Two-level Algorithm Research Articles

Exponential error reduction for glueball calculations using a two-level algorithm in pure gauge theory

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional SU(3) pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multilevel method. We discuss the physical distance at which the multilevel sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels. Published by the American Physical Society 2024

Distributed Nonconvex Optimization for Control of Water Networks with Time-coupling Constraints

AbstractIn this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are exacerbated by the transition between pressure and water quality controls. The resulting optimization problem is a nonconvex, nonlinear program with nonseparable structure across time steps. This problem proves challenging for state-of-the-art nonlinear solvers, often precluding their direct use for near real-time control in large-scale networks. To overcome this computational burden, we investigate a distributed optimization approach based on the alternating direction method of multipliers (ADMM). In particular, we implement and evaluate two algorithms: a standard ADMM scheme and a two-level variant that provides theoretical convergence guarantees for our nonconvex problem. We use a benchmarking water network and a large-scale operational network in the UK for our numerical experiments. The results demonstrate good convergence behavior across all problem instances for the two-level algorithm, whereas the standard ADMM approach struggles to converge in some instances. With an appropriately tuned penalty parameter, however, both distributed algorithms yield good quality solutions and computational times compatible with near real-time (e.g. hourly) control requirements for large-scale water networks.

A study of jamming resource allocation based on a hyperheuristic framework

There are massive data and rapidly changing battlefield situations in modern electronic warfare, which is a challenge to jamming resource allocation. It is difficult for the existing optimization algorithms to balance optimization capability and calculation speed at the same time. Above all, this study designs a fuzzy multiattribute evaluation model based on behavioral characteristics. The model comprehensively integrates the characteristics of signal behavior, motion behavior, and external intelligence and can effectively deal with unknown threat signals. Then, this study proposes an improved genetic selection electronic warfare operator (EWO) hyperheuristic (GAEWHH) algorithm. As an emergent optimization algorithm, the HH framework has not previously been applied to the problem of jamming resource allocation. This is a two-level algorithm framework that can isolate problem domains. The high level uses an improved genetic algorithm to search the heuristic space, and four EWOs based on the problem domain are designed for the low level to search the solution space. Combining different EWOs can change the population diversity, evolution direction, and algorithm complexity of the GAEWHH algorithm, which improves the algorithm performance to meet battlefield situation requirements. The experiment shows that for large-scale problems, the GAEWHH algorithm is better than the mainstream evolutionary algorithm in terms of optimization capability and better than Google OR-Tools in terms of calculation speed. In this way, the GAEWHH algorithm achieves a balance between optimization capability and calculation speed.

Deflated domain decomposition method for structural problems

The paper presents a fast and stable solver algorithm for structural problems. The point is the distance between the eigenvector of the constrained stiffness matrix and the unconstrained matrix. The coarse motions are close to the kernel of the unconstrained matrix. We use lower-frequency deformation modes to construct an iterative solver algorithm through domain decomposition expressing near-rigid-body motions, deflation algorithms, and two-level algorithms. We remove the coarse space from the solution space and hand over the iteration space to the fine space. Our solver is parallelized, and the solver thus has two sets of domain decomposition. One decomposition generates the coarse space, and the other is for parallelization. The basic framework of the solver is the parallel conjugate gradient (CG) method on the fine space. We use the CG method for the basic framework instead of the (simplest) domain decomposition method. We conducted benchmark tests using elastic static analysis for thin plate models. A comparison with the standard CG solver results shows the new solver’s high-speed performance and remarkable stability.

An ADMM-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow

When optimizing electric power system operational decisions, it is of great importance to prevent potential failures in both the system operation and the optimization algorithm. In “An Alternating Direction Method of Multipliers-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow,” Gholami, Sun, Zhang, and Sun propose a novel two-level algorithm that (1) effectively prevents power system operational failures through consideration of impactful contingencies and (2) guarantees convergence when parallelized on a computing cluster with multiple nodes. Extensive numerical experiments suggest that the proposed algorithm is able to provide high-quality feasible solutions under the time limit of 10–45 minutes for various synthetic and industrial networks with up to 30,000 buses and 22,000 contingencies, comparable with the size of the U.S. power grid.

Progressive Classifier Mechanism for Bridge Expansion Joint Health Status Monitoring System Based on Acoustic Sensors.

The application of IoT (Internet of Things) technology to the health monitoring of expansion joints is of great importance in enhancing the efficiency of bridge expansion joint maintenance. In this study, a low-power, high-efficiency, end-to-cloud coordinated monitoring system analyzes acoustic signals to identify faults in bridge expansion joints. To address the issue of scarce authentic data related to bridge expansion joint failures, an expansion joint damage simulation data collection platform is established for well-annotated datasets. Based on this, a progressive two-level classifier mechanism is proposed, combining template matching based on AMPD (Automatic Peak Detection) and deep learning algorithms based on VMD (Variational Mode Decomposition), denoising, and utilizing edge and cloud computing power efficiently. The simulation-based datasets were used to test the two-level algorithm, with the first-level edge-end template matching algorithm achieving fault detection rates of 93.3% and the second-level cloud-based deep learning algorithm achieving classification accuracy of 98.4%. The proposed system in this paper has demonstrated efficient performance in monitoring the health of expansion joints, according to the aforementioned results.

Global Maximum Power Point Tracking in Dynamic Partial Shading Conditions Using Ripple Correlation Control

Under partial shading conditions (PSC), a photovoltaic (PV) system may produce multiple local maximum power points (LMPPs). Traditional maximum power point tracking (MPPT) techniques are not able to distinguish between LMPPs and the global maximum power point (GMPP), leading to sub-optimal PV array power outputs. This article proposes a two-level algorithm for tracking the GMPP. The first level is a discretized global search, allowing the system to hone in on the neighborhood containing the GMPP. In the second level, the well-known ripple correlation control (RCC) technique is used to swiftly converge to the GMPP. Using the proposed two-level algorithm, it can be guaranteed that the GMPP is successfully found and tracked. A benchmark analysis involving other state of the art algorithm reveals that the proposed method is the most superior algorithm in terms of accurately and swiftly tracking the global maximum power point in dynamic partial shading conditions. The algorithm is implemented with a simple inexpensive microcontroller, and therefore can be readily adopted in a myriad of dynamic partial shading applications.Therefore, this work allows the penetration of future photovoltaic power conversion systems to be more efficient.

Conflict-Based Search for Optimal Multi-Agent Pathfinding

We are assumed a customary of mediators in the multi-agent pathfinding problem (MAPF), each of which has its own start and goal positions. The objective is to discovery paths for each agent without causing any collisions. The majority of previous work on the optimal solution to this issue has useful single-agent exploration variations of the A* algorithm and treated each agent as a single "joint agent." The Conflict Based Search (CBS) optimum multi-agent pathfinding algorithm is the subject of this paper. CBS has two layer algorithm that does not use a single "joint agent" model to solve the problem. A Conflict Tree (CT), which is a tree based on conflicts between individual agents, is the high-level search engine. In the CT, each node represents a set of constraints on the agents' motion. To meet the high-level CT node's constraints, quick single-agent searches are carried out at the low level. CBS can frequently examine fewer states than A* while still maintaining optimality thanks to this two-level formulation. We discuss CBS's advantages and disadvantages. The Meta-Agent CBS (MA-CBS) algorithm is also discussed.MA-CBS is a broadening of CBS.MA-CBS, in contrast to basic CBS, permits low-level single-agent searches. Instead, agents can be combined into small groups of joint agents with MA-CBS. Performance is further enhanced and some of the drawbacks of basic CBS are reduced as a result. In point of fact, MA-CBS is a framework that can be layered on top of any MAPF solver that is both complete and optimal to boost its performance. A speedup of up to an order of magnitude over previous methods is demonstrated by experimental results on various problems. We are given a set of agents in the multi-agent pathfinding problem (MAPF), each of which has its own start and goal positions. The objective is to find paths for each agent without causing any collisions. The majority of previous work on the optimal solution to this issue has applied single-agent search variants of the A* algorithm and treated each agent as a single "joint agent." The Conflict Based Search (CBS) optimal multi-agent pathfinding algorithm is the subject of this paper. CBS is a two-level algorithm that does not use a single "joint agent" model to solve the problem. A Conflict Tree (CT), which is a tree based on conflicts between individual agents, is the high-level search engine. In the CT, each node represents a set of constraints on the agents' motion. To meet the high-level CT node's constraints, quick single-agent searches are carried out at the low level. CBS can frequently examine fewer states than A* while still maintaining optimality thanks to this two-level formulation. We discuss CBS's advantages and disadvantages. The Meta-Agent CBS (MA-CBS) algorithm is also discussed.MA-CBS is a broadening of CBS.MA-CBS, in contrast to basic CBS, permits low-level single-agent searches. Instead, agents can be combined into small groups of joint agents with MA-CBS. Performance is further enhanced and some of the drawbacks of basic CBS are reduced as a result. In point of fact, MA-CBS is a framework that can be layered on top of any MAPF solver that is both complete and optimal to boost its performance. A speedup of up to an order of magnitude over previous methods is demonstrated by experimental results on various problems.

Iterative two-level algorithm for nonsymmetric or indefinite elliptic problems

In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional two-grid algorithm, but its “fine space” uses the higher order finite element space under the coarse grid. Therefore, the iterative two-level algorithm only needs one grid, and the computational cost is much lower than the traditional iterative two-grid algorithm. Finally, compared with the traditional two-grid algorithm, numerical experiments show that the computational cost is lower to achieve the same convergence order.

A two-level distributed algorithm for nonconvex constrained optimization

This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the recent development of distributed algorithms for nonconvex programs, highly complicated constraints still pose a significant challenge in theory and practice. We first identify some difficulties with the existing algorithms based on the alternating direction method of multipliers (ADMM) for dealing with such problems. We then propose a reformulation that enables us to design a two-level algorithm, which embeds a specially structured three-block ADMM at the inner level in an augmented Lagrangian method framework. Furthermore, we prove the global and local convergence as well as iteration complexity of this new scheme for general nonconvex constrained programs, and show that our analysis can be extended to handle more complicated multi-block inner-level problems. Finally, we demonstrate with computation that the new scheme provides convergent and parallelizable algorithms for various nonconvex applications, and is able to complement the performance of the state-of-the-art distributed algorithms in practice by achieving either faster convergence in optimality gap or in feasibility or both.

Resilience assessment and enhancement of urban road networks subject to traffic accidents: a network-scale optimization strategy

This study is aimed at investigating the resilience degradation caused by traffic accidents and developing relevant resilience optimization strategies. A two-stage accident resilience triangle framework was proposed by comparing the differences between natural disasters and traffic accidents. To maximize system resilience, a network-wide traffic signal optimization model was presented. Spillback constraints and equilibrium constraints were established to enhance the capacity of urban-road networks to minimize congestion escalation, in addition to rapid recovery. A two-level algorithm based on greedy strategy and gradient descent was designed to solve the proposed non-linear programming model. In the experiment, a virtual road network was constructed based on the Simulation of Urban Mobility (SUMO) platform for validation and sensitivity analysis. The experimental results revealed that: (1) Compared to the traditional resilience framework, the proposed two-stage accident resilience framework can more reasonably describe the change mechanism of road network resilience under disturbance. (2) The proposed resilience-based traffic signal optimization model improved the system resilience under different conditions of traffic demand, accident severity, and rescue time in terms of the maximum performance degradation and recovery time. Precisely, the resilience loss is reduced by a maximum of 1.4%. Finally, the proposed model was further implemented with field data. The resilience improvement was significant during the evening rush hour. The results of this study contribute toward transportation resilience research and accident rescue strategies with respect to traffic management and control.

A Jordan-Schur Algorithm for Solving Sylvester and Lyapunov Matrix Equations

This paper presents a version of the Bartels-Stewart algorithm for solving the Sylvester and Lyapunov equations that utilizes the Jordan-Schur form of the equation matrices. The Jordan-Schur form is a type of Schur form which contains additional information about the Jordan structure of the corresponding matrix. This information can be used to solve more efficiently the Sylvester and Lyapunov equations in some cases. A two-level algorithm is implemented which allows us to find directly non-scalar blocks of the solution matrix. These blocks have sizes that are determined by the Weyr characteristics associated with the eigenvalues of the equation matrices. In the case of large elements of the Weyr characteristics associated with multiple eigenvalues, the determination of the solution blocks can be done more efficiency. Also, the blocks equations can be more appropriate in solving the Sylvester and Lyapunov equations in the case of parallel computations. Results obtained from numerical experiments confirm that the accuracy of the new algorithm is comparable with the accuracy of the Bartels-Stewart algorithm.

MGRIT-Based Multi-Level Parallel-in-Time Electromagnetic Transient Simulation

In this paper, we present an approach for multi-level parallel-in-time (PinT) electromagnetic transient (EMT) simulation. We evaluate the approach in the context of power electronics system-level simulation. While PinT approaches to power electronics simulations based on two-level algorithms have been thoroughly explored in the past, multi-level PinT approaches have not yet been investigated. We use the multigrid-reduction-in-time (MGRIT) method to parallelize a dedicated EMT simulation tool which is capable of switching between different converter models as it operates. The presented approach yields a time-parallel speed-up of up to 10 times compared to the sequential-in-time implementation. We also show that special care has to be taken to synchronize the time grids with the electronic components’ switching periods, indicating that further research into the usage of different models from adequate model hierarchies is necessary.

Flex Distribution for Bounded-Suboptimal Multi-Agent Path Finding

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents that minimize the sum of path costs. EECBS is a leading two-level algorithm that solves MAPF bounded-suboptimally, that is, within some factor w of the minimum sum of path costs C*. It uses focal search to find bounded-suboptimal paths on the low level and Explicit Estimation Search (EES) to resolve collisions on the high level. EES keeps track of a lower bound LB on C* to find paths whose sum of path costs is at most w LB in order to solve MAPF bounded-suboptimally. However, the costs of many paths are often much smaller than w times their minimum path costs, meaning that the sum of path costs is much smaller than w C*. In this paper, we therefore propose Flexible EECBS (FEECBS), which uses a flex(ible) distribution of the path costs (that relaxes the requirement to find bounded-suboptimal paths on the low level) in order to reduce the number of collisions that need to be resolved on the high level while still guaranteeing to solve MAPF bounded suboptimally. We address the drawbacks of flex distribution via techniques such as restrictions on the flex distribution, restarts of the high-level search with EECBS, and low-level focal-A* search. Our empirical evaluation shows that FEECBS substantially improves the efficiency of EECBS on MAPF instances with large maps and large numbers of agents.

NCA-GA-SVM: A new two-level feature selection method based on neighborhood component analysis and genetic algorithm in hepatocellular carcinoma fatality prognosis.

Hepatocellular carcinoma (HCC) is one of the major challenges facing biomedical research. Despite the high lethality, methods to predict mortality for this type of aggressive malignant tumor are insufficient. Machine learning is recognized by many authors as a valuable, yet poorly studied tool in this field. Undoubtedly, searching for new feature selection methods is significant in building an effective machine-learning model. In this study, we propose the novel hybrid model using neighborhood components analysis, genetic algorithm and support vector machine classifier (NCA-GA-SVM). Because SVM works with default parameters characterized by low classification results, we decided to use GA for the proper optimization and feature selection. As reported in the available literature, NCA and GA obtain high classification results. Here, we decided to combine these approaches, building a two-level algorithm for HCC fatality prognosis. We used a well-known dataset collected from 165 patients at Coimbra's Hospital and University Center, Portugal. Our results revealed 96.36% classification accuracy and 95.52% F1-score. Additionally, we compared all data for these metrics published so far. We demonstrated that our algorithm achieved the highest accuracy and can be successfully applied for the assessment of hepatocellular carcinoma mortality in the future. Our findings bring methodological value for future HCC studies and emphasize the possibility of using machine-learning techniques to improve the quality of medical decisions.

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a two-level algorithm. On the high-order level, the CGKS with high-order compact initial reconstruction is used to evolve both cell-averaged conservative flow variables and their gradients at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two- and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has been achieved by the approach in comparison with the explicit counterpart.

Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations.

Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the m iterations on a coarse grid and correction once on a fine grid. A one-level Oseen iterative method on a fine mesh is further studied under a weak uniqueness condition. Moreover, the stability and error estimate are rigorously carried out, which prove that the proposed methods are stable and effective. Finally, some numerical examples corroborate the effectiveness of our theoretical analysis and the proposed methods.

Applied heat exchanger network retrofit for multi-period processes in industry: A hybrid evolutionary algorithm

In Swiss process industry, process integration is often applied to retrofit existing plants with multi-period operation. Such periods may experience a high degree of variation in temperature or mass flow. Some process streams may not exist in every period or are soft streams. The resulting retrofitted network needs to be able to ensure feasible heat transfer in each period by the integration of mixer configurations to control the temperature. These attributes increase the complexity of the solution space. Hence, this work proposes an evolutionary two-level algorithm for heat exchanger network retrofit. Genetic algorithm is used for topology optimization and a differential evolution algorithm handles the heat loads. The algorithm is extended with practical constraints such as a maximum number of heat exchangers. Explicit mixer temperature calculations are implemented using the Lambert W-function. The algorithm was successfully applied to an industrial case study, reducing its total annual cost by approximately 66%.

Fairness-Aware Task Offloading and Resource Allocation in Cooperative Mobile-Edge Computing

Currently, mobile-edge computing (MEC) becomes a burgeoning paradigm to tackle the contradiction between delay-sensitive tasks and resource-limited mobile/IoT devices. However, a single MEC server is usually not able to satisfy the heavy computation tasks considering its limited storage and computation capability. Thus, the cooperation of MEC servers provides an effective way to accommodate this issue. In this article, we study the joint task offloading and resource allocation problem in the scenario with cooperative MEC servers. We first define resource fairness among IoT devices from the user experience perspective. Then, we formulate a joint optimization problem by taking into account the system efficiency and fairness, which is shown to be NP-hard and thus, intractable. To solve this problem, we propose a two-level algorithm: the upper level algorithm, inspired by evolutionary strategies, is able to search superior offloading schemes globally; while the lower level algorithm, taking into account fairness among all tasks, is able to generate resource allocation schemes that make full use of server resources. Comprehensive evaluation results demonstrate the efficiency and fairness of the proposed algorithm compared to baselines.

E-Commerce Credit Risk Assessment Based on Fuzzy Neural Network.

In this paper, we propose a cooperative strategy-based self-organization mechanism to reconstruct the network. The mechanism includes a comprehensive evaluation algorithm and structure adjustment mechanism. The self-organization mechanism can be carried out simultaneously with the parameter optimization process. By calculating the similarity and independent contribution of normative neurons, the effectiveness of fuzzy rules can be jointly evaluated, and effective structural changes can be realized. Moreover, this mechanism should not set the threshold in advance in practical application. In order to optimize the parameters of SC-IR2FNN, we developed a parameter optimization mechanism based on an interaction strategy. The parameter optimization mechanism based on a joint strategy, namely multilayer optimization engine, can split SC-IR2FNN parameters into nonlinear and linear parameters for joint optimization. The nonlinear parameters are optimized by an advanced two-level algorithm, and the linear parameters are updated with the minimum biological multiplication. Two parameter optimization algorithms optimize nonlinear and linear parameters, reduce the computational complexity of SC-IR2FNN, and improve the learning rate. Using the principal component factor analysis method, seven representative common factors are selected to replace the original variables, which include the profitability factor of the financing enterprise, the solvency factor of the financing enterprise, the profitability factor of the core enterprise, the operation guarantee factor, and the growth ability of the financing enterprise. Factors, supply chain online degree factors, financing enterprise quality, and cooperation factors, can well measure the credit risk of online supply chains. The logistic model shows that the profitability factor of the financing company, the debt repayment factor of the financing company, and the profitability of the core company are three factors that have a significant impact on the credit risk of online supply chain finance. Based on the improved credit calculation model, we developed an online clue risk calculation. This method is based on site conditions and can evaluate credit risk. From the test results, the improved credit scoring system is the result of facing speculative and circular credit fraud and implies that the traders of risk commentators are in a leading position in each electronic device. The results show that risk analysis is effective in any case.