Generalized Pattern Search Method Research Articles

A general and accurate pattern search method for various scenarios

As chip designs grow in complexity, the optical proximity correction (OPC) process becomes increasingly time-consuming. As a result, pattern search technology is becoming a foundation stone of many tasks for manufacturing, such as lithography simulation, hotspot detection, mask optimization, and so on. The most difficult challenge of pattern search is to locate clips by specific patterns within the layout accurately and efficiently. In this paper, we present a generalized pattern search method capable in diverse scenarios, including patterns with hollow shapes, shifting edges, and multi-layer situations. Experimental results show that our method outperforms commercial tools in pattern locating accuracy and handling search problems involving complex patterns which is not directly support by commercial tools yet.

Obstacle avoidance extremum seeking control based on constrained derivative-free optimization

A new control scheme based on extremum seeking control (ESC) which employs a constrained derivative-free optimization algorithm has been proposed in this paper. A theorem has been formulated to prove the convergence result of ESC based on constrained derivative-free optimization. Generalized pattern search method with filter algorithm for constraint is used to generate a sequence of ESC control state. Since generalized pattern search (GPS) method does not require continuously differentiable and Lipschitz conditions, noise cancellation algorithm is added to the proposed ESC algorithm which is then used for multi-agent robot system. The obstacles are expressed as constraint functions instead of the traditional way of calculating the performance function of obstacles. Simulation results illustrate a multi-agent obstacle avoidance system which utilized the control algorithm to avoid obstacles that appear on the path of multi-agent robots. Based on the simulation results, it can be observed that multi-agents maintain their formation as per initial condition and follow the target without colliding into obstacles while navigating in a noisy environment. Performance comparison of the proposed algorithm with a reference algorithm shows the efficiency of the proposed algorithm.

Modeling dynamic urban land-use change with geographical cellular automata and generalized pattern search-optimized rules

ABSTRACTA novel generalized pattern search (GPS)-based cellular automata (GPS-CA) model was developed to simulate urban land-use change in a GIS environment. The model is built on a fitness function that computes the difference between the observed results produced from remote-sensing images and the simulated results produced by a general CA model. GPS optimization incorporating genetic algorithms (GAs) searches for the minimum difference, i.e. the smallest accumulated residuals, in fitting the CA transition rules. The CA coefficients captured by the GPS method have clear physical meanings that are closely associated with the dynamic mechanisms of land-use change. The GPS-CA model was applied to simulate urban land-use change in Kunshan City in the Yangtze River Delta from 2000 to 2015. The results show that the GPS method had a smaller root mean squared error (0.2821) than a logistic regression (LR) method (0.5256) in fitting the CA transition rules. The GPS-CA model thus outperformed the LR-CA model, with an overall accuracy improvement of 4.7%. As a result, the GPS-CA model should be a superior tool for modeling land-use change as well as predicting future scenarios in response to different conditions to support the sustainable urban development.

Drying Kinetic Analysis of Municipal Solid Waste Using Modified Page Model and Pattern Search Method

This work studied the drying kinetics of the organic fractions of municipal solid waste (MSW) samples with different initial moisture contents and presented a new method for determination of drying kinetic parameters. A series of drying experiments at different temperatures were performed by using a thermogravimetric technique. Based on the modified Page drying model and the general pattern search method, a new drying kinetic method was developed using multiple isothermal drying curves simultaneously. The new method fitted the experimental data more accurately than the traditional method. Drying kinetic behaviors under extrapolated conditions were also predicted and validated. The new method indicated that the drying activation energies for the samples with initial moisture contents of 31.1 and 17.2 % on wet basis were 25.97 and 24.73 kJ mol−1. These results are useful for drying process simulation and industrial dryer design. This new method can be also applied to determine the drying parameters of other materials with high reliability.

Microseismic location: using both P and S waves with new methods

In this paper we develop a new method on the basis of the two exist two methods, using both P and S waves recorded with surface array and borehole data. The new microseismic location method take the full advantage of Generalized Pattern Search Method and Simulated Annealing Method, improving the location accuracy. We use this method to do the cast study. Consequently, using both P and S waves information in the location technique reduces the position uncertainty as compared to single P or S wave relative location. And it will be more applicable to low signal-to-noise ratios data.

Generalized Pattern Search Methods for control of stable, unstable and integrating systems with unknown delay under step input

A number of different analytical and numerical methods have previously been proposed to identify and control systems with unknown delay. The methods have been based on the Smith Predictor for the stable case and on modified Smith predictor, for the unstable and integrating case. Among the proposed optimization techniques, the pattern-search-based method besides its computational advantage, provides better accuracy compared to other methods. However, the response of the methods under step input in some case is deficient. This paper presents an improved Generalized Pattern Search Method (GPSM) based optimization technique, where new updates ways are proposed. The proposed GPSM algorithm uses a simple structure based on the feedback of fitness value in the process. It provides better performance for delay identification and a reference tracking. Comparisons with existing methods for delay estimation are presented using both synthetic and experimental data under various conditions. The proposed scheme offers higher accuracy, and also eliminates the need for users to manually tune the control parameters of Pattern Search Methods.

Production optimization using derivative free methods applied to Brugge field case

Recently production optimization has achieved increasing attention in upstream petroleum industry. Here, we evaluate derivative free optimization methods for determination of the optimal production strategy using a numerical reservoir model which was prepared for a comparative study at the SPE Applied Technology Workshop in Brugge, June 2008. The pattern search Hooke–Jeeves, the reflection simplex Nelder–Mead, a new line-search derivative-free and a generalized pattern search methods are applied to the optimization problem. The line-search derivative-free algorithm is developed based on the existing line-search derivative free algorithms in combination with the Hooke–Jeeves pattern search method. The derivative free optimization results are compared with a gradient based sequential quadratic programming algorithm, but we clearly identify some issues limiting the performance of gradient based algorithms. In real applications our optimization problem is facing very costly function evaluations and at the same time one might have limitations in the computational budget. Therefore we are interested in methods that can improve the objective function with few function evaluations. The line-search derivative-free method performs more efficient and better than the other optimization methods. Ranking among the other four methods is somewhat more difficult, except that the Nelder–Mead method clearly has the slowest performance among these methods. We also observed that optimization with sequential quadratic programming had a high risk of getting trapped in a local optimum, which could be explained by properties of the objective function.

Identification and control of delayed unstable and integrative LTI MIMO systems using pattern search methods

In this paper, we develop a multi-model adaptive control strategy to be applied on delay compensation schemes for stable/unstable LTI MIMO systems. The only requirement is that the delay should be bounded and decoupled from the control strategy. The delay identification problem is formulated as an optimization one, and it is framed on the abstract definition of the Generalized Pattern Search Method (GPSM). Taking advantage of the global convergence analysis presented by GPSM, we make a stability analysis of the proposed approach and delay identification capabilities. Simulation examples show the usefulness of the proposed strategy proving that the scheme is capable of identifying the delay and stabilizing the system even with a larger delay. The capabilities of the approach are tested on a second-order delayed unstable process, a MIMO unstable systems and an irrigation channel model. Additionally, simulation examples on an irrigation channel with time-varying delay are presented.

Identification and control of delayed SISO systems through pattern search methods

In this study, an approach to identify and control stable, unstable and integrating systems with unknown delays, framed on the generalized Pattern Search Method is presented. The proposed method inherits the global convergence properties of the generalized Pattern Search Method, allowing us to make a stability analysis of the proposed approach and delay identification capabilities. The proposed approach identifies the delay and guarantees closed-loop stability, which could be a difficult task since in unstable and integrating cases, open-loop experiments are not feasible. Simulation examples show the usefulness of the proposed strategy proving that the scheme is capable of identifying the delay and stabilizing the system even with long delay.

Optimization of earth observation satellite system based on parallel systems and computational experiments

Earth observation satellite system (EOSS) is the main space platform to collect ground information. Optimization of EOSS is still a difficult problem, as it is a complex system concerning a great deal of design variables and uncertain factors. To solve the problem, an optimization framework based on parallel system and computational experiments is proposed. An artificial system for EOSS is firstly constructed, which is the integration of resource data, task data, environment data and related operation rules. Real EOSS together with artificial EOSS constitute the parallel systems for EOSS. Based on the parallel systems, concept of computational experiments is detailed. Moreover, surrogate models are built to approximate real EOSS. Genetic algorithm and improved general pattern search method are adopted to optimize the model. According to the framework, a case study is carried out. Through the results, we illustrated the proposed framework to be useful and effective for EOSS optimization problem.

Optimization of Earth Observation Satellite System Based on Design of Experiment and Surrogate Model

Earth observation satellite system (EOSS) is the main space platform collecting ground information. Optimization of EOSS is difficult, as it is a complex system referring a great deal of design variables and uncertain factors. Therefore, an optimization framework based on design of experiment and surrogate model is proposed. Design of experiment is used to generate simulation plan, which will greatly cut down cost of simulation. Then surrogate model is built to analyze simulation data and approximate real EOSS. Genetic algorithm and improved general pattern search method are adopted to solve the model. According to the framework, a case study is carried out. The final results illustrate the framework is useful and effective for the problem of EOSS optimization.

Amplitude-only pattern synthesis of nonuniform linear arrays using a generalized pattern search optimization

In this work, synthesis of linear array geometry and excitation amplitudes is first formulated as a linearly constrained multiobjective optimization problem with the goals of minimum sidelobe level, null control and high directivity and then solved by a generalized pattern search (GPS) algorithm for the optimum element locations and excitation amplitudes. The constraints are imposed on the interelement spacing and dynamic range ratio of the amplitude tapering to reduce mutual coupling effects between the elements. GPS methods are newly discovered, derivative-free methods where the current iterate is updated by sampling the fitness function at a finite number of points along a suitable set of search directions to find a decrease in the function value. Thus, GPS methods can be exploited efficiently in solving optimization problems without requiring any information about the gradient of the fitness function which may be even discontinuous, nondifferentiable, stochastic or highly nonlinear. Finally, four worked examples are presented that illustrate the use of the whole GPS synthesis method, and the optimization goal in each example is easily achieved. Furthermore the full-wave simulations of the synthesized arrays are also completed to examine the mutual coupling effects. Finally the results of the GPS algorithm are validated by comparing with results obtained using the genetic algorithm, and the results of the uniform and Dolph - Chebyshev arrays, having the same number of element and the same aperture length. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.

A Derivative-Free Optimization Method for Solving Classification Problem

Problem statement: The aim of data classification is to establish rul es for the classification of some observations assuming that we have a database, which includes of at least two classes. There is a training set for each class. Those problems oc cur in a wide range of human activity. One of the most promising ways to data classification is based on methods of mathematical optimization. Approach: The problem of data classification was studied as a problem of global, nonsmooth and nonconvex optimization; this approach consists of d escribing clusters for the given training sets. The data vectors are assigned to the closest cluster an d correspondingly to the set, which contains this cluster and an algorithm based on a derivative-free method is applied to the solution of this problem. Results: Proposed method had been tested on real-world data sets. Results of numerical experiments had been presented which demonstrate the effectiveness of the proposed algorithm. Conclusion: In this study we had studied a derivative-free optimiz ation approach to the classification. For optimization generalized pattern search method has been applied. The results of numerical experiments allowed us to say the proposed algorithms are effec tive for solving classification problems at least f or databases considered in this study.

Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure

We propose a Generalized Pattern Search ( GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method.

Generation of Optimal Artificial Neural Networks Using a Pattern Search Algorithm: Application to Approximation of Chemical Systems

A pattern search optimization method is applied to the generation of optimal artificial neural networks (ANNs). Optimization is performed using a mixed variable extension to the generalized pattern search method. This method offers the advantage that categorical variables, such as neural transfer functions and nodal connectivities, can be used as parameters in optimization. When used together with a surrogate, the resulting algorithm is highly efficient for expensive objective functions. Results demonstrate the effectiveness of this method in optimizing an ANN for the number of neurons, the type of transfer function, and the connectivity among neurons. The optimization method is applied to a chemistry approximation of practical relevance. In this application, temperature and a chemical source term are approximated as functions of two independent parameters using optimal ANNs. Comparison of the performance of optimal ANNs with conventional tabulation methods demonstrates equivalent accuracy by considerable savings in memory storage. The architecture of the optimal ANN for the approximation of the chemical source term consists of a fully connected feedforward network having four nonlinear hidden layers and 117 synaptic weights. An equivalent representation of the chemical source term using tabulation techniques would require a 500 x 500 grid point discretization of the parameter space.

Generalized pattern search methods for linearly equality constrained optimization problems

Torczon and several persons have designed pattern search methods for unconstrained optimization problem, bound constrained, and linearly constrained optimization problems. In this paper, we shall consider linear equality constrained problems as unconstrained ones using generalized pattern search algorithm, except for a feasible starting point.

A derivative-free filter method for solving nonlinear complementarity problems

In this work, nonlinear complementarity problems (NCPs) are considered. Some NCPs, which come from practice, have no derivatives or it is very difficult to obtain their derivatives. Derivative-free methods are hence considered. Generalized pattern search (GPS) method, as a kind of derivative-free method, plays a very significant role. We combine generalized pattern search method with filter method to attack NCPs because one can analyze the theory of generalized pattern search filter method without sufficient reduction conditions and avoid using of derivatives. Some interesting results are obtained in this work without sufficient reduction conditions. Furthermore, generalized pattern search filter method is efficient to some special problems.