Current Solution Methods Research Articles

Type parameter estimation of 2D‐GTD model based on ADMM approach

AbstractThe type parameter helps in scattering mechanism analysis and scattering centre identification. However, current approximate solution methods based on spectral estimation are noise‐sensitive and exhibit low accuracy. In this letter, a high‐precision approach for the type parameter based on the alternating direction method of multipliers (ADMM) is proposed. Logarithmic transformation is used to separate the type parameter and the amplitude from the coupling term, and initially obtain the closed‐form solution of the type parameter. Then, the regularization term of l2‐norm is used for denoising. Finally, a joint optimization model based on ADMM is constructed to effectively estimate the type parameter. Simulation results confirm the high accuracy of the proposed approach.

Research on the Time-Domain Explicit and Implicit Solution Methods of the Shallow Water Seismic Wavefield Equations

The current time-domain solution methods for the wavefield equations of a single medium do not apply to the wavefield equations of shallow water seismic with a fluid–elastomer coupling. To solve this problem, based on the explicit central difference method and implicit Newmark method, the explicit–explicit method, implicit–implicit method, and explicit–implicit method time-domain expressions for the local solution are derived, and the time-domain expressions for the explicit and implicit methods in the global solution are derived.The stability and computational efficiency of different time-domain solving methods for the shallow water seismic wavefield equations are theoretically analyzed. The numerical results are compared with the simulation data from the multiphysics field simulation software COMSOL 6.0, and the numerical stability, computational efficiency and accuracy of the different solving methods are also analyzed theoretically. The results show that the implicit method in the global solution is relatively optimal among the methods proposed in this paper, which ensures numerical stability at the larger step size for improving the computational efficiency and considers the higher computational efficiency and accuracy.

On Integrating and Operating Distributed Energy Resources in Distribution Networks: A Review of Current Solution Methods, Challenges, and Opportunities

On Integrating and Operating Distributed Energy Resources in Distribution Networks: A Review of Current Solution Methods, Challenges, and Opportunities

Carbon–Carbon Composite Metallic Alloy Joints and Corresponding Nanoscale Interfaces, a Short Review: Challenges, Strategies, and Prospects

Brazing of carbon–carbon (C/C) composites with metallic materials currently faces a series of difficulties, such as the poor wettability of metallic materials on the surface, the nanoscale interface bonding of C/C composites and metallic materials, thermal stress problems for these different materials, etc. Especially, the practical problems, including the low joint strength and insufficient reliability, still limit the large-scale practical application of brazing technology for C/C composites and metal materials. Herein, in order to guide the fabrication of high-quality joints, we present a brief discussion on the latest research progress in the joints of C/C composites and metallic materials, including current challenges, solution methods, mechanisms, and future prospects. More importantly, the nanoscale interface in the carbon–carbon composites and metallic alloys is paid very little attention, which has been critically discussed for the first time. Then, we further outline the possible solutions in joint problems of C/C composites and metallic materials, proposing feasible strategies to control the reaction in the brazing process, such as surface treatments, the addition of reinforcing phases, a transition layer sandwiched between the base material and the intermediate layer, etc. These strategies are being envisioned for the first time and further contribute to promoting the converged applications of C/C composites and metallic materials.

A Comparative Investigation on Peak Current Solution Methods for Lithium-Ion Battery Peak Power Capability Prediction

Accurate battery peak power capability prediction plays an essential role in improving the safety and efficiency of battery operations. The end of battery charge or discharge is caused by depleted or saturated surface lithium-ion concentrations of electrode solid particles to avoid damaging side reactions. Precise battery peak power capability prediction necessitates a high-fidelity electrochemical model (EM) that accurately depicts dynamic changes of lithium-ion concentrations inside a battery. One of the critical challenges to apply battery EMs for peak power prediction is how to accurately solve the peak charge and discharge currents from a set of complex model equations. To address the issue, this paper mainly investigates four different peak current solution algorithms, including bisection method, genetic algorithm method, particle swarm optimization method, and grey wolf optimizer (GWO) method for battery EM-based peak power prediction. The dependences of the prediction results using different current solution methods on the predictive time horizon and ambient temperature are validated. Their performance in terms of prediction accuracy, computational speed, complexity, convergence rate, and random-access memory are also evaluated. Among these peak current solution methods, the GWO method is proven to have a better performance in convergence rate and computing time while maintaining high prediction accuracy.

Optimizing bilinear multi-source water supply systems using mixed-integer linear programming approximations: An analysis of the Israeli seawater desalination array

Decision support systems (DSSs) in water resources management often use optimization models to make decisions. Therefore, the quality of these models is crucial for the success of DSSs. However, optimization models can struggle with reaching global optima, resulting in inconsistent and untrustworthy results for decision-makers. Additionally, current solution methods can be slow and inefficient, hindering real-time interaction with the DSS. This study addresses the optimal regional Multisource Water Supply Systems (MWSS) management using efficient global optimization techniques. The MWSS problem is formulated as a nonlinear optimization program due to using bilinear terms, which can result in multiple local optima. To overcome this challenge, four Mixed Integer Linear Program (MILP) formulations are proposed, which can be globally solved in a computationally effective manner using readily available MILP solvers. Our proposed formulations are tested on the Israeli Water Supply System (IWSS), which presents a unique challenge due to the inclusion of the seawater desalination array. In addition, this system must balance conventional and non-conventional water sources with varying qualities and characteristics. The results show that the proposed formulations provide a computationally efficient solution for the IWSS problem, allowing for the optimal utilization of different water sources in the IWSS.

Power Grid Infrastructural Resilience against Extreme Events

Extreme weather events are one of the main causes of large-scale power outages in distribution systems. The changing climate has led to an increase in the frequency and severity of these events, which, if not mitigated, are expected to lead to more instances of widespread outages and the severe societal and economic damages that ensue. Protecting the power grid against such events, which are high impact yet low frequency, requires a paradigm shift in grid design practices. In recent years, many researchers have focused on the resilience of the power grid against extreme weather events by proposing various grid hardening and/or redundancy solutions. The goal of this paper is to provide a survey of the literature related to the infrastructural resilience of the power grid against extreme events. Currently, no standard definitions or metrics exist for power grid resilience, and researchers adopt various models for quantifying and assessing it. Hence, a review of the most commonly used definitions and metrics for resilience is provided first, with a discussion of their advantages and disadvantages. Next, the paper presents an extensive and critical review of the solution methodologies proposed in the literature for improving the infrastructural resilience of the power grid. The shortcomings of the current solution methods and gaps in research are identified, followed by a discussion of the future directions in research.

Solving Inverse Electrocardiographic Mapping Using Machine Learning and Deep Learning Frameworks.

Electrocardiographic imaging (ECGi) reconstructs electrograms at the heart’s surface using the potentials recorded at the body’s surface. This is called the inverse problem of electrocardiography. This study aimed to improve on the current solution methods using machine learning and deep learning frameworks. Electrocardiograms were simultaneously recorded from pigs’ ventricles and their body surfaces. The Fully Connected Neural network (FCN), Long Short-term Memory (LSTM), Convolutional Neural Network (CNN) methods were used for constructing the model. A method is developed to align the data across different pigs. We evaluated the method using leave-one-out cross-validation. For the best result, the overall median of the correlation coefficient of the predicted ECG wave was 0.74. This study demonstrated that a neural network can be used to solve the inverse problem of ECGi with relatively small datasets, with an accuracy compatible with current standard methods.

Arc Routing with Time-Dependent Travel Times and Paths

Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, and heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules, and completion bounds to find optimal solutions for problems counting up to 75 services. From these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy.

Bridge-Block Partitioning Algorithm for Speeding Up Analysis of Water Distribution Systems

Many water distribution system (WDS) solution methods have been developed to perform demand-driven steady-state analysis. These methods are used to solve the nonlinear system of equations that model a WDS. WDS networks have structural properties that can often be exploited to speed up these solution methods. One solution method that exploits these structural properties is the forest-core partitioning algorithm that was proposed as a preprocessing and postprocessing method that can be used to separate the network into a linear forest component and a nonlinear core component. This paper presents a complementary method for preprocessing and postprocessing called the bridge-block partitioning algorithm (BBPA). This method further partitions the core component of the network into a number of linear bridge components and a number of nonlinear block components. The use of BBPA to partition a WDS network provides significant advantages over current solution methods in terms of both speed and solution reliability.

A Nonparametric GMM Series Approach to Solving Multi-equation Asset Pricing Models with Recursive Preferences

In an exchange economy with recursive preferences (Epstein and Zin, 1989), we propose a novel nonparametric generalized method of moment (GMM) series approach to estimate unknown policy functions which are recursively specified in a system of nonlinear conditional expectation models simultaneously as opposed to sequentially, thereby avoiding accumulation of approximation errors. Unlike current numerical solution methods, this new method does not require the imposition of tight auxiliary assumptions on the conditional distributions or matching moments of state variables and thus avoids spurious model conclusions due to mis-specification errors on state dynamics. Because there is an infinite number of moments and parameters due to series approximations, we propose a series continuously updated estimator (CUE) and establish a new result on consistency and asymptotic normality, which further helps facilitate rigorous inference on general equilibrium models in the presence of misspecified state variables or those with unknown dynamics. Three simulation studies are considered, and our new method has been proven to perform reasonably well in the finite sample in comparison with popular numerical solution methods.

Data-Driven Look-Ahead Unit Commitment Considering Forbidden Zones and Dynamic Ramping Rates

Look-ahead unit commitment (LAUC) is recently introduced among independent system operators (ISOs) in the U.S. to increase generation capacity by committing more generators after day-ahead unit commitment when facing various uncertainties in the power system operations. However, as the share of intermittent renewable energy increases significantly in the power generation portfolio, the load continues to fluctuate, and unexpected events and market behaviors happen nowadays, the ISOs are facing new critical challenges to maintain the reliability of power system. To systematically manage these uncertainties and corresponding challenges, new advanced approaches are urgently required to improve current LAUC models and solution methods. Therefore, in this paper, we first propose a new formulation to represent forbidden zones and dynamic ramping rate limits, which help capture the system operation status more accurately and hedge against the uncertainties more effectively, and then correspondingly propose a data-driven risk-averse LAUC model. Our computational experiments show how the size of data influences operational decisions and how the inclusion of forbidden zones and dynamic ramping provide better decisions.

Solving a large multi-product production-routing problem with delivery time windows

Even though the joint optimization of sequential activities in supply chains is known to yield significant cost savings, the literature concerning optimization approaches that handle the real-life features of industrial problems is scant. The problem addressed in this work is inspired by industrial contexts where vendor-managed inventory policies are applied. In particular, our study is motivated by a meat producer whose supply chain comprises a single meat processing centre with several production lines and a fleet of vehicles that is used to deliver different products to meat stores spread across the country. A considerable set of characteristics, such as product family setups, perishable products, and delivery time windows, needs to be considered in order to obtain feasible integrated plans. However, the dimensions of the problem make it impossible to be solved exactly by current solution methods. We propose a novel three-phase methodology to tackle a large Production-Routing Problem (PRP) combining realistic features for the first time. In the first phase, we attempt to reduce the size of the original problem by simplifying some dimensions such as the number of products, locations and possible routes. In the second phase, an initial PRP solution is constructed through a problem decomposition comprising several inventory-routing problems and one lot-sizing problem. In the third phase, the initial solution is improved by different mixed-integer programming models which focus on small parts of the original problem and search for improvements in the production, inventory management and transportation costs. Our solution approach is tested both on simpler instances available in the literature and on real-world instances containing additional details, specifically developed for a European company’s case study. By considering an integrated approach, we achieve global cost savings of 21.73% compared to the company’s solution.

A greedy heuristic for shift minimization personnel task scheduling problem

Shift Minimization Personnel Task Scheduling Problem (SMPTSP) is assigning a given set of predetermined tasks (with known start and finish times) to a minimum number of heterogeneous workers with predetermined shifts. Each task can be performed only by a specific subset of workers. Every task must be assigned to a worker. A worker cannot perform more than one task at a time, and tasks cannot be pre-empted. SMPTSP is NP-hard, but there is practical interest in solving very large instances of it in ground crew scheduling of a large airline in a large airport. Recently, there have been a few papers reporting various solution methods for large instances of SMPTSP. However, solving very large instances of SMPTSP remains a challenge. In this paper, we propose a novel greedy heuristic solution method for SMPTSP. A reduced problem is solved iteratively by selecting the best possible assignment of tasks to one worker. We have tested the Greedy heuristic method on 3 sets of available large test problems. The results show that the heuristic method performs well relative to the current solution methods, and has the added advantage of being able to solve very large instances fast.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics.

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

Ultra-precise detection of mutations by droplet-based amplification of circularized DNA

BackgroundNGS (next generation sequencing) has been widely used in studies of biological processes, ranging from microbial evolution to cancer genomics. However, the error rate of NGS (0.1 % ~ 1 %) is still remaining a great challenge for comprehensively investigating the low frequency variations, and the current solution methods have suffered severe amplification bias or low efficiency.ResultsWe creatively developed Droplet-CirSeq for relatively efficient, low-bias and ultra-sensitive identification of variations by combining millions of picoliter uniform-sized droplets with Cir-seq. Droplet-CirSeq is entitled with an incredibly low error rate of 3 ~ 5 X 10-6. To systematically evaluate the performances of amplification uniformity and capability of mutation identification for Droplet-CirSeq, we took the mixtures of two E. coli strains as specific instances to simulate the circumstances of mutations with different frequencies. Compared with Cir-seq, the coefficient of variance of read depth for Droplet-CirSeq was 10 times less (p = 2.6 X 10-3), and the identified allele frequency presented more concentrated to the authentic frequency of mixtures (p = 4.8 X 10-3), illustrating a significant improvement of amplification bias and accuracy in allele frequency determination. Additionally, Droplet-CirSeq detected 2.5 times genuine SNPs (p < 0.001), achieved a 2.8 times lower false positive rate (p < 0.05) and a 1.5 times lower false negative rate (p < 0.001), in the case of a 3 pg DNA input. Intriguingly, the false positive sites predominantly represented in two types of base substitutions (G- > A, C- > T). Our findings indicated that 30 pg DNA input accommodated in 5 ~ 10 million droplets resulted in maximal detection of authentic mutations compared to 3 pg (p = 1.2 X 10-8) and 300 pg input (p = 2.2 X 10-3).ConclusionsWe developed a method namely Droplet-CirSeq to significantly improve the amplification bias, which presents obvious superiority over the currently prevalent methods in exploitation of ultra-low frequency mutations. Droplet-CirSeq would be promisingly used in the identification of low frequency mutations initiated from extremely low input DNA, such as DNA of uncultured microorganisms, captured DNA of target region, circulation DNA of plasma et al, and its creative conception of rolling circle amplification in droplets would also be used in other low input DNA amplification fields.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-016-2480-1) contains supplementary material, which is available to authorized users.

A Scalable Framework to Choose Sellers in E-Marketplaces Using POMDPs

In multiagent e-marketplaces, buying agents need to select good sellers by querying other buyers (called advisors). Partially Observable Markov Decision Processes (POMDPs) have shown to be an effective framework for optimally selecting sellers by selectively querying advisors. However, current solution methods do not scale to hundreds or even tens of agents operating in the e-market. In this paper, we propose the Mixture of POMDP Experts (MOPE) technique, which exploits the inherent structure of trust-based domains, such as the seller selection problem in e-markets, by aggregating the solutions of smaller sub-POMDPs. We propose a number of variants of the MOPE approach that we analyze theoretically and empirically. Experiments show that MOPE can scale up to a hundred agents thereby leveraging the presence of more advisors to significantly improve buyer satisfaction.

Solving intertemporal CGE models in parallel using a singly bordered block diagonal ordering technique

The paper introduces a direct ordering method that employs a special feature of an intertemporal Computable General Equilibrium (CGE) model to reorder its first-order partial derivative matrix into a Singly Bordered Block Diagonal (SBBD) form. The matrix can then be decomposed into LU form and solved in parallel. With this method, the numerical results from the paper show a substantial advantage in computational time and memory use for parallel solutions of intertemporal CGE models in comparison to current serial solution methods. A solution for an intertemporal and regional model of the Vietnamese economy is provided as an example and comparator for the different methods.

A Continuous-Time Examination of End-of-Life Parts Acquisition With Limited Customer Information

Manufacturers often encounter difficulties in supplying an adequate number of spare parts for a product that is in its post-production phase. Current solution methods for optimal spare part order amounts use assumptions that require knowledge of the number of products in operation at any time t. In the business situation presented here, the manufacturer only has knowledge of the part and product failure rates and a probability distribution on the number of products still in operation; unless the manufacturer and customer have a close working relationship, it is likely that this information is all that the manufacturer will have available in a typical business environment. We model time-discounted revenues and costs as a function of the spare parts order amount. We consider two different versions of the problem—incremental replenishment and no replenishment—that operate by determining the rate of change of the total profit with respect to the order amount q.

SOLVING THE SAILING PROBLEM WITH A NEW PRIORITIZED VALUE ITERATION

In this paper we tackle the sailing strategies problem, a stochastic shortest-path Markov decision process. The problem of solving large Markov decision processes accurately and quickly is challenging. Because the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings, but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm, which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose improved value iteration algorithms based on Dijkstra's algorithm for solving shortest path Markov decision processes. The experimental results on a stochastic shortest-path problem show the feasibility of our approach.