Abstract not found

This paper focuses on a particular algorithm, Efficient Global Optimization (EGO) that uses kriging metamodels. Several infill sampling criteria are reviewed, namely criteria for selecting the points added to the data set for fitting the metamodel. The infill sampling criterion has a strong influence on how efficiently and accurately EGO locates the optimum. Variance-reducing criteria substantially reduce the RMS error of the resulting metamodels, while other criteria influence how locally or globally EGO searches. Criteria that place more emphasis on global searching require more iterations to locate optima and do so less accurately than criteria emphasizing local search

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.

Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood Preprint submitted to Elsevier 14 January 2008of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.

AQ1Š ABSTRACT Finding the near-native structure of a protein is one of the most important open problems in structural biology and AQ2Š biological physics. The problem becomes dramatically more difficult when a given protein has no regular secondary structure or it does not show a fold similar to structures already known. This situation occurs frequently when we need to predict the tertiary structure of small molecules, called peptides. In this research work, we propose a new ab initio algorithm, the generalized pattern search algorithm, based on the well-known class of Search-and-Poll algorithms. Inspired by the approach proposed by other researchers, we performed an extensive set of simulations over a well-known set of 44 peptides to investigate the robustness and reliability of the proposed algorithm, and we compared the peptide conformation with a state-of-the-art algorithm for peptide structure prediction known as PEPstr. In particular, we tested the algorithm on the instances proposed by the originators of PEPstr, to validate the proposed algorithm; the experimental results confirm that the generalized pattern search algorithm outperforms AQ3Š When analyzing the complex structure of a biological system, proteins are the most attracting molecular devices. They are likely involved in all processes of a living organism; they are responsible for behavioral changes in the cells. Due to the

Abstract—We present an algorithm that coevolves fitness predictors, optimized for the solution population, which reduce fitness evaluation cost and frequency, while maintaining evolutionary progress. Fitness predictors differ from fitness models in that they may or may not represent the objective fitness, opening opportunities to adapt selection pressures and diversify solutions. The use of coevolution addresses three fundamental challenges faced in past fitness approximation research: 1) the model learning investment; 2) the level of approximation of the model; and 3) the loss of accuracy. We discuss applications of this approach and demonstrate its impact on the symbolic regression problem. We show that coevolved predictors scale favorably with problem complexity on a series of randomly generated test problems. Finally, we present additional empirical results that demonstrate that fitness prediction can also reduce solution bloat and find solutions more reliably. Index Terms—Bloat Reduction, coevolution, fitness modeling, symbolic regression.

Surrogate-based-optimization methods provide a means to minimize expensive highfidelity models at reduced computational cost. The methods are useful in problems for which two models of the same physical system exist: a high-fidelity model which is accurate and expensive, and a low-fidelity model which is less costly but less accurate. A number of model management techniques have been developed and shown to work well for the case in which both models are defined over the same design space. However, many systems exist with variable fidelity models for which the design variables are defined over different spaces, and a mapping is required between the spaces. Previous work showed that two mapping methods, corrected space mapping and POD mapping, used in conjunction with a trust-region model management method, provide improved performance over conventional non-surrogate-based optimization methods for unconstrained problems. This paper extends that work to constrained problems. Three constraint-management methods are demonstrated with each of the mapping methods: Lagrangian minimization, an sequential quadratic programming-like surrogate method, and MAESTRO. The methods are demonstrated on a fixed-complexity analytical test problem and a variable-complexity wing design problem. The SQP-like method consistently outperformed optimization in the high-fidelity space and the other variable complexity methods. Corrected space mapping performed slightly better on average than POD mapping. On the wing design problem, the combination of the SQP-like method and corrected space mapping achieved 58 % savings in high-fidelity function calls over optimization directly in the high-fidelity space. I.

Previous analyses of pattern search algorithms for unconstrained and linearly constrained minimization have focused on proving convergence of a subsequence of iterates to a limit point satisfying either directional or first-order necessary conditions for optimality, depending on the smoothness of the objective function in a neighborhood of the limit point. Even though pattern search methods require no derivative information, we are able to prove some limited directional second-order results. Although not as strong as classical second-order necessary conditions, these results are stronger than the first order conditions that many gradient-based methods satisfy. Under fairly mild conditions, we can eliminate from consideration all strict local maximizers and an entire class of saddle points.

www.itwm.fraunhofer.de Abstract — Micro-electronics component and circuit design requires long computation time; to reduce this time, the use of simplification techniques has been introduced. In order to obtain a first validation of the method, a first test case is presented; the simplification techniques have been applied to the analytical expression of Y parameters of an inductor equivalent circuit. The resulting expressions have been used in the fitting process in order to reproduce the behaviour of a simulated inductor. Five different optimization algorithms, both deterministic (POWELL and DIRECT) and stochastic (CRS, CRS ENHANCED and OPTIA) have been tested for the fitting. The result of the introduction of the simplification techniques has been the reduction of the running time during the fitting. From an optimization point of view, the best results have been obtained by the stochastic algorithms CRS, and OPTIA. I.

Abstract. Proteins are the most interesting molecular entities of a living organism and understanding their function is a an important task to treat diseases and synthesize new drugs. It is largely known that the function of a protein is strictly related to its spatial conformation: to tackle this problem, we have proposed a new approach based on the class of pattern search algorithms that are largely used in optimization of real problems. The results obtained by this approach are interesting in terms of the quality of the structures found. 1