Hany L. Abdel-Malek

The ellipsoidal technique for design centering and region approximation

A technique for design centering and feasible region approximation that is based on generating a sequence of ellipsoids of decreasing volume and preserves the property of containing a bounded convex feasible region is introduced. The technique converges to an ellipsoid the center of which is the proposed design center. The ellipsoid matrix can be used to give what is called a preferable covariance matrix, assuming a multinormal distribution of parameters. This covariance matrix is preferred since it significantly increases the production yield for the feasible region under consideration. In addition, an ellipsoidal region approximation can be obtained by scaling the final ellipsoid, which allows an inexpensive yield estimate using the Monte Carlo method. Numerical and practical examples are considered. >

A boundary gradient search technique and its applications in design centering

A boundary gradient search technique is introduced. The technique generates a sequence of points on the boundary of the feasible region converging to a fixed point. The gradient of the boundary at this fixed point has a prespecified directional ratio. The boundary search technique is exploited in a modification of the ellipsoidal technique for design centering. This modification allows the use of double-sided ellipsoidal sections instead of single-sided ellipsoidal sections. It improves the speed of convergence of the ellipsoidal technique. Also, a computationally inexpensive technique of determining the gradient of the gain constraints is introduced. Practical examples are given to demonstrate the new technique.

Non-derivative design centering algorithm using trust region optimization and variance reduction

Fluctuations in manufactured integrated circuit parameters may dramatically reduce the parametric yield. Yield maximization can be formulated as an unconstrained optimization problem in nominal parameter values, which is known as design centering. The high expense of yield evaluations, the absence of any gradient information, and the presence of some numerical noise obstruct the use of the traditional derivative-based optimization methods. In this article, a novel design centering algorithm is presented, which consists of a non-derivative unconstrained optimizer coupled with a variance reduction estimator. The used optimizer combines a trust region mechanism with quadratic interpolation and provides efficient use of yield evaluations. The stratified sampling technique is used to develop a lower variance yield estimator that reduces the number of circuit simulations required to reach a desired accuracy level. Numerical and practical circuit examples are used to demonstrate the efficiency of the proposed algorithm with respect to other methods in the same field.

A new approach for the selection of test points for fault diagnosis

A new criterion and an efficient algorithm for the selection of test points in multifrequency fault diagnosis of linear circuits are presented. The proposed criterion exploits the biquadratic nature of the response in terms of circuit parameters instead of the common use of first order sensitivities. Accordingly it is capable of handling catastrophic faults. Employing the proposed criterion, an efficient two-phase fault diagnosis algorithm is introduced. The first phase selects a set of test points and characterizes the response for possible faults. This is done without the simulation of a preselected set of faults. The second phase efficiently isolates on-line actual faults using test points without any computation. A test example is presented to demonstrate the effectiveness of the proposed criterion and algorithm.

Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

A new technique for constructing a polyhedral approximation of the feasible region and finding the associated design center through a parallel-cuts ellipsoidal technique is presented. The linearizations of the feasible region boundary required to implement the parallel-cuts ellipsoidal technique are saved from one iteration to another in a non-redundant form. These linearizations are used in the construction of the parallel cuts as well as in the generation of an exterior polyhedral approximation of the feasible region at no additional cost. Numerical and practical examples are given to demonstrate the effectiveness of the new technique.

RF cavity design exploiting a new derivative-free trust region optimization approach

In this article, a novel derivative-free (DF) surrogate-based trust region optimization approach is proposed. In the proposed approach, quadratic surrogate models are constructed and successively updated. The generated surrogate model is then optimized instead of the underlined objective function over trust regions. Truncated conjugate gradients are employed to find the optimal point within each trust region. The approach constructs the initial quadratic surrogate model using few data points of order O(n), where n is the number of design variables. The proposed approach adopts weighted least squares fitting for updating the surrogate model instead of interpolation which is commonly used in DF optimization. This makes the approach more suitable for stochastic optimization and for functions subject to numerical error. The weights are assigned to give more emphasis to points close to the current center point. The accuracy and efficiency of the proposed approach are demonstrated by applying it to a set of classical bench-mark test problems. It is also employed to find the optimal design of RF cavity linear accelerator with a comparison analysis with a recent optimization technique.

Optimal Design of Computationally Expensive EM-Based Systems: A Surrogate-Based Approach

It is quite a challenge to find the optimal design of computationally expensive engineering systems in different areas such as electrical engineering, structural mechanics, fluid dynamics, and electromagnetic-based (EM-based) systems. The optimal design of such systems requires solving huge optimization problems involving a lot of expensive function evaluations. For example, in microwave circuit design, a function evaluation requires running a full-wave electromagnetic simulator which may exhaust hours of CPU time. The total computational overhead makes the optimization of these engineering systems practically prohibitive. Computationally cheap surrogates (Response Surfaces, Space Mapping, Kriging models, Neural Networks, etc.) offer a good solution of such problems. Throughout the optimization process, iteratively updated surrogates are employed to replace the computationally expensive function evaluations.

An exterior point algorithm for some linear complementarity problems with applications

An exterior point algorithm for positive definite (PD) and positive semidefinite (PSD) linear complementarity problems (LCPs) is introduced. The algorithm exploits the ellipsoid method to find a starting point in the case of positive definite linear complementarity problems (PDLCPs) and to check for the problem feasibility in case of positive semidefinite linear complementarity problems (PSDLCPs). The algorithm starts from a point on the boundary on which the complementarity condition is satisfied and generates a sequence of points on that same boundary. These points converge to the solution. The algorithm is modified to speed up the convergence for some PDLCPs and PSDLCPs that arise in certain mechanical models. A numerical example and a practical example in robotics are solved to test the algorithm.

A trust region approach with multivariate Padé model for optimal circuit design

ABSTRACT Since the optimization process requires a significant number of consecutive function evaluations, it is recommended to replace the function by an easily evaluated approximation model during the optimization process. The model suggested in this article is based on a multivariate Padé approximation. This model is constructed using data points of , where is the number of parameters. The model is updated over a sequence of trust regions. This model avoids the slow convergence of linear models of and has features of quadratic models that need interpolation data points of . The proposed approach is tested by applying it to several benchmark problems. Yield optimization using such a direct method is applied to some practical circuit examples. Minimax solution leads to a suitable initial point to carry out the yield optimization process. The yield is optimized by the proposed derivative-free method for active and passive filter examples.

Scheduling In High-Level Synthesis Using A Hybrid Constraint Logic Programming /Integer Programming Approach

Scheduling is a very important step in high-level synthesis. Integer programming (IP) approach was successfully used to solve the scheduling problem, but it suffers from its restricted mathematical model. Constraint logic programming (CLP) was also proposed as a solution technique. Although its flexible model, CLP suffers from high runtimes in large problems. The objective of this paper is to compare the two approaches and to present a hybrid approach that use complementary strengths of integer programming (IP) and constraint logic programming (CLP). These approaches were applied to fifth order elliptic wave filter to solve scheduling with module selection problem and the results show the effectiveness of the proposed hybrid approach