Linear Optimization Techniques Research Articles

Modelling the impact of introducing first-generation narrowbody hydrogen aircraft on the passenger air transportation network in Europe

The global aviation industry faces a pronounced challenge to mitigate its contribution to anthropogenic climate change, which is caused by burning fossil fuels. One potential pathway is the transition towards using green hydrogen as zero-carbon fuel. Next to technological, infrastructural, and economical challenges, this would introduce a wide range of operational and infrastructural changes to a system centred around safety and reliability. This study employs a holistic approach and examines these changes from a flight network perspective, focusing on passenger transport in Europe. It utilizes network modelling and linear optimization techniques to determine network changes imposed by the introduction of first-generation narrowbody hydrogen aircraft. The findings are threefold: First, the study shows that the air transportation network can be adequately re-created using demand and direct operating cost optimization only, without considering revenue and airline-specific factors. Second, the introduction of hydrogen aircraft will have substantial impact on network structure, incl. flight frequency, capacity, and stopover routes, depending on seat capacity and range of the hydrogen aircraft design. Lastly, it also shows that airports that have a favourable green hydrogen supply will benefit from the introduction of hydrogen aviation.

Graph attention network and radial basis function neural network-based hybrid framework for epileptic seizure detection from EEG signal

<p>Epileptic seizure is a neurological disorder characterized by recurrent, abrupt behavioral changes attributed to transient shifts in excessive electrical discharges within specific brain cell groups. Electroencephalogram (EEG) signals are the primary modality for capturing seizure activity, offering real-time, computer-assisted detection through long-term monitoring. Over the last decade, extensive experiments through deep learning techniques on EEG signal analysis, and automatic seizure detection. Nevertheless, realizing the full potential of deep neural networks in seizure detection remains a challenge, primarily due to limitations in model architecture design and their capacity to handle time series brain data. The fundamental drawback of current deep learning methods is their struggle to effectively represent physiological EEG recordings; as it is irregular and unstructured in nature, which is difficult to fit into matrix format in traditional methods. Because of this constraint, a significant research gap remains in this research field. In this context, we propose a novel approach to bridge this gap, leveraging the inherent relationships within EEG data. Graph neural networks (GNNs) offer a potential solution, capitalizing on their ability to naturally encapsulate relational data between variables. By representing interacting nodes as entities connected by edges with weights determined by either temporal associations or anatomical connections, GNNs have garnered substantial attention for their potential in configuring brain anatomical systems. In this paper, we introduce a hybrid framework for epileptic seizure detection, combining the Graph Attention Network (GAT) with the Radial Basis Function Neural Network (RBFN) to address the limitations of existing approaches. Unlike traditional graph-based networks, GAT automatically assigns weights to neighbouring nodes, capturing the significance of connections between nodes within the graph. The RBFN supports this by employing linear optimization techniques to provide a globally optimal solution for adjustable weights, optimizing the model in terms of the minimum mean square error (MSE). Power spectral density is used in the proposed method to analyze and extract features from electroencephalogram (EEG) signals because it is naturally simple to analyze, synthesize, and fit into the graph attention network (GAT), which aids in RBFN optimization. The proposed hybrid framework outperforms the state-of-the-art in seizure detection tasks, obtaining an accuracy of 98.74%, F1-score of 96.2%, and Area Under Curve (AUC) of 97.3% in a comprehensive experiment on the publicly available CHB-MIT EEG dataset.</p>

Novel Bayesian Inference-Based Approach for the Uncertainty Characterization of Zhang's Camera Calibration Method.

Camera calibration is necessary for many machine vision applications. The calibration methods are based on linear or non-linear optimization techniques that aim to find the best estimate of the camera parameters. One of the most commonly used methods in computer vision for the calibration of intrinsic camera parameters and lens distortion (interior orientation) is Zhang's method. Additionally, the uncertainty of the camera parameters is normally estimated by assuming that their variability can be explained by the images of the different poses of a checkerboard. However, the degree of reliability for both the best parameter values and their associated uncertainties has not yet been verified. Inaccurate estimates of intrinsic and extrinsic parameters during camera calibration may introduce additional biases in post-processing. This is why we propose a novel Bayesian inference-based approach that has allowed us to evaluate the degree of certainty of Zhang's camera calibration procedure. For this purpose, the a prioriprobability was assumed to be the one estimated by Zhang, and the intrinsic parameters were recalibrated by Bayesian inversion. The uncertainty of the intrinsic parameters was found to differ from the ones estimated with Zhang's method. However, the major source of inaccuracy is caused by the procedure for calculating the extrinsic parameters. The procedure used in the novel Bayesian inference-based approach significantly improves the reliability of the predictions of the image points, as it optimizes the extrinsic parameters.

3D fictitious wave domain CSEM inversion by adjoint source estimation

Marine controlled-source electromagnetic (CSEM) method has proved its potential in detecting highly resistive hydrocarbon bearing formations. To image the subsurface resistivity, this paper presents the first application of a frequency domain CSEM inversion approach using fictitious wave domain timestepping modelling. Each inversion iteration requires the gradient of the misfit with respect to resistivity computed by the product between the forward and adjoint fields. Simulation of the adjoint field using fictitious time modelling is challenging as it requires the time domain adjoint source functions while only a few discrete frequencies of the data residual are available for the inversion. To overcome this issue, we formulate a regularized linear inverse problem to estimate a long time series from very few frequency samples. It can then be solved using linear optimization technique in matrix-free manner. Instead of computing adjoint source time function one by one at each receiver location, a basis function implementation has been designed, such that the linear inversion can be solved only once and then reused every time to construct all time-domain adjoint sources. The method allows computing all frequencies of the EM fields in one go without heavy memory and computational overhead. Numerical examples are employed to demonstrate the application of our method.

A comparison of the homotopy method with linearisation approaches for a non-linear optimization problem of operations in a reservoir cascade

AbstractReservoir systems are often operated for multiple purposes. This can result conflicting operational goals. To efficiently control these systems and to satisfy the different interests as good as possible, mathematical optimization models can be used to support operational decisions. Common approaches for reservoir optimization apply linear optimization techniques. However, real-world systems often require non-linear functions to describe the relation between water level and volume in a reservoir or to account for the hydropower equation. When the non-linear equations form a non-convex optimization problem, the problem is not necessarily solved to a global optimum. Piecewise-linear or linear formulations of the non-linear equations are a common way to address non-linear non-convex optimization problems. In this paper, the novel homotopy method is compared with two established approaches—the piecewise-linear and the linear approximation—to account for non-linear components in the optimization problem. The analysis is carried out for a cascade of three reservoirs under two scenarios—a flood scenario and a load balance scenario. The optimization software is the open source package RTC-Tools 2.4. Compared to the piecewise-linear and the linear approach the homotopy method shows a better accuracy for the analysed cases, because the method solves the flow equations within the optimization in a non-simplified form. Different to the piecewise-linear and the linear approach, however, the homotopy method does not guarantee a global optimum. The solution is still path-stable, which is a basic pre-requisite for its application in an operational context of hydropwer scheduling. Compared to the piecewise-linear approach, the homotopy method is easier to implement under the condition that the software supports the method.

A measurement-based approach to voltage-constrained hosting capacity analysis with controllable reactive power behind-the-meter

We propose an efficient method for the assessment of localized voltage-constrained distributed generation hosting capacity given an engineer’s choice or estimate of a power factor control setpoint for each customer. The advantage of the proposed method is that it extends recent methods to perform HCA using only advanced metering infrastructure (AMI) measurements with no prior knowledge of the network or its topology. This is achieved by developing efficient decision-making algorithms based on linear algebra and optimization techniques. The performance of the method is benchmarked against conventional model-based hosting capacity analysis (HCA) techniques, and we demonstrate the success of the method on several real-world AMI datasets. We find that comparable performance is achieved to model-based methods. Calculating HC from AMI datasets has the potential to avoid modeling errors common in circuit models.

Selection of TCC Curve and Protection Cooperation Method of Distribution Line Using Linear Optimization

Distribution systems are mostly composed of radial structures, which are susceptible to an increased variability and complexity of system operation due to frequent line changes during operation. When multiple changes in distribution lines occur simultaneously, the relative positions of protective devices also change. The existing protection coordination method of distribution lines is configured by considering the operation characteristics and coordination time interval (CTI) of all protective devices in series from the substation to the terminal load. Therefore, the protection coordination algorithm needs to be redesigned whenever a line is changed or a protective device is added to the distribution line for which the existing protection coordination algorithm has been set. In addition, existing protection coordination methods require complex calculations and procedures, which are subject to human errors and are less feasible for responding in real-time to changes in the distribution system. In this paper, we propose the adaptive time–current curve (TCC) method by selecting the time dial setting (TDS) and minimum response time (MRT) of individual protective devices in accordance with the relative distance based on the linear optimization technique. Using PSCAD/EMTDC, a power system analysis program, the minimum operating current and the fault current of each protective device are obtained, and the proposed protection coordination algorithm is verified according to the series configuration relationship of the protective devices. Finally, the proposed method is applied to an actual distribution line to verify the improvement over the existing protection coordination.

Precise Configuring of Actuators/Sensors for Active Control of Sound Quality in Cabs with Modal Vibration Energy and LA-PSO

Active control of structural modal vibration is an effective strategy to enhance the sound quality of cabs in commercial vehicles. However, accurate determination of the positioning and quantity of modal active control sensors and actuators is crucial for cabs with intricate structures, owing to the presence of multiorder modes and their coupling. The study presented herein focuses on the cab of a commercial vehicle and contemplates the features of the irregular large-space structure of the cab. By capitalizing on the modal frequency and mode shape of the cab, utilizing the piezoelectric control principle and modal vibration energy as the assessment index, an advanced multimode composite control criterion is postulated to ascertain the configuration of primary sensors and actuators. The particle swarm optimization (PSO) objective function is constructed to accomplish the optimal position matching of the actuator/sensor, using the multimodal surface velocity vector of the vibration sensor as the core parameter. Furthermore, an improved linear adaptive particle swarm optimization (LA-PSO) technique is advanced to satisfy the requirements of optimal convergence performance and accuracy of the complex cab structure. The optimization culminates in a 9 × 9 multichannel active control scheme for determining the optimal position of the actuators/sensors. This investigation provides a technical foundation for the active control of sound quality in automotive cabs and presents an innovative method for implementing effective noise control systems in large-scale machinery and equipment.

Feedback-based fault-tolerant and health-adaptive optimal charging of batteries

The key technology barriers that hinder the growth of Electric Vehicles (EVs) are long charging time, the shorter life-time of EV batteries, and battery safety. Specifically, EV charging protocols have significant effects on battery lifetime and safety. If not charged properly, the battery could end up with shorter life, and more importantly, improper charging can cause battery faults leading to catastrophic failures. To overcome these barriers, we propose a closed-loop feedback based approach, that enables real-time optimal fast charging protocol adaptation to battery health and possess active diagnostic capabilities in the sense that, during charging, it detects real-time faults and takes corrective action to mitigate such fault effects. We utilize battery electrical–thermal model, explicit battery capacity and power fade aging models, and thermal fault model to capture battery behavior. In conjunction with the models, we adopt linear quadratic optimal control techniques to realize the feedback-based control algorithm. Simulation studies are presented to illustrate the effectiveness of the proposed scheme.

Methodology to develop a capital improvement plan using optimization technique: case study

Capital Improvement Plan (CIP) plays a critical role in maintaining and upgrading a road system by determining which road segments should receive treatment for a year. The funding provided by the local government is considered as the available budget, and by synchronizing the available budget, the CIP ensures that the overall pavement condition is optimized. The primary factors included in the methodology are the following: budget, Pavement Surface Evaluation and Rating (PASER), deterioration model, cost matrix, and improvement associated with selecting the treatment. A combined priority index was determined for each roadway segment based on the functional classification of roadways and the maintenance treatment type. The linear integer optimization technique was applied to identify the best projects for improvement. The overall methodology was applied to the City of Fort Wayne’s Road system to verify the method’s applicability as a case study.

A systemic model predictive control based on adaptive power pinch analysis for load shifting and shedding in an isolated hybrid energy storage system

This paper presents a novel systemic algorithm based on conservative power pinch analysis principles using a computationally efficient insight-based binary linear programming optimization technique in a model predictive framework for integrated load shifting and shedding in an isolated hybrid energy storage system. In a receding 24-hour predictive horizon, the energy demand and supply are integrated via an adaptive power grand composite curve tool to form a diagonal matrix of predicted hourly minimum and maximum energy constraints. The intgrated energy constraints must be satisfied recursively by the binary optimisation to ensure the energy storage’s state of charge only operates within 30% and 90%. Hence, the control command to shift or shed load is contingent on the energy storage state of the charge violating the operating constraints. The controllable load demand is shifted and/or shed to prevent any violations while ensuring energy supply to the most critical load without sacrificing the consumers' comfort. The proposed approach enhances efficient energy use from renewable energy supply as well as limits the use of the Hydrogen resources by a fuel cell to satisfy controllable load demands which can be shifted to periods in the day with excess renewable energy supply.

Optimal sourcing strategy for enterprises to achieve 100% renewable energy

RE100 is a voluntary campaign for global companies to use 100% renewable energy in their business and production processes. Many global companies participating in RE100 have adopted various approaches for renewable energy sourcing. There is increasing awareness that global companies cannot indefinitely avoid participating in the RE100 campaign, however, there has been limited research on economically achieving RE100. This paper provides an optimal strategy for companies to source renewable energy to economically achieve RE100 in the future. The approaches for meeting energy demands with renewable electricity are analyzed, and a feasible sourcing strategy is presented. Additionally, using the linear programming optimization technique for quantitative analysis, an annual strategy is derived for cost minimization while achieving RE100 during the analysis period. The analysis shows that as the renewable energy generation cost decreases over time, the cost-effective strategy is to deviate from the utility environment at a specific time and select corporate power purchase agreements for implementing RE100, and it further demonstrates the need for policymakers to create an environment in which companies can freely choose from a combination of power purchase options and various certification methods to maximize their enterprise competitive power.

Comparative Appraisal of Metro Stations in Delhi Using Data Envelopment Analysis in a Multimodal Context

Urban public transit is a critical component for sustainable urban development and is crucial to multisector expansion of a developing economy. Continuous monitoring of infrastructure performance and assessment of its effectiveness are required to continually improve service quality. The urban agglomeration of Delhi, India, was studied for the efficacy of its multimodal urban public transit system. The toolkit used was Data Envelopment Analysis (DEA), a linear optimization technique that estimates relative efficiencies of its decision making units (DMUs) for a multitude of inputs and outputs. The study area includes the Red and Yellow lines of the Delhi Metro network. Commuter-based questionnaires were used to collect 1,328 valid responses about demographic, travel time, and quality perception parameters, which were analyzed, and relative rankings of the DMUs were evaluated. The efficiency was analyzed according to the Red and Yellow lines divided into seven corridor segments and individual stations. Results revealed efficiency scores and inefficiency slacks for which improvement strategies are proposed.

An unrefinement algorithm for planar THB-spline parameterizations

Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with respect to THB-splines, so that the coarser geometry approximates the initial geometry with a given level of the precision and is regular. The algorithm is based on the unrefinement of cells of the parameter domain, on which the geometry is defined, thus obtaining the new subdivision of the domain (the new subdomain hierarchy). The algorithm uses local linear projectors and optimization techniques in order to ensure the regularity and the approximation properties.

Personalized recommender systems based on social relationships and historical behaviors

Recommender systems have a wide range of applications in the age suffering information overload. A promising way to design better recommender systems in the presence of ubiquitous social media is to utilize social relationships in recommendation algorithms, named social recommendation. One critical challenge in social recommendation is how to mine valuable information intrinsic to social relationships and integrate such information into the algorithm design. In this paper, we argue that both social relationships and historical behaviors are affected by the same implicit factors. For example, due to the existence of implicit factors such as peer influence or common interests in social networks, users with similar implicit factors will have a high probability to become friends and collect similar objects. Accordingly, we propose a recommendation algorithm that jointly utilizes social relationships and historical behaviors, based on the extended linear optimization technique. We test the performance of our algorithm for four groups of users on real networks, including all users, active users, inactive users and cold-start users. Results show that, in all the above four scenarios, the proposed algorithm performs overall best subject to accuracy and diversity metrics compared with the benchmarks. In particular, the algorithm remarkably improves the recommendation performance for cold-start users. Further analysis shows that the contribution of social relationships depends on the coupling strength between social relationships and historical behaviors.

A Collection of Numerical Recipes Useful for Building Scalable Psychometric Applications

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms for dealing with correlated data, computational concepts for linear models, multivariable integration, and optimization techniques.

What Incentives Are Required for Renewables to Provide Redispatch Services? A Simulation in a Multi-Market Setting

Renewable energy sources (RES) can provide valuable flexibility potential for multiple markets and grid services in the future. In this paper, the focus lies on the development of algorithms for an optimal dispatch and bidding of a RES-based virtual power plant (VPP) by considering current short-term and balancing market conditions in Austria, as well as a proposed redispatch market. Specifically, different pricing and bidding strategies for a redispatch market are compared and their feasibility is analyzed. The attractiveness of different pricing models and remuneration mechanisms for redispatch, as well as the influence of the redispatch call probability on the bidding behavior of the VPP, is investigated. The simulation of the bidding behavior is carried out using linear optimization techniques. The paper describes the algorithms as well as the assumptions for market rules in redispatch, balancing and short-term electricity markets. The results show that the probability to be activated for redispatch and thus the required incentives depend highly on the location of the plant. Pre-curtailment of the plant to offer positive redispatch is not recommended as the prices would need to be set at up to 200–300% of the day-ahead price.

New smart home energy management systems based on inclining block-rate pricing scheme

AbstractThere are wide applications of block-rate pricing schemes in many countries. However, there are no significant studies that apply this common tariff for smart home energy management systems. In this paper, a three-time-frame energy management scheme has been proposed for photovoltaic (PV)-powered grid-connected smart homes based on the well-known mixed-integer linear programming optimization technique. This paper provides three original and novel smart home energy management algorithms that depend on the most common residential tariff specifically in developing countries. Three different management concepts have been studied for a typical Egyptian house. The concepts of shifting load, vehicle-to-home and reducing air conditioning have been tested according to a commonly applied slab tariff. The proposed scheme considers the home battery extending lifetime constraints. It also preserves comfortable lifestyle limits for home users according to Arab housing climatic conditions and culture. Moreover, the economic feasibility of integrated PV modules for the studied home has been verified according to the Egyptian tariff. The proposed energy management scheme of PV-powered home reduces the electrical power bill significantly in a wide range from 61% to only 19% of the default case bill according to the applied management technique.

3D Reconstruction of cellular images from microfabricated imagers using fully-adaptive deep neural networks

Millimeter-scale multi-cellular level imagers enable various applications, ranging from intraoperative surgical navigation to implantable sensors. However, the tradeoffs for miniaturization compromise resolution, making extracting 3D cell locations challenging—critical for tumor margin assessment and therapy monitoring. This work presents three machine-learning-based modules that extract spatial information from single image acquisitions using custom-made millimeter-scale imagers. The neural networks were trained on synthetically-generated (using Perlin noise) cell images. The first network is a convolutional neural network estimating the depth of a single layer of cells, the second is a deblurring module correcting for the point spread function (PSF). The final module extracts spatial information from a single image acquisition of a 3D specimen and reconstructs cross-sections, by providing a layered “map” of cell locations. The maximum depth error of the first module is 100 µm, with 87% test accuracy. The second module’s PSF correction achieves a least-square-error of only 4%. The third module generates a binary “cell” or “no cell” per-pixel labeling with an accuracy ranging from 89% to 85%. This work demonstrates the synergy between ultra-small silicon-based imagers that enable in vivo imaging but face a trade-off in spatial resolution, and the processing power of neural networks to achieve enhancements beyond conventional linear optimization techniques.

Food intake pattern to achieve nutritional goals for Indian adults by linear programming optimization techniques

This paper discusses about the student diet selection taking some food items to complete the daily needs of nutrition. The objective of the present study was to minimize the cost of per day. To make a mathematical model of diet selection for the students in Indian Institute of Technology, Mumbai. This model is helped in the student’s diet problem with minimum possible cost. This model is the application of ILP of the food selection. The ILP model is prepared to pick suitable food items and minimize the cost of the diet taking by the students which makes all students are healthy. The result obtained from the mathematical model disclosed the minimum cost of a balanced diet is Rs 58.05 per day.