Two-step Optimization Technique Research Articles

Mesh-Based Two-Step Convex Optimization for Spacecraft Landing Trajectory Planning on Irregular Asteroid

The problem investigated in this paper is how to rapidly optimize a landing trajectory on an arbitrarily shaped asteroid, subject to practical constraints and a gravitational model suitable for irregular asteroids. The fundamental idea is to convert the nonlinearity involved in the gravitational field into an equivalent convex version and further generate the optimal trajectory using the two-step convex optimization technique to achieve efficient and robust computation. For a given mission area, the positional space is discretized as an exactly sufficient number of small tetrahedron meshes, within which the real gravitations are interpolated as the linear gravitational representation with nonconvex mesh tracking constraints. A solution space relaxation–penalization technique is proposed to convexify the mesh tracking constraints and keep the feasibility of the resulting convex optimization problem. A series of optimal active meshes are generated by solving this problem and transcribed as corresponding convex active meshing constraints, and further imposing them on the landing trajectory to construct the final convex optimization problem equaling to the original problem. The strength and correctness of this method are demonstrated from both perspectives of theoretical analyses and numerical simulations for landing on 4769 Castalia asteroid, with the comparisons of the state-of-the-art convex-optimization-based methods.

Design and development of auxetic structure using a two-step hybrid optimization technique

ABSTRACT Structures that possess Negative Poisson’s Ratio are known as auxetics. The successful application of auxetics requires appropriate design optimisation. Hence, in the present work, customised auxetics namely re-entrant honeycomb, missing rib and anti-tri-chiral has been developed using a two-step hybrid optimisation technique. The technique is based on the amalgamation of multiobjective optimisation and topological optimisation. A combined objective is set as maximum elastic moduli and minimum Poisson’s ratio with prioritised objective as maximum elastic moduli and mass as the response constraint. Initially, an optimal shape of a unit cell based on the Pareto front has been chosen considering the prioritised objective. Thereafter, finite element simulation was performed to evaluate the auxetic behaviour followed by topological optimisation using the density-based method. Using the developed model, the morphological and mechanical properties of the designed auxetics have been compared. The re-entrant honeycomb structure has been found as the most reliable auxetics with the highest elastic modulus and auxetic behaviour. The induced maximum stress in the array and structure of re-entrant honeycomb was 320.7 MPa and 168.77 MPa respectively. The results revealed that the developed methodology can be utilised as an advanced tool for achieving topologically optimised auxetics with desired properties.

Multi-View Polarimetric Scattering Cloud Tomography and Retrieval of Droplet Size

Tomography aims to recover a three-dimensional (3D) density map of a medium or an object. In medical imaging, it is extensively used for diagnostics via X-ray computed tomography (CT). We define and derive a tomography of cloud droplet distributions via passive remote sensing. We use multi-view polarimetric images to fit a 3D polarized radiative transfer (RT) forward model. Our motivation is 3D volumetric probing of vertically-developed convectively-driven clouds that are ill-served by current methods in operational passive remote sensing. Current techniques are based on strictly 1D RT modeling and applied to a single cloudy pixel, where cloud geometry defaults to that of a plane-parallel slab. Incident unpolarized sunlight, once scattered by cloud-droplets, changes its polarization state according to droplet size. Therefore, polarimetric measurements in the rainbow and glory angular regions can be used to infer the droplet size distribution. This work defines and derives a framework for a full 3D tomography of cloud droplets for both their mass concentration in space and their distribution across a range of sizes. This 3D retrieval of key microphysical properties is made tractable by our novel approach that involves a restructuring and differentiation of an open-source polarized 3D RT code to accommodate a special two-step optimization technique. Physically-realistic synthetic clouds are used to demonstrate the methodology with rigorous uncertainty quantification.

Super-Oscillatory Metalens at Terahertz for Enhanced Focusing with Reduced Side Lobes

In this paper, we design and numerically demonstrate an ultra-thin super-oscillatory metalens with a resolution below the diffraction limit. The zones of the lens are implemented using metasurface concepts with hexagonal unit cells. This way, the transparency and, hence, efficiency is optimized, compared to the conventional transparent–opaque zoning approach that introduces, inevitably, a high reflection in the opaque regions. Furthermore, a novel two-step optimization technique, based on evolutionary algorithms, is developed to reduce the side lobes and boost the intensity at the focus. After the design process, we demonstrate that the metalens is able to generate a focal spot of 0.46λ0 (1.4 times below the resolution limit) at the design focal length of 10λ0 with reduced side lobes (the side lobe level being approximately −11 dB). The metalens is optimized at 0.327 THz, and has been validated with numerical simulations.

Optimal Siting and Sizing of Multiple DG Units for the Enhancement of Voltage Profile and Loss Minimization in Transmission Systems Using Nature Inspired Algorithms.

Power grid becomes smarter nowadays along with technological development. The benefits of smart grid can be enhanced through the integration of renewable energy sources. In this paper, several studies have been made to reconfigure a conventional network into a smart grid. Amongst all the renewable sources, solar power takes the prominent position due to its availability in abundance. Proposed methodology presented in this paper is aimed at minimizing network power losses and at improving the voltage stability within the frame work of system operation and security constraints in a transmission system. Locations and capacities of DGs have a significant impact on the system losses in a transmission system. In this paper, combined nature inspired algorithms are presented for optimal location and sizing of DGs. This paper proposes a two-step optimization technique in order to integrate DG. In a first step, the best size of DG is determined through PSO metaheuristics and the results obtained through PSO is tested for reverse power flow by negative load approach to find possible bus locations. Then, optimal location is found by Loss Sensitivity Factor (LSF) and weak (WK) bus methods and the results are compared. In a second step, optimal sizing of DGs is determined by PSO, GSA, and hybrid PSOGSA algorithms. Apart from optimal sizing and siting of DGs, different scenarios with number of DGs (3, 4, and 5) and PQ capacities of DGs (P alone, Q alone, and P and Q both) are also analyzed and the results are analyzed in this paper. A detailed performance analysis is carried out on IEEE 30-bus system to demonstrate the effectiveness of the proposed methodology.

An Efficient VLSI Architecture of a Reconfigurable Pulse-Shaping FIR Interpolation

This brief proposes a two-step optimization technique for designing a reconfigurable VLSI architecture of an interpolation filter for multistandard digital up converter (DUC) to reduce the power and area consumption. The proposed technique initially reduces the number of multiplications per input sample and additions per input sample by 83% in comparison with individual implementation of each standard’s filter while designing a root-raised-cosine finite-impulse response filter for multistandard DUC for three different standards. In the next step, a 2-bit binary common subexpression (BCS)-based BCS elimination algorithm has been proposed to design an efficient constant multiplier, which is the basic element of any filter. This technique has succeeded in reducing the area and power usage by 41% and 38%, respectively, along with 36% improvement in operating frequency over a 3-bit BCS-based technique reported earlier, and can be considered more appropriate for designing the multistandard DUC.

Increased dipicolinic acid production with an enhanced spoVF operon in Bacillus subtilis and medium optimization.

Dipicolinic acid (DPA) is a multi-functional agent for cosmetics, antimicrobial products, detergents, and functional polymers. The aim of this study was to design a new method for producing DPA from renewable material. The Bacillus subtilis spoVF operon encodes enzymes for DPA synthase and the part of lysine biosynthetic pathway. However, DPA is only synthesized in the sporulation phase, so the productivity of DPA is low level. Here, we report that DPA synthase was expressed in vegetative cells, and DPA was produced in the culture medium by replacement of the spoVFA promoter with other highly expressed promoter in B. subtilis vegetative cells, such as spoVG promoter. DPA levels were increased in the culture medium of genetically modified strains. DPA productivity was significantly improved up to 29.14 g/L in 72 h culture by improving the medium composition using a two-step optimization technique with the Taguchi methodology.

A two-step optimization technique for functions placement, partitioning, and priority assignment in distributed systems

Modern development methodologies from the industry and the academia for complex real-time systems define a stage in which application functions are deployed onto an execution platform. The deployment consists of the placement of functions on a distributed network of nodes, the partitioning of functions in tasks and the scheduling of tasks and messages. None of the existing optimization techniques deal with the three stages of the deployment problem at the same time. In this paper, we present a staged approach towards the efficient deployment of real-time functions based on genetic algorithms and mixed integer linear programming techniques. Application to case studies shows the applicability of the method to industry-size systems and the quality of the obtained solutions when compared to the true optimum for small size examples.

Characterizing responses of translation-invariant neurons to natural stimuli: maximally informative invariant dimensions.

The human visual system is capable of recognizing complex objects even when their appearances change drastically under various viewing conditions. Especially in the higher cortical areas, the sensory neurons reflect such functional capacity in their selectivity for complex visual features and invariance to certain object transformations, such as image translation. Due to the strong nonlinearities necessary to achieve both the selectivity and invariance, characterizing and predicting the response patterns of these neurons represents a formidable computational challenge. A related problem is that such neurons are poorly driven by randomized inputs, such as white noise, and respond strongly only to stimuli with complex high-order correlations, such as natural stimuli. Here we describe a novel two-step optimization technique that can characterize both the shape selectivity and the range and coarseness of position invariance from neural responses to natural stimuli. One step in the optimization is finding the template as the maximally informative dimension given the estimated spatial location where the response could have been triggered within each image. The estimates of the locations that triggered the response are updated in the next step. Under the assumption of a monotonic relationship between the firing rate and stimulus projections on the template at a given position, the most likely location is the one that has the largest projection on the estimate of the template. The algorithm shows quick convergence during optimization, and the estimation results are reliable even in the regime of small signal-to-noise ratios. When we apply the algorithm to responses of complex cells in the primary visual cortex (V1) to natural movies, we find that responses of the majority of cells were significantly better described by translation-invariant models based on one template compared with position-specific models with several relevant features.

Video Coding With Rate-Distortion Optimized Transform

Block-based discrete cosine transform (DCT) has been successfully adopted into several international image/video coding standards, e.g., MPEG-2, H.264/AVC, as it can achieve a good tradeoff between performance and complexity. Although DCT theoretically approximates the optimum Karhunen-Loeve transform under first-order Markov conditions, one fixed set of transform basis functions (TBF) cannot handle all the cases efficiently due to the non-stationary nature of video contents. To further improve the performance of block-based transform coding, in this paper, we present the design of rate-distortion optimized transform (RDOT) which contributes to both intraframe and interframe coding. The most important property which makes a difference between RDOT and the conventional DCT is that, in the proposed method, transform is implemented with multiple TBF candidates which are obtained from off-line training. With this feature, for coding each residual block, the encoder is capable to select the optimal set of TBF in terms of rate-distortion performance, and better energy compaction is achieved in the transform domain. To obtain an optimum group of candidate TBF, we have developed a two-step iterative optimization technique for the off-line training, with which the TBF candidates are refined at each iteration until the training process becomes converged. Moreover, analysis on the optimal group of candidate TBF is also presented in this paper, with a detailed description of a practical implementation for the proposed algorithm on the latest VCEG key technical area software platform. Extensive experimental results show that, compared with the conventional DCT-based transform scheme adopted into the state-of-the-art H.264/AVC video coding standard, significant improvement of coding performance has been achieved for both intraframe and interframe coding with our proposed method.

Pose Space Surface Manipulation

Example-based mesh deformation techniques produce natural and realistic shapes by learning the space of deformations from examples. However, skeleton-based methods cannot manipulate a global mesh structure naturally, whereas the mesh-based approaches based on a translational control do not allow the user to edit a local mesh structure intuitively. This paper presents an example-driven mesh editing framework that achieves both global and local pose manipulations. The proposed system is built with a surface deformation method based on a two-step linear optimization technique and achieves direct manipulations of a model surface using translational and rotational controls. With the translational control, the user can create a model in natural poses easily. The rotational control can adjust the local pose intuitively by bending and twisting. We encode example deformations with a rotation-invariant mesh representation which handles large rotations in examples. To incorporate example deformations, we infer a pose from the handle translations/rotations and perform pose space interpolation, thereby avoiding involved nonlinear optimization. With the two-step linear approach combined with the proposed multiresolution deformation method, we can edit models at interactive rates without losing important deformation effects such as muscle bulging.

A Two-Step Optimization Method for Improving Multiple Brain Lesion Treatments with Robotic Radiosurgery

Planning robotic radiosurgery treatments for multiple (n > 3) metastatic brain lesions is challenging due to the need of satisfying a large number of dose-volume constraints and the requirement of prescribing different dose levels to individual targets. In this study, we developed a sequential two-step optimization technique to improve the planning quality of such treatments. In contrast to the conventional approach of where all targets are simultaneously planned, we have developed a two-step optimization method. In this method, the first step was to create treatment plans for individual targets. In the second step, the 3D dose matrices associated with each plan were exported to Dicom-RT digital files and subsequently optimized. For the optimization, a singular-value-decomposition (SVD) algorithm was implemented to minimize the dose interferences among different targets. Finally, we compared the optimized treatment plans with the treatment plans created using the conventional method to determine the effectiveness of the new method. Large improvements in target dose distributions as well as normal brain sparing were found for the two-step optimization treatment plans as compared with the conventional treatment plans. The two-step optimization significantly lowered the volume of normal brain receiving relatively low doses. For example, the normal brain volume receiving 12-Gy was reduced by averaged 42% (range 34%-47%) with the two-step optimization. Such improvements generally enlarged with increasing number of targets being treated regardless of target sizes. Of note, normal brain dose was found to increase non-linearly with increasing number of targets. In summary, a two-step optimization technique is demonstrated to significantly improve the treatment plan quality as well as reduce the planning effort for multi-target robotic radiosurgery.

Parameter Identification of Arc Furnace Based on Stochastic Nature of Arc Length Using Two-Step Optimization Technique

Recent studies on the effect of arc furnaces in a power system lack accurate predicting voltage waveform of an arc furnace. This is mainly due to the random nature of the arc length. In this paper, a novel two-step optimization technique is presented to identify the arc furnace parameters considering the stochastic nature of the arc length. The proposed method is based on a genetic algorithm (GA) which adopts the arc current and voltage waveforms to estimate parameters of the nonlinear time-varying model of an electric arc furnace. Simulation results are compared with data obtained from two real arc furnace plants. Analyses show that the proposed method is profitable to identify accurate values of the arc furnace parameters which incorporate the stochastic nature of the arc length.

SU-GG-T-510: A Two-Step Optimization Technique for Planning Multi-Target Treatments with Robotic Radiotherapy

Purpose: Planning roboticradiosurgery for patients with 3 or more metastatic brain lesions is due to the need for a large number of constraints and the requirement of prescribing different doses to separate targets. A two‐step optimization technique was developed to improve the plan quality of such treatments.Method and Materials: First, separate treatment plans were developed for individual targets via setting nominal doses to each target disregarding contributions from other lesions. Then the 3D dose matrix associated with each target was exported and a singular‐value‐decomposition algorithm was applied to balance the background dose changes as well as dose interferences among targets via adjusting relative weightings among the dose matrices. Comparisons were carried out for such approach versus a planning‐for‐all approach implemented on the latest commercial system. Results: Significant improvements were found in the target volume coverage with the new technique as compared with the existing plan‐for‐all techniques due to the capability to select individualized isodose levels for each target. Additionally, improvement was particularly noted for low‐level peripheral normal brain sparing. On average, the volume of the normal brain receiving more than 4‐Gy was reduced by 13% with the new technique for the studied cases. The improvement was especially notable when a high number (n>5) of targets are considered. Conclusion: A two‐step optimization technique has been demonstrated to improve treatment planning quality as well as the flexibility of dose prescription for multi‐target treatment planning for roboticradiosurgery.

Neural Network Algorithm for Designing FIR Filters Utilizing Frequency-Response Masking Technique

This paper presents a new joint optimization method for the design of sharp linear-phase finite-impulse response (FIR) digital filters which are synthesized by using basic and multistage frequency-response-masking (FRM) techniques. The method is based on a batch back-propagation neural network algorithm with a variable learning rate mode. We propose the following two-step optimization technique in order to reduce the complexity. At the first step, an initial FRM filter is designed by alternately optimizing the subfilters. At the second step, this solution is then used as a start-up solution to further optimization. The further optimization problem is highly nonlinear with respect to the coefficients of all the subfilters. Therefore, it is decomposed into several linear neural network optimization problems. Some examples from the literature are given, and the results show that the proposed algorithm can design better FRM filters than several existing methods.

A method for planar development of 3D surfaces in shoe pattern design

This paper presents a new method for planar development of the 3D surfaces of a shoe upper. The 3D surface is first faceted into triangular elements and then roughly laid down on a 2D plane. Next, the nodal points of elements are repositioned by a refinement technique that minimizes the geometric errors. Even after elements have been refined by minimizing geometric errors, the resulting 2D shape still has some strain energy that needs to be reduced by a relaxation process. Hence, these elements are then used as an initial guess for further optimization during which the finite element inverse method is used to minimize the total strain energy. In fact, the two-step optimization technique not only can prevent the divergence of solutions (e.g., interferences between elements) but also yields a more reliable result. The method has been implemented as a module of the shoe design system by which a prototype shoe can be designed and manufactured more precisely and quickly.

A neural network approach to FIR filter design using frequency-response masking technique

This paper presents a new optimization method for the design of various frequency-response-masking (FRM)-based linear-phase finite-impulse response (FIR) digital filters. The method is based on a batch back-propagation neural network algorithm (NNA), which is taken as a variable learning rate mode. In order to reduce the complexity, the following two-step optimization technique is proposed. At the first step, an initial FRM filter is designed by alternately optimizing the sub-filters. This solution is then used as a start-up solution for further optimization. At the second step, the coefficients of overall sub-filters are optimized simultaneously by the NNA. Algorithm details for the design of basic and multistage FRM filters are presented to show that the proposed approach offers a unified design framework for a variety of FRM filters. Some examples taken from the literatures are included and the results show that the proposed algorithm can design better FRM filters than several existing methods.

OPTIMIZATION OF FREQUENCY-RESPONSE MASKING BASED FIR FILTERS

A very efficient technique to drastically reduce the number of multipliers and adders in implementing linear-phase finite-impulse response (FIR) digital filters in applications demanding a narrow transition band is to use the frequency-response masking (FRM) approach originally introduced by Lim. The arithmetic complexity can be even further reduced using a common filter part for constructing the masking filters originally proposed by Lim and Lian. A drawback in the above-mentioned original FRM synthesis techniques is that the subfilters in the overall implementations are separately designed. In order to further reduce the arithmetic complexity in these two FRM approaches, the following two-step optimization technique is proposed for simultaneously optimizing the subfilters. At the first step, a good suboptimal solution is found by using a simple iterative algorithm. At the second step, this solution is then used as a start-up solution for further optimization being carried out by using an efficient unconstrained nonlinear optimization algorithm. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized filter are less than 80% compared with those of the FRM filter obtained using the original FRM design schemes in the case where the masking filters are separately implemented. If a common filter part is used for realizing the masking filters, then an additional reduction of more than 10% is achieved compared with the optimized design with separately implemented masking filters.

Thermal dose optimization for ultrasound tissue ablation

A formal and general thermal dose optimisation method is developed and tested. Prior methods require brute force searches wherein the temperature and dose distributions must be computed at each iteration by solving the bioheat transfer equation (BHTE) numerically. This is extremely time-consuming and can only be used to compare a few prespecified strategies instead of obtaining a more general optimal result. With the method developed here, dose distribution can be calculated without solving the BHTE numerically. This can be done in a matter of a few minutes compared with many hours. Moreover, general thermal dose optimization can now be performed to find the optimal strength and location of each focus so that an optimal dose distribution is obtained while the specified constraint is satisfied. The algorithm developed here consists of a closed-form solution to the BHTE, a Gaussian model for parameterizing a temperature distribution created by a power deposition pattern, and a two-step optimization technique for obtaining the model parameters that optimize the thermal dose distribution. Several examples are given to demonstrate the effectiveness of the algorithm and its robustness under different initial conditions and under assumptions of different sizes of the target region and different numbers of foci. The algorithm developed here provides an efficient and effective tool for treatment planning in ultrasound tissue ablation.

An optimal cam profile design considering dynamic characteristics of a cam-valve system

In this work, an optimal cam profile design method for an OHV-type cam-valve train is studied considering the dynamic characteristics of the valve system. When designing a cam profile for an internal combustion engine, it is desirable to make the valve lift area be as large as possible and the valve peak acceleration and seating velocity be as low as those can be within the cam-event angle. But, as we know, those features conflict with one another. An optimal design must strike a compromise between the two. Another important factor in valve train design is avoiding abnormal valve motions such as jump and bounce. It is known that jump and bounce are closely related to valve train dynamic characteristics. In this paper, a two-step optimization technique to design an optimal cam profile is proposed. In the first step, an attempt was made to maximize valve lift area without causing abnormal valve motions while satisfying all the given constraints such as cam-event angle, maximum valve acceleration, and cam displacements at both ends of the cam-event angle. Then, in the second step, minor modifications of the cam developed in the first step were made in order to reduce the cam acceleration while maintaining the maximized valve lift area and satisfying constrains obtained in the first step. In order to prove the effectiveness of the optimization method, the valve motion driven by the optimized cam was not only simulated with a four degree of freedom model but was also tested experimentally. It was found that the measured valve motions agree quite well with the simulation results. Comparing the valve motions of the optimized cam with those of the original cam, it was found that the optimized cam can increase the valve-lift area by 8.6 percent while reducing the peak cam acceleration by 28.7 percent. Also, it was noted that the optimized cam increases the cam-valve train operating speed at which jump and bounce occur.