Proposed Merit Function Research Articles

Local tolerance and quality evaluation for optical surfaces

The manufacture of high-precision surfaces is the foundation of building high-performance optical systems. For over 50 years, the tolerance for optical surfaces has been specified by the root-mean-square (rms) or peak-to-valley (PV) value over the entire surface geometry. However, different regions on optical surfaces do not contribute equally to image quality and, thus, can tolerate different levels of errors. A global tolerance described by a single or few parameters cannot precisely provide the manufacturing requirements of each region on the surface, which may result in unnecessary accuracy specifications for surfaces. Furthermore, the components with the same PV or rms figure errors can produce different imaging qualities; however, this difference cannot be distinguished by the conventional figure of merit. To address these problems, a framework that includes a local tolerance model and a quality merit function for optical surfaces is proposed. The local tolerance model can provide an accurate tolerance for each region on the surface so the targeted wave aberration requirements are met during components manufacturing. More importantly, the proposed merit function closely ties the surface figure error to imaging performance, e.g., the findings can explain that the component with lower geometric accuracy may produce better imaging quality. This framework provides new insights into optical design, manufacture, and metrology and especially paves the way for the manufacture of high-precision large-aperture systems.

Probabilistic Stone’s Blind Source Separation with application to channel estimation and multi-node identification in MIMO IoT green communication and multimedia systems

By the increasing growth of the Internet of Things (IoT) which provides interconnection and communications between electronic devices and corresponding sensors, a large volume of data is exchanged by multi-input multi-output (MIMO) telecommunication systems. In the case of IoT, reducing the data volume by removing the data redundancy results in more green communication by less power consumption for data transmission and less required storage memory. An approach to avoid the pilot data thus having less redundant data is using blind techniques. This research work presents an improvement to Stone’s blind source separation (BSS) precision, robustness, and computation load and its application to blind MIMO IoT interference channel estimation, multi-nodes IoT data detection, separation and identification in a MIMO-OFDM IoT network. Stone’s BSS is based on complexity conjecture indicating the independent sources have higher predictability than the mixtures. The presented improvement to Stone’s BSS is by a probabilistic modification to the short-term predictability merit by acquiring the prediction coefficients proportional to probability weights which follow a super Gaussian distribution assumption for sources. The probabilistic modification to Stone’s BSS (P-Stone) makes it maximally compatible with a pre-specified probability distribution model, and thereof the signal recovery is not only due to predictability maximization, but it is also inherent to increasing non-gaussianity which results in more independent recoveries, and less dependent on serial dependency of sources. Despite the Stone’s BSS, the proposed merit function does not need any long-term predictor; thus, it achieves around fifty times lower complexity load using just short-term predictors. The superiority of P-Stone to Stone BSS, AMUSE, and SOBI as well-known second-order techniques has been statistically evaluated and clarified through the experiments over MIMO-IoT networks of different combinations. As well, the comparative analysis over multimedia mixtures of music, speech, and images demonstrates its efficiency dominance.

Convex preference cone-based approach for many objective optimization problems

Many objective optimization problems have turned out to be a considerable challenge for evolutionary algorithms due to the difficulty of finding and visualizing high-dimensional Pareto frontiers. Fortunately, however, the task can be simplified whenever an interaction with a human decision maker is possible. Instead of finding the entire Pareto frontier, the evolutionary search can be guided to the parts of the space that are most relevant for the decision maker. In this paper, we propose an interactive method for solving many objective optimization problems. Drawing on the recent developments in multiple criteria decision making, we introduce an effective strategy for leveraging polyhedral preference cones within an evolutionary algorithm. The approach is mathematically motivated and is applicable to situations, where the user’s preferences can be assumed to follow an unknown quasi-concave and increasing utility function. In addition to considering the preference cones as a tool for eliminating non-preferred solution candidates, we also present how the the cones can be leveraged in approximating the directions of steepest ascent to guide the subsequent search done by the evolutionary algorithm through a proposed merit function. To evaluate the performance of the algorithm, we consider well known test problems as well as a practical facility location problem.

Design space exploration using Self-Organizing Map based adaptive sampling

In engineering design, a set of potentially competitive designs is conceived in the early part of the design process. The purpose of this research is to help such a process by investigating algorithm that enables approximate identification of a set of inputs of real variables that return desired responses from a function or a computer simulation. We explore sequential or adaptive sampling methods based on Self-Organizing Maps (SOM). The proposed method does not rely on parameterized distributions, and can sample from multi-modal and non-convex distributions. Furthermore, the proposed merit function provides infill characteristics by favoring sampling points that lay farther from existing points.The results indicate that multiple feasible solutions can be efficiently obtained by the new adaptive sampling algorithm. The iterative use of the SOM in density learning to identify feasible or good designs is our new contribution and it shows a very rapid increase in number of feasible solutions to total number of function evaluation ratio. Application examples to planing hull designs (such as in powerboats and seaplanes) indicate the merits of the feasible region approach to observe trends and design rules. Additionally, the well distributed sampling points of the proposed method played favorable effect in improving the prediction performance of a classification problem learned by Support Vector Machine.

A new merit function to accommodate high wind power penetration of WGRs (wind generating resources)

In this paper, we propose a new merit function to provide practical information to find optimal wind farm locations and projects based on spatial wind farm output prediction, including correlation with other wind farms. Our approach can predict what will happen when a new wind farm is added at various locations. Spatial power prediction of geographically distributed wind farms and their statistics through the proposed prediction model based on Kriging techniques will be presented. Using the proposed prediction model of wind generating resources, the performance of the spatial merit function in the context of the McCamey areas of ERCOT (Electric Reliability Council of Texas) will be provided. A new merit function through the prediction of wind farm outputs can play a key role to accommodate high wind power penetration from spatially distributed wind farms in power system planning models. In addition, we also propose the Kriged Wind Farm-SMES (Superconducting Magnetic Energy Storage System) hybrid model to enhance the higher wind power penetration levels using a new merit function. The proposed merit function requires only the existing data of wind generating resources around the candidate wind farm sites in order to reduce the time and costs for the installation of an anemometry tower as a practical method of wind resource assessment study compared to MCP (Measure-Correlate-Predict).

A new merit function for custom instruction selection under an area budget constraint

This paper presents a new merit function for custom instruction selection phase of the design flow of application-specific instruction-set processors (ASIPs) in the presence of an area budget constraint. In contrast to nearly all of the previously proposed approaches where ratio of the ASIP speed to layout area is used as a merit function to select the candidate custom instructions (CIs), we show that a merit function based on normalized cycle saving and area function can result in better CI selections in terms of the achievable speedup under a given area budget for both greedy and branch-and-bound techniques. The efficacy of the proposed approach is assessed by comparing the results of using the proposed and conventional merit functions for different benchmarks. The comparison points toward an average (maximum) speed enhancement of 3.65 % (27.4 %) for the proposed merit function compared to the conventional merit functions.

Considering the effect of process variations during the ISA extension design flow

In this paper, we present a technique for custom instruction (CI) extension considering process variations. The technique bridges the gap between the high level custom instruction extension and chip fabrication in nanotechnologies. In particular, instead of using the conventional Static Timing Analysis (STA), it utilizes Statistical Static Timing Analysis (SSTA). Therefore, the approach becomes probabilistic where the delay of each CI is modeled by a Probability Density Function (PDF). Using this probabilistic approach, different subsets of the CIs extension are identified to meet predefined constraints (identification phase) and eventually selected for realization to improve a given merit function (selection phase). In the identification phase, performance yield under both random and systematic variations is added as a constraint. Also, a pruning technique is proposed to decrease the runtime of the systematic variation modeling. The results show that the technique reduces the number of the CIs which need systematic variation modeling by about 24.6% for the cases studied in this work. In the selection phase, both greedy and branch-and-bound approaches are used. In the greedy approach, the conventional merit function based on the cycle saving and area is modified to include the performance yield. The results show the proposed merit function leads to about 3.2% increasing in the speedup. In the branch-and-bound method an effective pruning technique is described to reduce the runtime. The pruning technique is able to reduce the search space about 62%.

Automated method for optimization of electric field distributions and optical parameters in thin-film polarizers

An efficient method based on the modified needle optimization technique is proposed to design high-power laser thin-film polarizers. In order to minimize the influence of the standing-wave electric field on the laser-induced damage threshold of the polarizers, a crucial optimization parameter, the maximum electric field intensity in the high-refractive-index layers, is included in the proposed merit function. The electric field distribution and optical performance obtained by the proposed method are studied. Improved electric field and identical optical characteristics are observed in comparison with those of the designs obtained by optimizing the traditional merit function without a standing-wave electric field term and by the analytical synthesis method.

Phase mask selection in wavefront coding systems: A design approach

Abstract A method for optimizing the strength of a parametric phase mask for a wavefront coding imaging system is presented. The method is based on an optimization process that minimizes a proposed merit function. The goal is to achieve modulation transfer function invariance while quantitatively maintaining final image fidelity. A parametric filter that copes with the noise present in the captured images is used to obtain the final images, and this filter is optimized. The whole process results in optimum phase mask strength and optimal parameters for the restoration filter. The results for a particular optical system are presented and tested experimentally in the laboratory. The experimental results show good agreement with the simulations, indicating that the procedure is useful.

Phase retrieval of non-continuous fringe patterns by a genetic data reduction algorithm

In this work we focus on the possibilities of recovering the phase from a single fringe pattern that do not have a fringe order sequence or whose fringes are broken. The phase is obtained with a polynomial fitting method whose coefficients are calculated with a genetic algorithm technique that constrains the smoothness of the solutions of a merit function. It is explained how conjugate gradient methods fail in the solution of the proposed merit function. Experimental results are presented using discontinuous fringe patterns obtained from a grazing incidence interferometer while testing a polishing tool.

An alternative approach to spectrum base line estimation

We present a new form of merit function which measures agreement between a large number of data and the model function with a particular choice of parameters. We demonstrate the efficiency of the proposed merit function on the common problem of finding the base line of a spectrum. When the base line is expected to be a horizontal straight line, the use of minimization algorithms is not necessary, i.e. the solution is achieved in a small number of steps. We discuss the advantages of the proposed merit function in general, when explicit use of a minimization algorithm is necessary. The hardcopy text is accompanied by an electronic archive, stored on the SAE homepage at http://www1.elsevier.com/homepage/saa/sab/content/lower.htm. The archive contains fully functional demo program with tutorial, examples and Visual Basic source code of the key subroutine.

A New Merit Function and a Successive Quadratic Programming Algorithm for Variational Inequality Problems

Recently, various merit functions for variational inequality problems have been proposed and their properties have been studied. Unfortunately, these functions may not be easy to evaluate unless the constraints of the problem have a relatively simple structure. In this paper, a new merit function for variational inequality problems with general convex constraints is proposed. At each point, the proposed function is defined as an optimal value of a quadratic programming problem whose constraints consist of a linear approximation of the given nonlinear constraints. It is shown that the set of constrained minima of the proposed merit function coincides with the set of solutions to the original variational inequality problem. It is also shown that this function is directionally differentiable in all directions and, under suitable assumptions, any stationary point of the function over the constraint set actually solves the original variational inequality problem. Finally, a descent method for solving the variational inequality problem is proposed and its convergence is proved. The method is closely related to a successive quadratic programming method for solving nonlinear programming problems.