Estimation Of Cost Function Research Articles

Quantum annealing solution for the unrelated parallel machine scheduling with priorities and delay of task switching on machines

Quantum computing has emerged in recent years as an alternative to classical computing, which could improve the latter in solving some types of problems. One of the quantum programming models, Adiabatic Quantum Computing, has been successfully used to solve problems such as graph partitioning, traffic routing, and task scheduling. In this paper, the focus is on the scheduling of the problem of unrelated parallel machines, where the processing time of tasks on any of the available processing elements is known. Moreover, the proposed model is extended in two relevant aspects for this kind of problem: the existence of some degree of priority of tasks, and the introduction of a delay or penalty every time a processing unit or machine changes the type of task that executes.In all cases, the problem is expressed as Quadratic Unconstrained Binary Optimization, which can be subsequently solved using quantum annealers. The quantum nonlinear programming framework discussed in this work consists of three steps: quadratic approximation of cost function, a binary representation of parameter space, and solving the resulting Quadratic Unconstrained Binary Optimization on the quantum annealer platform D-Wave. One of the novelties in tackling this problem is the compaction of the model bearing in mind the repetitions of each task, to allow solving larger scheduling problems with the quantum resources available in the experimentation platform. An estimation of the number of qubits required in relation to the scheduling parameters is analyzed. The models have been implemented on the D-Wave platform and validated with respect to other traditional methods. Furthermore, the proposed extensions to consider priorities and to switch the delay of tasks have been analyzed using a case study.

Hospital cost efficiency: an examination of US acute care inpatient hospitals.

The use of stochastic frontier models for inference on hospital efficiency is complicated by the inability to fully control for quality differences across hospitals. Additionally, the potential existence of cross-sectional dependence due to the presence of unobserved common factors leads to endogeneity problems that can bias both cost function and efficiency estimates. Using a panel consisting of 1518 hospitals for the years 1996-2013 (T=18), I adopt techniques for dealing with long, cross-sectionally dependent panel data in order to estimate cost parameters and hospital specific efficiency. In particular, I employ the estimation technique proposed by Bai (Econometrica 77(4):1229-1279, 2009), which assumes that the unobservable heterogenous effects have a factor structure. I find evidence of considerable scale economies and that hospital cost inefficiencies have been increasing during the period of 1996-2013, and that the growth in expenditures is, in part, driven by spending that increases patient satisfaction, but that does not significantly contribute to improved patient health outcomes.

Event‐triggered‐based integral reinforcement learning output feedback optimal control for partially unknown constrained‐input nonlinear systems

AbstractIn this paper, an adaptive output feedback event‐triggered optimal control algorithm is proposed for partially unknown constrained‐input continuous‐time nonlinear systems. First, a neural network observer is constructed to estimate unmeasurable state. Next, an event‐triggered condition is established, and only when the event‐triggered condition is violated will the event be triggered and the state be sampled. Then, an event‐triggered‐based synchronous integral reinforcement learning (ET‐SIRL) control algorithm with critic‐actor neural networks (NNs) architecture is proposed to solve the event‐triggered Hamilton–Jacobi–Bellman equation under the established event‐triggered condition. The critic and actor NNs are used to approximate cost function and optimal event‐triggered optimal control law, respectively. Meanwhile, the event‐triggered‐based closed‐loop system state and all the neural network weight estimation errors are uniformly ultimately bounded proved by Lyapunov stability theory, and there is no Zeno behavior. Finally, two numerical examples are presented to show the effectiveness of the proposed ET‐SIRL control algorithm.

Transfer learning-based cost function approximation for look-ahead dispatch of power systems

In this paper, a transfer learning-based cost function approximation (TL-CFA) algorithm is proposed for the look-ahead dispatch of power systems. Cost function approximation (CFA) provides an effective sequential decision framework in the stochastic environment, which is suitable for the look-ahead dispatch of power systems with uncertainties. However, the parameters of CFA need to be iteratively updated, which may lead to additional computational burden, and thus hinder its real-time decision-making. Different from the traditional CFA algorithm, a transfer learning (TL) technique is used to describe the relationship between the parameters and stochastic information in the proposed TL-CFA algorithm. Thus, in the look-ahead dispatch process, the parameters of CFA can be directly obtained through the transfer function, which saves the computational time, while almost not losing the accuracy. Case studies are carried out on a modified IEEE 30-bus system and a real 2778-bus system, and the results demonstrate the effectiveness of the proposed approach.

An ADMM-qSPICE-Based Sparse DOA Estimation Method for MIMO Radar

In recent years, sparse direction-of-arrival (DOA) estimation for multiple-input multiple-output (MIMO) radar has attracted extensive attention and been extensively studied, especially the method based on the classic least absolute shrinkage and selection operator (LASSO) estimator. The alternating-direction method of multipliers (ADMM) is an effective method for solving this problem at the cost of introducing an additional user parameter. To avoid introducing an additional user parameter, this paper adopts an equivalent transformation in the form of the generalized SParse Iterative Covariance-based Estimation (qSPICE) cost function to obtain a mean squared minimized form of the cost function. Then, the problem is transformed into a sparse optimization problem in the form of a weighted LASSO. Next, this unconstrained optimization problem is decomposed into three subproblems, which are solved separately to reduce the dimension of each problem and thus reduce the overall computational complexity based on ADMM. Simulation results and measured data indicate that the proposed method significantly outperforms the traditional super-resolution DOA estimation method and ADMM-LASSO method and slightly outperforms qSPICE in terms of resolution and sidelobe suppression capability. In addition, the proposed method has a much lower computational complexity and substantially fewer iterations than qSPICE.

The impacts of imports and trade liberalization in Brazil: Insights from an aggregate cost function

AbstractBrazil has faced and continues to struggle with difficult economic challenges, including achieving noninflationary economic growth and a manageable external deficit. This paper presents the results of the estimation of an aggregate translog cost function with inputs of domestic capital and labor and imports and outputs of consumption and investment goods. The resulting calculated elasticities give insights into the relationships among the inputs, as well as the possible impacts of further reducing international trade barriers. The findings suggest that all of the inputs are substitutes for one another and that an increase in imports may have at least short‐run negative effects on the demand for domestic capital and labor. However, imports appear to be particularly important in the production of investment goods, so an increase in imports may result in a more than proportionate increase in the output of those products and enhance the long‐term growth of the economy. The responses to current challenges facing Brazil will affect its future economic growth as well as have a broader impact on the international scene. The results described here may help to inform policy makers as they address these issues, particularly with respect to international trade policies.

Imaging-based musculoskeletal models alter muscle and joint contact forces but do not improve the agreement with experimentally measured electromyography signals in children with cerebral palsy

BackgroundMusculoskeletal simulations are used to estimate muscle-tendon and joint contact forces (JCF). Personalizing the model’s femoral geometry has been shown to improve the accuracy of JCF calculations. It is, however, unknown if the personalized geometry improves the agreement between estimated muscle activations and experimentally measured electromyography (EMG) signals. Research questionDoes personalizing the musculoskeletal geometry improve the agreement between estimated muscle activations and EMG signals in terms of timing? MethodsWe retrospectively analysed data from Bosmans et al. [5], which included three-dimensional motion capture data, EMG signals of eight lower limb muscles on each leg, and magnetic resonance imaging (MRI) data from seven children with cerebral palsy. For each patient we created a generic-scaled model and MRI-based model, which accounted for the subject-specific musculoskeletal geometry. We calculated muscle activations, muscle-tendon forces and JCF. Muscle activations were compared to the EMG signals using coefficient of determination and cosines similarity. ResultsMRI-based models altered the magnitude of muscle activations and had a large impact on JCF but did not change the muscle activations profiles and therefore did not improve the agreement with EMG signals. SignificanceMRI-based models do not alter the shape of muscle activations. Hence, if detailed muscle activations are a desired output of the simulations, EMG-informed modeling approaches should be used for musculoskeletal simulation in children with cerebral palsy. Furthermore, our study highlighted that altered JCF does not necessarily mean accurate muscle activations. To improve patient-specific simulations, future work should focus on developing methods to estimate cost functions representative for the neural control of children with cerebral palsy.

A stochastic dynamic programming approach for the machine replacement problem

This paper addresses both the modeling and the resolution of the replacement problem for a population of machines. The main objective is the computation of a minimum cost replacement policy, which, based on the status of each machine, determines whether one or more machines have to be replaced over a given finite time horizon.The replacement problem of a set of machines can be regarded as a sequential decision-making problem under uncertainty. Thanks to this, we propose a novel formulation for such problems consisting of a composition of discrete-time multi-state Markov Decision Processes (MDPs), one for each specific machine. The underlying optimization problem is formulated as a stochastic Dynamic Programming (DP), and then solved by using the principles of the backward DP algorithm. Moreover, to deal with the curse of dimensionality due to the high-cardinality state–space of real-world/industrial applications, a new generalized multi-trajectory Least-Squares Temporal Difference (LSTD) based method is introduced. The resulting algorithm computes an approximate optimal cost function by: (i) running Monte Carlo simulations over different trajectories of a given length; (ii) embedding the policy improvement step within the recursive LSTD iterations; (iii) enforcing an off-policy mechanism to improve the LSTD exploration capabilities. A study on the convergence properties of the proposed approach is also provided. Several numerical examples are given to illustrate its effectiveness in terms of parametric sensitivity, computational burden, and performance of the computed policies compared with some heuristics defined in the literature.

Finite-Time Distributed Approximate Optimization Algorithms of Higher Order Multiagent Systems via Penalty-Function-Based Method

This article investigates the finite-time distributed approximate optimization problem of higher order multiagent systems, where the local cost functions are considered to be quadratic functions. This problem is solved via penalty-function-based method. First, by the penalty-function method, a global approximate cost function is constructed. Second, nonlinear distributed optimization algorithms are proposed for higher order multiagent systems by the tool of adding a power integrator technique. In the optimization algorithms design, the gradients of the approximate cost function are utilized. Under the proposed optimization algorithms, the agents approach the approximate optimal solution in finite time. Although there exist errors (they may be called approximation errors) between the approximate minimizers and the global accurate minimizer, the approximation errors can be regulated by penalty parameter and the relationship between the bound of the approximation errors and the penalty parameter is given explicitly. Furthermore, the proposed distributed approximate optimization algorithms are applied to the optimal rendezvous problem of wheeled multimobile robots, making the mobile robots achieve approximate optimization rendezvous in finite time. The effectiveness of the proposed distributed optimization algorithms and their applications to optimal rendezvous problem are validated by simulations.

Distributed multi-agent collision avoidance using robust differential game

This paper proposes a novel robust differential game scheme to solve the collision avoidance problem for networked multi-agent systems (MASs), subject to linear dynamics, external disturbances and limited observation capabilities. Compared with the existing differential game approaches only considering obstacle avoidance objectives, we explicitly incorporate the trajectory optimization target by penalizing the deviation from reference trajectories, based on the artificial potential field (APF) concept. It is proved that the strategies of each agent defined by individual optimization problems will converge to a local robust Nash equilibrium (R-NE), which further, with a fixed strong connection topology, will converge to the global R-NE. Additionally, to cope with the limited observation for MASs, local robust feedback control strategies are constructed based on the best approximate cost function and distributed robust Hamilton–Jacobi–Isaacs (DR-HJI) equations, which does not require global information of agents as in the traditional Riccati equation form. The feedback gains of the control strategies are found via the ant colony optimization (ACO) algorithm with a non-dominant sorting structure with convergence guarantees. Finally, simulation results are provided to verify the efficacy and robustness of the novel scheme. The agents arrived at the targeted position collision-free with a reduced arrival time, and reached the targeted positions under disturbance.

Special Feature: Linking capture-recapture and movement.

Special Feature: Linking capture-recapture and movement.

FGOT: Graph Distances Based on Filters and Optimal Transport

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph distance. It is an optimal transport based distance which drives graph comparison through the probability distribution of filtered graph signals. This creates a highly flexible distance, capable of prioritising different spectral information in observed graphs, offering a wide range of choices for a comparison metric. We tackle the problem of graph alignment by computing graph permutations that minimise our new filter distances, which implicitly solves the graph comparison problem. We then propose a new approximate cost function that circumvents many computational difficulties inherent to graph comparison and permits the exploitation of fast algorithms such as mirror gradient descent, without grossly sacrificing the performance. We finally propose a novel algorithm derived from a stochastic version of mirror gradient descent, which accommodates the non-convexity of the alignment problem, offering a good trade-off between performance accuracy and speed. The experiments on graph alignment and classification show that the flexibility gained through filter graph distances can have a significant impact on performance, while the difference in speed offered by the approximation cost makes the framework applicable in practical settings.

Combining Multiple Solution and Cost Function for Better LAI Estimation

پوشش گیاهی موتور محرک کرة زمین است؛ تبادلات انرژی و آب بین اتمسفر و زمین را کنترل می‌کند و در چرخه‏های جهانی انرژی، اکسیژن، دی‏اکسیدکربن و آب نقش مهمی دارد. پایش و مدیریت پوشش‌های گیاهی با استفاده از پارامتر‌های بیوفیزیکی و بیوشیمیایی آن، مانند LAI، انجام می‌پذیرد. شاخص سطح برگ (LAI) از مهم‌ترین پارامترهای پوشش گیاهی است که در اغلب مدل‌سازی‌ها مانند مدل‌سازی چرخه‌های آب، انرژی و کربن استفاده می‌شود. رویکردهای بازیابی متفاوتی، به‌منظور استخراج اطلاعات پارامترهای بیوفیزیکی از داده‌های سنجش از دوری، توسعه یافته است. در تحقیق حاضر، از روش فیزیکی معکوس مدل انتقال تابش PROSAIL، مبتنی‌بر جدول LUT، با هدف بازیابی متغیر LAI استفاده شده است. همچنین داده‌های زمینی برداشت‌شده طی کمپین SPARC 2003 برای ارزیابی صحت متغیر بازیابی‌شده به‌کار رفت. برای رفع مشکل ill-posed، چهار دسته از معیارهای هزینه با عنوان اندازه‌گیر اطلاعات (IM)، حداقل اختلاف (MC)، اندازه‌گیر زاویه (SAM) و خطای حداقل مربعات (LSE) به‌همراه نرمال‌سازی و میانگین بهترین جواب‌ها استفاده شد. نتایج بهبود تخمین متغیر LAI را با استفاده از معیار اندازه‌گیر اطلاعات (Kulbak-liebler)، به‌میزان 12% و با استفاده از 11% میانگین بهترین جواب‌ها نشان دادند. تابع هزینة LSE نیز در قیاس با حالت نرمال‌نشده، 7% بهبود یافت.

Open-Circuit Fault Detection in PMSM Drives Using Model Predictive Control and Cost Function Error

This article proposes a cost function error-based approach to diagnose open-circuit faults (OCFs) in permanent magnet synchronous machine drives with model predictive current control. The intrinsic relations of motor currents and cost functions under fault conditions are investigated. The residuals of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis currents are utilized to detect the fault type associated with the number of faulty devices. Instead of deriving the explicit values of cost functions, an estimation model is built according to the analytical expressions of currents and the optimal voltage vector. The error between the estimated cost function and the actual one is analyzed for fault localization. The faulty switch is finally diagnosed by assessing the minimum average absolute value of the cost function error. Simulated and experimental results confirm that the developed approach can achieve a fast diagnosis of single and multiple OCFs with good robustness to the motor parameter and operating power variations.

Ecological optimization and LCA of TiO2-SiC/ water hybrid nanofluid in a shell and tube heat exchanger by ANN

The current study estimates the environmental impact and cost model for the early-stage design of a shell and tube heat exchanger (STHE). Additionally, the lifecycle analysis (LCA) compares the effects of use of nanofluid in the chemical processing industry to increase the effectiveness of the heat transfer to the typical STHE system. Nanofluids increase heat transfer, as evidenced by the results of the experiments. The Nusselt number and pressure drop were both increased by roughly 65% and 8%, respectively, using 0.5 vol% of TiO2-SiC/water hybrid nanofluid compared to water as coolant. The ecological impact of STHE was estimated as s attribute of Ecological (EF) and total cost estimation function using artificial neural networks (ANN). Finally, the IdematLightLCA (2.8.6 version) software was used to calculate energy content, Carbon footprint, and cost over the lifespan of the baseline. The results show that nanofluid-based STHE has an average payback period considerably longer than typical coolant systems but saves superior economic value at the end of its lifetime. According to the findings, the suggested novel method is both cost-effective and environmentally feasible.

Statistical and Economic Estimation of Cost Functions in the Long Run and Economies of Scale to Date Palm in Giza Governorate

Statistical and Economic Estimation of Cost Functions in the Long Run and Economies of Scale to Date Palm in Giza Governorate

Approach for Cost Functions for the Use in Trade-Off Investigations Assessing the Environmental Impact of a Future Energy Efficient European Aviation

Aircraft emissions represent a relevant amount of human induced CO2. Globally, up to 2.5 per cent of such emissions stem from the aviation industry. In order to investigate the effects within the atmosphere, realistic flight profiles are necessary to provide quantitatively tangible values of emissions. The flight profiles and the according fuel consumption can be calculated by using waypoints from flight plans and Base of Aircraft Data (BADA). This paper presents an approach to refine the fuel consumption by integrating the passenger load into the calculation. Since effects of emissions have to be assessed on a greater scale, such as on the European air traffic network, the presented approach provides cost functions for CO2 emissions for different aircraft types and load factors. The cost functions were derived by means of regression analyses of BADA based calculated flight profiles with a step size of one second. The calculations are based on real historic traffic scenarios over several days. The derived aircraft specific fuel burn coefficients enable a simple and efficient integration of CO2 estimations depending on the flight distance, load factor and aircraft type. This can be applied to large traffic scenarios to also study different set-ups such as travel restrictions, other disruptions or an alteration in the traffic system as a whole. In order to enable the assessment of further aspects of such changes to the European air traffic system at large and to foster reproducibility and comparability of related studies, we provide further general-purpose cost estimation functions for several important key characteristics. Besides fuel consumption, we develop cost estimations for air navigation fees and maintenance for conventional aircraft. Those functions are also provided for the design concept of a short-range all-electric aircraft. This propeller aircraft features game-changing technologies such as active laminar flow control, active load alleviation and advanced materials and structure concepts. The approaches discussed in this paper will focus on the generic aspects of aircraft related costs, which can be derived from general available data. For the sake of reproducibility, the results will be made publicly available.

Multi-Period Workload Balancing in Last-Mile Urban Delivery

In the daily dispatching of last-mile urban delivery, a delivery manager has to consider workload balance among couriers to maintain workforce morale. We consider two types of workload: incentive workload, which relates to the delivery quantity and affects a courier’s income, and effort workload, which relates to the delivery time and affects a courier’s health. Incentive workload has to be balanced over a relatively long period of time (a payroll cycle—a week or a month), whereas effort workload has to be balanced over a relatively short period of time (a shift or a day). We introduce a multi-period workload balancing problem under stochastic demand and dynamic daily dispatching, formulate it as a Markov decision process (MDP), and derive a lower bound on the optimal value of the MDP model. We propose a balanced penalty policy based on cost function approximation and use a hybrid algorithm combining the modified nested partitions method and the KN++ procedure to search for an optimal policy parameter. A comprehensive numerical study demonstrates that the proposed balanced penalty policy performs close to optimal on small instances and outperforms four benchmark policies on large instances, and provides insight into the impact of demand variation and a manager’s importance weighting of operating cost and workload balance.

Parameter estimation of a gyroless micro-satellite from telemetry data

This paper presents a new approach for the simultaneous inertia and actuator alignment parameter estimation. One of the strengths of the proposed estimation algorithm consists in its ability to work directly with the star tracker attitude measurements and it is therefore also suitable for small and medium size satellites, where the gyroscope measures are not reliable or not available. In the algorithm, the satellite inverse dynamics model is exploited for the estimation cost function to take advantage of the linearity with respect to the main satellite parameters. The overall proposed solution is based on the instrumental variable method which has been deeply adapted to take into account several practical issues. The main components of the disturbance torques are modeled and simultaneously estimated with the satellite parameters to compensate for their effect. Inspired by the prefiltering technique used in the optimal refined instrumental variable method, a tailor-made filter design is proposed and implemented to deal with noisy measurements and the unmodeled disturbance torques. Such prefilter considerably improves the algorithm performance by achieving low-variance parameter estimates, while still requiring little to no tuning. A final but important novelty of this work consists in proposing an effective solution for estimating and compensating synchronism errors in the sensor measurements. This latter aspect has never been considered in the literature, although the lack of synchronism has a non-negligible effect on the accuracy of the parameter estimates. The proposed method is analyzed and validated via Monte Carlo simulations using data coming from a high-fidelity satellite simulator designed by the French space agency, and the results show the effectiveness of the algorithm.

A Two-Layer Model for Microgrid Real-Time Scheduling Using Approximate Future Cost Function

Microgrids incorporate an increasing number of distributed energy resources (DERs), which induce a higher variability and faster dispatch capabilities in power systems. This paper proposes a two-layer real-time scheduling model for microgrids, based on approximate future cost function (AFCF), where the future cost represents the opportunity cost for the microgrid operation in subsequent periods. At the upper layer, the look-ahead rolling scheduling is adopted to optimize microgrid operations, in which the future cost function (FCF) in deterministic and stochastic scenarios is approximated by a piecewise linear function. At the lower layer, a real-time parameter updating strategy based on real-time data is proposed. In this case, the real-time scheduling readjusts the look-ahead schedule using the immediate cost in the current period and the future cost calculated by the updated AFCF. The proposed two-layer real-time scheduling model uses an offline optimization, in which most of the computation tasks are completed at the upper layer, and applies a real-time optimization, in which the time-consuming problem is avoided at the lower layer. The effectiveness of the proposed two-layer real-time scheduling model of microgrids is validated by using a grid-connected microgrid system. For comparison, other existing real-time scheduling methods are also implemented in the same microgrid system.