Load estimation data using direct search method based on pattern search.

Accurately estimating load is essential for effective electric distribution planning, assets management, precise power flow predictions, accurate power losses calculations, and efficient integration of distributed energy resources. This work describes a dataset that was generated using Matlab and OpenDSS to produce several simulations in which load estimation is performed using a direct search method called pattern search. These simulations were conducted on three typical distribution feeders (IEEE 13-bus, 37-bus, and 123-bus) that support studies in distribution planning, assets management, power flow predictions, power losses calculations, and distributed resource integration. The dataset includes individual demand profiles of residential, commercial, and industrial consumers specified for the three distribution feeders, comprising 96 distinct scenarios. An optimization method was developed to obtain the dataset, which employs the pattern search technique to estimate loads through the optimization of objective functions and specified constraints. The load estimation quality was assessed for all three feeders, utilizing estimation quality indices proposed by the authors. These indices evaluated both the initial and proposed load estimation methods across the developed scenarios. Furthermore, the data provided in this article can be utilized for comparison with future load estimation studies, particularly regarding the quality of the method's results.

Estimating linear mixed effect models with non-normal random effects through saddlepoint approximation and its application in retail pricing analytics.

Linear Mixed Effects (LME) models are powerful statistical tools that have been employed in many different real-world applications such as retail data analytics, marketing measurement, and medical research. Statistical inference is often conducted via maximum likelihood estimation with Normality assumptions on the random effects. Nevertheless, for many applications in the retail industry, it is often necessary to consider non-Normal distributions on the random effects when considering the unknown parameters' business interpretations. Motivated by this need, a linear mixed effects model with possibly non-Normal distribution is studied in this research. We propose a general estimating framework based on a saddlepoint approximation (SA) of the probability density function of the dependent variable, which leads to constrained nonlinear optimization problems. The classical LME model with Normality assumption can then be viewed as a special case under the proposed general SA framework. Compared with the existing approach, the proposed method enhances the real-world interpretability of the estimates with satisfactory model fits.

Optimizing quasi-dynamic wireless charging for urban electric buses: A two-scenario mathematical framework with grid and PV-battery systems.

This paper presents a mathematical optimization framework for the strategic placement of quasi-dynamic wireless charging (QWC) stations within road networks to address the charging needs of battery electric buses (BEBs). This study evaluates two scenarios for powering the buses. In the first scenario, a grid-connected system is considered. The optimization aims to minimize annual costs related to capital, operation, and energy losses of the electric bus fleet. This involves determining the optimal locations for QWC stations, the length of power transmitters, and the corresponding battery capacities for the BEBs. Using MATLAB-based optimization tools Casadi and Yalmip, with solvers Bonmin and Fmincon, the optimal configuration includes a 13 kWh battery capacity and a 300 m power transmitter distributed across five bus stop areas. The second scenario employs a chance-constrained optimization approach for an isolated solar photovoltaic (PV) and battery energy storage system (BESS). This system is designed to reliably meet the BEBs' energy requirements throughout the day, considering different seasonal data (winter, summer, all seasons/year-round). The optimization results for the PV and BESS capacities vary with the seasons: 394.247 kW and 2012.6 kWh using summer data, 1762.1 kW and 2738.2 kWh using winter data, and 1610.8 kW and 2741.9 kWh using year-round data. Additionally, the paper examines the impact of varying bus fleet sizes on the optimal battery size and power transmitter combination using a real-world example of the bus route between Khalifa City and Abu Dhabi Downtown in the UAE. The findings suggest that larger batteries with fewer or no charging stations are more economical for smaller fleets. Conversely, as the fleet size increases, a combination of smaller battery sizes and a greater number (and length) of QWC (power transmitters) becomes more cost-effective. This research offers significant insights into the efficient deployment of QWC stations and the integration of renewable energy and energy storage for sustainable urban electric bus networks. The proposed optimization models provide a systematic approach to designing and operating charging infrastructure, contributing to sustainable urban transportation systems. Moreover, the study highlights the influence of seasonal data on PV system sizing and costs.

Cause-specific hazard Cox models with partly interval censoring - Penalized likelihood estimation using Gaussian quadrature.

The cause-specific hazard Cox model is widely used in analyzing competing risks survival data, and the partial likelihood method is a standard approach when survival times contain only right censoring. In practice, however, interval-censored survival times often arise, and this means the partial likelihood method is not directly applicable. Two common remedies in practice are (i) to replace each censoring interval with a single value, such as the middle point; or (ii) to redefine the event of interest, such as the time to diagnosis instead of the time to recurrence of a disease. However, the mid-point approach can cause biased parameter estimates. In this article, we develop a penalized likelihood approach to fit semi-parametric cause-specific hazard Cox models, and this method is general enough to allow left, right, and interval censoring times. Penalty functions are used to regularize the baseline hazard estimates and also to make these estimates less affected by the number and location of knots used for the estimates. We will provide asymptotic properties for the estimated parameters. A simulation study is designed to compare our method with the mid-point partial likelihood approach. We apply our method to the Aspirin in Reducing Events in the Elderly (ASPREE) study, illustrating an application of our proposed method.

Performance analyses of weighted superposition attraction-repulsion algorithms in solving difficult optimization problems.

The purpose of this paper is to test the performance of the recently proposed weighted superposition attraction-repulsion algorithms (WSA and WSAR) on unconstrained continuous optimization test problems and constrained optimization problems. WSAR is a successor of weighted superposition attraction algorithm (WSA). WSAR is established upon the superposition principle from physics and mimics attractive and repulsive movements of solution agents (vectors). Differently from the WSA, WSAR also considers repulsive movements with updated solution move equations. WSAR requires very few algorithm-specific parameters to be set and has good convergence and searching capability. Through extensive computational tests on many benchmark problems including CEC'2015 and CEC'2020 performance of the WSAR is compared against WSA and other metaheuristic algorithms. It is statistically shown that the WSAR algorithm is able to produce good and competitive results in comparison to its predecessor WSA and other metaheuristic algorithms.

Gossip-based distributed stochastic mirror descent for constrained optimization.

This paper considers a distributed constrained optimization problem over a multi-agent network in the non-Euclidean sense. The gossip protocol is adopted to relieve the communication burden, which also adapts to the constantly changing topology of the network. Based on this idea, a gossip-based distributed stochastic mirror descent (GB-DSMD) algorithm is proposed to handle the problem under consideration. The performances of GB-DSMD algorithms with constant and diminishing step sizes are analyzed, respectively. When the step size is constant, the error bound between the optimal function value and the expected function value corresponding to the average iteration output of the algorithm is derived. While for the case of the diminishing step size, it is proved that the output of the algorithm uniformly approaches to the optimal value with probability 1. Finally, as a numerical example, the distributed logistic regression is reported to demonstrate the effectiveness of the GB-DSMD algorithm.

High-resolution cell imaging using white light phase shifting interferometry and iterative phase deconvolution.

An optimization algorithm is presented for the deconvolution of a complex field to improve the resolution and accuracy of quantitative phase imaging (QPI). A high-resolution phase map can be recovered by solving a constrained optimization problem of deconvolution using a complex gradient operator. The method is demonstrated on phase measurements of samples using a white light based phase shifting interferometry (WLPSI) method. The application of the algorithm on real and simulated objects shows a significant resolution and contrast improvement. Experiments performed on Escherichia coli bacterium have revealed its sub-cellular structures that were not visible in the raw WLPSI images obtained using a five phase shifting method. These features can give valuable insights into the structures and functioning of biological cells. The algorithm is simple in implementation and can be incorporated into other QPI modalities .

Aligning opportunity cost and net benefit criteria: the health shadow price.

Given constrained healthcare budgets and many competing demands, public health decision-making requires comparing the expected cost and health outcomes of alternative strategies and associated adoption and financing actions. Opportunity cost (comparing outcomes from the best alternative use of budgets or actions in decision making) and more recently net benefit criteria (relative valuing of effects at a threshold value less costs) have been key concepts and metrics applied toward making such decisions. In an ideal world, opportunity cost and net benefit criteria should be mutually supportive and consistent. However, that requires a threshold value to align net benefit with opportunity cost assessment. This perspective piece shows that using the health shadow price as the ICER threshold aligns net benefit and opportunity cost criteria for joint adoption and financing actions that arise when reimbursing any new strategy or technology under a constrained budget. For an investment strategy with ICER at the health shadow price Bc = 1/(1/n + 1/d-1/m), net benefit of reimbursing (adopting and financing) that strategy given an incremental cost-effectiveness ration (ICER) of actual displacement, d, in financing, is shown to be equivalent to that of the best alternative actions, the most cost-effective expansion of existing programs (ICER = n) funded by the contraction of the least cost-effective programs (ICER = m). Net benefit is correspondingly positive or negative if it is below or above this threshold. Implications are discussed for creating pathways to optimal public health decision-making with appropriate incentives for efficient displacement as well as for adoption actions and related research.

Dual therapy of cancer using optimal control supported by swarm intelligence.

BACKGROUND: The scientific revolution in the treatment of many illnesses has been significantly aided by stem cells. This paper presents an optimal control on a mathematical model of chemotherapy and stem cell therapy for cancer treatment. OBJECTIVE: To develop effective hybrid techniques that combine the optimal control theory (OCT) with the evolutionary algorithm and multi-objective swarm algorithm. The developed technique is aimed to reduce the number of cancerous cells while utilizing the minimum necessary chemotherapy medications and minimizing toxicity to protect patients' health. METHODS: Two hybrid techniques are proposed in this paper. Both techniques combined OCT with the evolutionary algorithm and multi-objective swarm algorithm which included MOEA/D, MOPSO, SPEA II and PESA II. This study evaluates the performance of two hybrid techniques in terms of reducing cancer cells and drug concentrations, as well as computational time consumption. RESULTS: In both techniques, MOEA/D emerges as the most effective algorithm due to its superior capability in minimizing tumour size and cancer drug concentration. CONCLUSION: This study highlights the importance of integrating OCT and evolutionary algorithms as a robust approach for optimizing cancer chemotherapy treatment.

Cautious Bayesian Optimization: A Line Tracker Case Study.

In this paper, a procedure for experimental optimization under safety constraints, to be denoted as constraint-aware Bayesian Optimization, is presented. The basic ingredients are a performance objective function and a constraint function; both of them will be modeled as Gaussian processes. We incorporate a prior model (transfer learning) used for the mean of the Gaussian processes, a semi-parametric Kernel, and acquisition function optimization under chance-constrained requirements. In this way, experimental fine-tuning of a performance objective under experiment-model mismatch can be safely carried out. The methodology is illustrated in a case study on a line-follower application in a CoppeliaSim environment.

Cartesian constraints in QM/MM optimizations.

With the rise of quantum mechanical/molecular mechanical (QM/MM) methods, the interest in the calculation of molecular assemblies has increased considerably. The structures and dynamics of such assemblies are usually governed to a large extend by intermolecular interactions. As a result, the corresponding potential energy surfaces are topological rich and possess many shallow minima. Therefore, local structure optimizations of QM/MM molecular assemblies can be challenging, in particular if optimization constraints are imposed. To overcome this problem, structure optimization in normal coordinate space is advocated. To do so, the external degrees of freedom of a molecule are separated from the internal ones by a projector matrix in the space of the Cartesian coordinates. Here we extend this approach to Cartesian constraints. To this end, we devise an algorithm that adds the Cartesian constraints directly to the projector matrix and in this way eliminates them from the reduced coordinate space in which the molecule is optimized. To analyze the performance and stability of the constrained optimization algorithm in normal coordinate space, we present constrained minimizations of small molecular systems and amino acids in gas phase as well as water employing QM/MM constrained optimizations. All calculations are performed in the framework of auxiliary density functional theory as implemented in the program deMon2k.

A Bayesian Spatio-temporal Model to Optimize Allocation of Buprenorphine in North Carolina.

The opioid epidemic is an ongoing public health crisis. In North Carolina, overdose deaths due to illicit opioid overdose have sharply increased over the last 5-7 years. Buprenorphine is a U.S. Food and Drug Administration approved medication for treatment of opioid use disorder and is obtained by prescription. Prior to January 2023, providers had to obtain a waiver and were limited in the number of patients that they could prescribe buprenorphine. Thus, identifying counties where increasing buprenorphine would yield the greatest overall reduction in overdose death can help policymakers target certain geographical regions to inform an effective public health response. We propose a Bayesian spatiotemporal model that relates yearly, county-level changes in illicit opioid overdose death rates to changes in buprenorphine prescriptions. We use our model to forecast the statewide count and rate of illicit opioid overdose deaths in future years, and we use nonlinear constrained optimization to identify the optimal buprenorphine increase in each county under a set of constraints on available resources. Our model estimates a negative relationship between death rate and increasing buprenorphine after accounting for other covariates, and our identified optimal single-year allocation strategy is estimated to reduce opioid overdose deaths by over 5.

Convexity constraints on linear background models for electron energy-loss spectra.

In this paper convexity constraints are derived for a background model of electron energy loss spectra (EELS) that is linear in the fitting parameters. The model outperforms a power-law both on experimental and simulated backgrounds, especially for wide energy ranges, and thus improves elemental quantification results. Owing to the model's linearity, the constraints can be imposed through fitting by quadratic programming. This has important advantages over conventional nonlinear power-law fitting such as high speed and a guaranteed unique solution without need for initial parameters. As such, the need for user input is significantly reduced, which is essential for unsupervised treatment of large datasets. This is demonstrated on a demanding spectrum image of a semiconductor device sample with a high number of elements over a wide energy range.

Sparse solution of least-squares twin multi-class support vector machine using ℓ0 and ℓp-norm for classification and feature selection.

In the realm of multi-class classification, the twin K-class support vector classification (Twin-KSVC) generates ternary outputs {-1,0,+1} by evaluating all training data in a "1-versus-1-versus-rest" structure. Recently, inspired by the least-squares version of Twin-KSVC and Twin-KSVC, a new multi-class classifier called improvements on least-squares twin multi-class classification support vector machine (ILSTKSVC) has been proposed. In this method, the concept of structural risk minimization is achieved by incorporating a regularization term in addition to the minimization of empirical risk. Twin-KSVC and its improvements have an influence on classification accuracy. Another aspect influencing classification accuracy is feature selection, which is a critical stage in machine learning, especially when working with high-dimensional datasets. However, most prior studies have not addressed this crucial aspect. In this study, motivated by ILSTKSVC and the cardinality-constrained optimization problem, we propose ℓp-norm least-squares twin multi-class support vector machine (PLSTKSVC) with 0

Constrained Optimization for Decision Making in Health Care Using Python: A Tutorial.

HIGHLIGHTS: This tutorial provides a user-friendly guide to mathematically formulating constrained optimization problems and implementing them using Python.Two examples are presented to illustrate how constrained optimization is used in health applications, with accompanying Python code provided.

Anatomy-guided domain adaptation for 3D in-bed human pose estimation.

3D human pose estimation is a key component of clinical monitoring systems. The clinical applicability of deep pose estimation models, however, is limited by their poor generalization under domain shifts along with their need for sufficient labeled training data. As a remedy, we present a novel domain adaptation method, adapting a model from a labeled source to a shifted unlabeled target domain. Our method comprises two complementary adaptation strategies based on prior knowledge about human anatomy. First, we guide the learning process in the target domain by constraining predictions to the space of anatomically plausible poses. To this end, we embed the prior knowledge into an anatomical loss function that penalizes asymmetric limb lengths, implausible bone lengths, and implausible joint angles. Second, we propose to filter pseudo labels for self-training according to their anatomical plausibility and incorporate the concept into the Mean Teacher paradigm. We unify both strategies in a point cloud-based framework applicable to unsupervised and source-free domain adaptation. Evaluation is performed for in-bed pose estimation under two adaptation scenarios, using the public SLP dataset and a newly created dataset. Our method consistently outperforms various state-of-the-art domain adaptation methods, surpasses the baseline model by 31%/66%, and reduces the domain gap by 65%/82%. Source code is available at https://github.com/multimodallearning/da-3dhpe-anatomy.

Symbolic expression generation via variational auto-encoder.

There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. Widespread deep neural networks do not provide interpretable solutions. Meanwhile, symbolic expressions give us a clear relation between observations and the target variable. However, at the moment, there is no dominant solution for the symbolic regression task, and we aim to reduce this gap with our algorithm. In this work, we propose a novel deep learning framework for symbolic expression generation via variational autoencoder (VAE). We suggest using a VAE to generate mathematical expressions, and our training strategy forces generated formulas to fit a given dataset. Our framework allows encoding apriori knowledge of the formulas into fast-check predicates that speed up the optimization process. We compare our method to modern symbolic regression benchmarks and show that our method outperforms the competitors under noisy conditions. The recovery rate of SEGVAE is 65% on the Ngyuen dataset with a noise level of 10%, which is better than the previously reported SOTA by 20%. We demonstrate that this value depends on the dataset and can be even higher.

Interpretable HER2 scoring by evaluating clinical guidelines through a weakly supervised, constrained deep learning approach.

The evaluation of the Human Epidermal growth factor Receptor-2 (HER2) expression is an important prognostic biomarker for breast cancer treatment selection. However, HER2 scoring has notoriously high interobserver variability due to stain variations between centers and the need to estimate visually the staining intensity in specific percentages of tumor area. In this paper, focusing on the interpretability of HER2 scoring by a pathologist, we propose a semi-automatic, two-stage deep learning approach that directly evaluates the clinical HER2 guidelines defined by the American Society of Clinical Oncology/ College of American Pathologists (ASCO/CAP). In the first stage, we segment the invasive tumor over the user-indicated Region of Interest (ROI). Then, in the second stage, we classify the tumor tissue into four HER2 classes. For the classification stage, we use weakly supervised, constrained optimization to find a model that classifies cancerous patches such that the tumor surface percentage meets the guidelines specification of each HER2 class. We end the second stage by freezing the model and refining its output logits in a supervised way to all slide labels in the training set. To ensure the quality of our dataset's labels, we conducted a multi-pathologist HER2 scoring consensus. For the assessment of doubtful cases where no consensus was found, our model can help by interpreting its HER2 class percentages output. We achieve a performance of 0.78 in F1-score on the test set while keeping our model interpretable for the pathologist, hopefully contributing to interpretable AI models in digital pathology.

A Concurrent Mission-Planning Methodology for Robotic Swarms Using Collaborative Motion-Control Strategies.

Swarm robotic systems comprising members with limited onboard localization capabilities rely on employing collaborative motion-control strategies to successfully carry out multi-task missions. Such strategies impose constraints on the trajectories of the swarm and require the swarm to be divided into worker robots that accomplish the tasks at hand, and support robots that facilitate the movement of the worker robots. The consideration of the constraints imposed by these strategies is essential for optimal mission-planning. Existing works have focused on swarms that use leader-based collaborative motion-control strategies for mission execution and are divided into worker and support robots prior to mission-planning. These works optimize the plan of the worker robots and, then, use a rule-based approach to select the plan of the support robots for movement facilitation - resulting in a sub-optimal plan for the swarm. Herein, we present a mission-planning methodology that concurrently optimizes the plan of the worker and support robots by dividing the mission-planning problem into five stages: division-of-labor, task-allocation of worker robots, worker robot path-planning, movement-concurrency, and movement-allocation. The proposed methodology concurrently searches for the optimal value of the variables of all stages. The proposed methodology is novel as it (1) incorporates the division-of-labor of the swarm into worker and support robots into the mission-planning problem, (2) plans the paths of the swarm robots to allow for concurrent facilitation of multiple independent worker robot group movements, and (3) is applicable to any collaborative swarm motion-control strategy that utilizes support robots. A unique pre-implementation estimator, for determining the possible improvement in mission execution performance that can achieved through the proposed methodology was also developed to allow the user to justify the additional computational resources required by it. The estimator uses a machine learning model and estimates this improvement based on the parameters of the mission at hand. Extensive simulated experiments showed that the proposed concurrent methodology improves the mission execution performance of the swarm by almost 40% compared to the competing sequential methodology that optimizes the plan of the worker robots first and, then, the plan of the support robots. The developed pre-implementation estimator was shown to achieve an estimation error of less than 5%.

Hypertension treatment capacity in India by increased workforce, greater task-sharing, and extended prescription period: a modelling study.

Background: The worldwide control rate for hypertension is dismal. An inadequate number of physicians to treat patients with hypertension is one key obstacle. Innovative health system approaches such as delegation of basic tasks to non-physician health workers (task-sharing) might alleviate this problem. Massive scale up of population-wide hypertension management is especially important for low- and middle-income countries such as India. Methods: Using constrained optimization models, we estimated the hypertension treatment capacity and salary costs of staff involved in hypertension care within the public health system of India and simulated the potential effects of (1) an increased workforce, (2) greater task-sharing among health workers, and (3) extended average prescription periods that reduce treatment visit frequency (e.g., quarterly instead of monthly). Findings: Currently, only an estimated 8% (95% uncertainty interval 7%-10%) of ∼245 million adults with hypertension can be treated by physician-led services in the Indian public health system (assuming the current number of health workers, no greater task-sharing, and monthly visits for prescriptions). Without task-sharing and with continued monthly visits for prescriptions, the least costly workforce expansion to treat 70% of adults with hypertension would require ∼1.6 (1.0-2.5) million additional staff (all non-physicians), with ∼INR 200 billion (≈USD 2.7 billion) in additional annual salary costs. Implementing task-sharing among health workers (without increasing the overall time on hypertension care) or allowing a 3-month prescription period was estimated to allow the current workforce to treat ∼25% of patients. Joint implementation of task-sharing and a longer prescription period could treat ∼70% of patients with hypertension in India. Interpretation: The combination of greater task-sharing and extended prescription periods could substantially increase the hypertension treatment capacity in India without any expansion of the current workforce in the public health system. By contrast, workforce expansion alone would require considerable, additional human and financial resources. Funding: Resolve to Save Lives, an initiative of Vital Strategies, was funded by grants from Bloomberg Philanthropies; the Bill and Melinda Gates Foundation; and Gates Philanthropy Partners (funded with support from the Chan Zuckerberg Foundation).