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Pattern Search Methods for Linearly Constrained Minimization
We extend pattern search methods to linearly constrained minimization. We develop a general class of feasible point pattern search algorithms and prove global convergence to a Karush-Kuhn-Tucker point. As in the case of unconstrained minimization, pattern search methods for linearly constrained problems accomplish this without explicit recourse to the gradient or the directional derivative. Key to the analysis of the algorithms is the way in which the local search patterns conform to the geometry of the boundary of the feasible region.
On the Local Convergence of Pattern Search
We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a traditional stopping criterion for pattern search methods. Using this measure of first-order stationarity, we analyze the behavior of pattern search in the neighborhood of an isolated local minimizer. We show that a recognizable subsequence converges r-linearly to the minimizer.
Pattern Search Algorithms for Bound Constrained Minimization
We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexibility present in pattern search methods for unconstrained problems. We prove global convergence despite the fact that pattern search methods do not have explicit information concerning the gradient and its projection onto the feasible region and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.
A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds
We give a pattern search adaptation of an augmented Lagrangian method due to Conn, Gould, and Toint. The algorithm proceeds by successive bound constrained minimization of an augmented Lagrangian. In the pattern search adaptation we solve this subproblem approximately using a bound constrained pattern search method. The stopping criterion proposed by Conn, Gould, and Toint for the solution of this subproblem requires explicit knowledge of derivatives. Such information is presumed absent in pattern search methods; however, we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm. In this way we proceed by successive, inexact, bound constrained minimization without knowing exactly how inexact the minimization is. So far as we know, this is the first provably convergent direct search method for general nonlinear programming.
Pattern Search in Multi-structure Data: A Framework for the Next-Generation Evidence-based Medicine
With the advent of personalized and evidence-based medicine, the need for a framework to analyze/interpret quantitative measurements (blood work, toxicology, etc.) with qualitative descriptions (specialist reports after reading images, bio-medical knowledge-bases) to predict diagnostic risks is fast emerging. Addressing this need, we pose and address the following questions (i) How can we jointly analyze both qualitative and quantitative data ? (ii) Is the fusion of multi-structure data expected to provide better insights than either of them individually ? We present experiments on two bio-medical data sets - mammography and traumatic brain studies to demonstrate architectures and tools for evidence-pattern search.
Google search patterns monitoring the daily health impact of heatwaves in England: How do the findings compare to established syndromic surveillance systems from 2013 to 2017?
Highlights: • Heat health-related Google search term frequency increased during heatwave events. • Google data correlated well with validated syndromic heat health indicators. • A similar timeliness was seen between daily Google and syndromic data in England. • Google search data could be of benefit in monitoring heat-related morbidity. One of the implications of climate change is a predicted increase in frequent and severe heatwaves. The impact of heatwaves on the health of the population is captured through real-time syndromic healthcare surveillance systems monitored daily in England during the summer months. Internet search data could potentially provide improved timeliness and help to assess the wider population health impact of heat by capturing a population sub-group who are symptomatic but do not seek healthcare. A retrospective observational study was carried out from June 2013 to September 2017 in England to compare daily trends in validated syndromic surveillance heat-related morbidity indicators against symptom-based heatwave related Google search terms. The degree of correlation was determined with Spearman correlation coefficients and lag assessment was carried out to determine timeliness. Daily increases in frequency in Google search terms during heatwave events correlated well with validated syndromic indicators. Correlation coefficients between search term frequency and syndromic indicators from 2013 to 2017 were highest with the telehealth service NHS 111 (range of 0.684–0.900 by search term). Lag analysis revealed a similar timeliness between the data sources, suggesting Google data did not provide a delayed or earlier signal in the context of England's syndromic surveillance systems. This work highlights the potential benefits for countries which lack established public health surveillance systems to monitor heat-related morbidity and the use of internet search data to assess the wider population health impact of exposure to heat.
Searching for patterns in remote sensing image databases using neural networks
We have investigated a method, based on a successful neural network multispectral image classification system, of searching for single patterns in remote sensing databases. While defining the pattern to search for and the feature to be used for that search (spectral, spatial, temporal, etc.) is challenging, a more difficult task is selecting competing patterns to train against the desired pattern. Schemes for competing pattern selection, including random selection and human interpreted selection, are discussed in the context of an example detection of dense urban areas in Landsat Thematic Mapper imagery. When applying the search to multiple images, a simple normalization method can alleviate the problem of inconsistent image calibration. Another potential problem, that of highly compressed data, was found to have a minimal effect on the ability to detect the desired pattern. The neural network algorithm has been implemented using the PVM (Parallel Virtual Machine) library and nearly-optimal speedups have been obtained that help alleviate the long process of searching through imagery.
SU-E-T-295: Simultaneous Beam Sampling and Aperture Shape Optimization for Station Parameter Optimized Radiation Therapy (SPORT)
Purpose: Station Parameter Optimized Radiation Therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital LINACs, in which the station parameters of a delivery system, (such as aperture shape and weight, couch position/angle, gantry/collimator angle) are optimized altogether. SPORT promises to deliver unprecedented radiation dose distributions efficiently, yet there does not exist any optimization algorithm to implement it. The purpose of this work is to propose an optimization algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: We build a mathematical model whose variables are beam angles (including non-coplanar and/or even nonisocentric beams) and aperture shapes. To solve the resulting large scale optimization problem, we devise an exact, convergent and fast optimization algorithm by integrating three advanced optimization techniques named column generation, gradient method, and pattern search. Column generation is used to find a good set of aperture shapes as an initial solution by adding apertures sequentially. Then we apply the gradient method to iteratively improve the current solution by reshaping the aperture shapes and updating the beam angles toward the gradient. Algorithm continues by pattern search method to explore the part of the search space that cannot be reached by the gradient method. Results: The proposed technique is applied to a series of patient cases and significantly improves the plan quality. In a head-and-neck case, for example, the left parotid gland mean-dose, brainstem max-dose, spinal cord max-dose, and mandible mean-dose are reduced by 10%, 7%, 24% and 12% respectively, compared to the conventional VMAT plan while maintaining the same PTV coverage. Conclusion: Combined use of column generation, gradient search and pattern search algorithms provide an effective way to optimize simultaneously the large collection of station parameters and significantly improves quality of resultant treatment plans as compared with conventional VMAT or IMRT treatments.
Design of the VISITOR Tool: A Versatile ImpulSive Interplanetary Trajectory OptimizeR
The design of trajectories for interplanetary missions represents one of the most complex and important problems to solve during conceptual space mission design. To facilitate conceptual mission sizing activities, it is essential to obtain sufficiently accurate trajectories in a fast and repeatable manner. To this end, the VISITOR tool was developed. This tool modularly augments a patched conic MGA-1DSM model with a mass model, launch window analysis, and the ability to simulate more realistic arrival and departure operations. This was implemented in MATLAB, exploiting the built-in optimization tools and vector analysis routines. The chosen optimization strategy uses a grid search and pattern search, an iterative variable grid method. A genetic algorithm can be selectively used to improve search space pruning, at the cost of losing the repeatability of the results and increased computation time. The tool was validated against seven flown missions: the average total mission (Delta)V offset from the nominal trajectory was 9.1%, which was reduced to 7.3% when using the genetic algorithm at the cost of an increase in computation time by a factor 5.7. It was found that VISITOR was well-suited for the conceptual design of interplanetary trajectories, while also facilitating future improvements due to its modular structure.
Simultaneous beam sampling and aperture shape optimization for SPORT
Purpose: Station parameter optimized radiation therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital linear accelerators, in which the station parameters of a delivery system, such as aperture shape and weight, couch position/angle, gantry/collimator angle, can be optimized simultaneously. SPORT promises to deliver remarkable radiation dose distributions in an efficient manner, yet there exists no optimization algorithm for its implementation. The purpose of this work is to develop an algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: The authors build a mathematical model with the fundamental station point parameters as the decision variables. To solve the resulting large-scale optimization problem, the authors devise an effective algorithm by integrating three advanced optimization techniques: column generation, subgradient method, and pattern search. Column generation adds the most beneficial stations sequentially until the plan quality improvement saturates and provides a good starting point for the subsequent optimization. It also adds the new stations during the algorithm if beneficial. For each update resulted from column generation, the subgradient method improves the selected stations locally by reshaping the apertures and updating the beam angles toward a descent subgradient direction. The algorithm continues to improve the selected stations locally and globally by a pattern search algorithm to explore the part of search space not reachable by the subgradient method. By combining these three techniques together, all plausible combinations of station parameters are searched efficiently to yield the optimal solution. Results: A SPORT optimization framework with seamlessly integration of three complementary algorithms, column generation, subgradient method, and pattern search, was established. The proposed technique was applied to two previously treated clinical cases: a head and neck and a prostate case. It significantly improved the target conformality and at the same time critical structure sparing compared with conventional intensity modulated radiation therapy (IMRT). In the head and neck case, for example, the average PTV coverage D99% for two PTVs, cord and brainstem max doses, and right parotid gland mean dose were improved, respectively, by about 7%, 37%, 12%, and 16%. Conclusions: The proposed method automatically determines the number of the stations required to generate a satisfactory plan and optimizes simultaneously the involved station parameters, leading to improved quality of the resultant treatment plans as compared with the conventional IMRT plans.
Search for patterns by combining cosmic-ray energy and arrival directions at the Pierre Auger Observatory
Energy-dependent patterns in the arrival directions of cosmic rays are searched for using data of the Pierre Auger Observatory. We investigate local regions around the highest-energy cosmic rays with E ≥ 6×10 19 eV by analyzing cosmic rays with energies above E ≥ 5×10 18 eV arriving within an angular separation of approximately 15°. We characterize the energy distributions inside these regions by two independent methods, one searching for angular dependence of energy-energy correlations and one searching for collimation of energy along the local system of principal axes of the energy distribution. No significant patterns are found with this analysis. As a result, the comparison of these measurements with astrophysical scenarios can therefore be used to obtain constraints on related model parameters such as strength of cosmic-ray deflection and density of point sources.
Optimization technique for problems with an inequality constraint
General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.
Temporal Stability of Visual Search-Driven Biometrics
Previously, we have shown the potential of using an individual s visual search pattern as a possible biometric. That study focused on viewing images displaying dot-patterns with different spatial relationships to determine which pattern can be more effective in establishing the identity of an individual. In this follow-up study we investigated the temporal stability of this biometric. We performed an experiment with 16 individuals asked to search for a predetermined feature of a random-dot pattern as we tracked their eye movements. Each participant completed four testing sessions consisting of two dot patterns repeated twice. One dot pattern displayed concentric circles shifted to the left or right side of the screen overlaid with visual noise, and participants were asked which side the circles were centered on. The second dot-pattern displayed a number of circles (between 0 and 4) scattered on the screen overlaid with visual noise, and participants were asked how many circles they could identify. Each session contained 5 untracked tutorial questions and 50 tracked test questions (200 total tracked questions per participant). To create each participant s "fingerprint", we constructed a Hidden Markov Model (HMM) from the gaze data representing the underlying visual search and cognitive process. The accuracy of the derived HMM models was evaluated using cross-validation for various time-dependent train-test conditions. Subject identification accuracy ranged from 17.6% to 41.8% for all conditions, which is significantly higher than random guessing (1/16 = 6.25%). The results suggest that visual search pattern is a promising, fairly stable personalized fingerprint of perceptual organization.
Using Eye Tracking to Elucidate the Mechanisms Underlying Stimulation-Enhanced Visual Target Detection
Transcranial direct current stimulation (tDCS) is a noninvasive form of brain stimulation that involves passing a weak electrical current between electrodes on the scalp to modulate underlying neural tissue. TDCS has been shown to modulate cognition in a variety of domains, including memory, attention, and visual processing. Prior work from our laboratory has shown positive effects of tDCS on learning to detect target objects hidden in complex naturalistic visual scenes and learn rules for categorizing images, though the mechanism for these benefits remains unknown. One possibility is that tDCS optimizes visual search by modulating visual attention or via the reduction in search errors. One method of quantifying visual attention is to use eye tracking to record search patterns to determine if and how visual search is adjusted under verum stimulation conditions. Eye tracking data allows classification of errors into error types, including sampling errors (failing to look in the relevant region), recognition errors (looking at the critical portion of a scene, but failing to recognize it as such as evidenced by visual fixation), and decision-making errors (fixating on the relevant portion of a scene, but making the wrong determination). Our results indicate that the benefit tDCS confers on visual search for targets stems from the reduction in decision-making errors when targets are present (Cohen’s d = 0.86). Also reported is a replication of previous findings showing a tDCS-dependent improvement in learning this task, learning score (Cohen’s d = 0.88); d’ (Cohen’s d = 1.00). This provides support for moving tDCS into the application space by pairing it with analysts who are concerned with the type of search error that is corrected via stimulation.
GrammarViz 3.0: Interactive Discovery of Variable-Length Time Series Patterns
The problems of recurrent and anomalous pattern discovery in time series, e.g., motifs and discords, respectively, have received a lot of attention from researchers in the past decade. However, since the pattern search space is usually intractable, most existing detection algorithms require that the patterns have discriminative characteristics and have its length known in advance and provided as input, which is an unreasonable requirement for many real-world problems. In addition, patterns of similar structure, but of different lengths may co-exist in a time series. In order to address these issues, we have developed algorithms for variable-length time series pattern discovery that are based on symbolic discretization and grammar inference—two techniques whose combination enables the structured reduction of the search space and discovery of the candidate patterns in linear time. In this work, we present GrammarViz 3.0—a software package that provides implementations of proposed algorithms and graphical user interface for interactive variable-length time series pattern discovery. The current version of the software provides an alternative grammar inference algorithm that improves the time series motif discovery workflow, and introduces an experimental procedure for automated discretization parameter selection that builds upon the minimum cardinality maximum cover principle and aids the time series recurrent and anomalous pattern discovery.
Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis
Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.
Efficient Algorithm for Rectangular Spiral Search
An algorithm generates grid coordinates for a computationally efficient spiral search pattern covering an uncertain rectangular area spanned by a coordinate grid. The algorithm does not require that the grid be fixed; the algorithm can search indefinitely, expanding the grid and spiral, as needed, until the target of the search is found. The algorithm also does not require memory of coordinates of previous points on the spiral to generate the current point on the spiral.