlinear constraints by incorporating a filter in which new iterates are accepted whenever they decrease the incumbent objective function value or constraint violation function value Additionally, the algorithm can exploit any available derivative information (or rough approximation thereof) to speed convergence without sacrificing the flexibility often employed by GPS methods to find better local optima. In generalizing existing GPS algorithms, the new theoretical convergence results presented here reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are made, a hierarchy of theoretical convergence results is given, in which the assumptions dictate what can be proved about certain limit points of the algorithm. A new Matlab software package was developed to implement these algorithms. Numerical results are provided for several nonlinear optimization problems from the CUTE test set.

Parallel continuous optimization

Abstract: Parallel continuous optimization methods are motivated here by applications in science and engineering The key issues are addressed at di erent computational levels including local and global optimization as well as strategies for large sparse versus small but expensive problems Topics covered include global optimization direct search with and without surrogates optimization of linked subsystems and variable and constraint distribution Finally there is a discussion of future research directions

Constrained Aeroacoustic Shape Optimization Using the Surrogate Management Framework

Abstract: Reduction of noise generated by turbulent flow past the trailing-edge of a lifting surface is a challenge in many aeronautical and naval applications. Numerical predictions of trailing-edge noise necessitate the use of advanced simulation techniques such as large-eddy simulation (LES) in order to capture a wide range of turbulence scales which are the source of broadband noise. Aeroacoustic calculations of the flow over a model airfoil trailing edge using LES and aeroacoustic theory have been presented in Wang and Moin and were shown to agree favorably with experiments. The goal of the present work is to apply shape optimization to the trailing edge flow previously studied, in order to control aerodynamic noise.

Pattern search methods for linearly constrained minimization in the presence of degeneracy

Abstract: : This paper deals with generalized pattern search (GPS) algorithms for linearly constrained optimization. At each iteration, the GPS algorithm generates a set of directions that conforms to the geometry of any nearby linear constrains, and this is used to define the POLL set for that iteration. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions at a current iterate whether or not the constraints are degenerate. The main difficulty in the degenerate case is in classifying constraints as redundant and nonredundant . We give a short survey of the main definitions and methods concerning redundancy and propose an approach, which may be useful for other active set algorithms, to identify the nonredundant constraints.

Pattern Search for Mixed Variable Optimization Problems

Abstract: : CONCLUSIONS: We have found an effective method for mixed variable problems ... BUT ... It requires serious thinking by the user as to what constitutes an acceptable solution for each problem * It is not easy to incorporate surrogates with categorical variables * It is unlikely to be effective for many categorical variables * We have analyzed the method, BUT..., better results depend on the filter method for continuous variables.