Set Of Solutions Research Articles

Digital Resource Management and Sharing for Teaching and Learning in Higher Education by Integrating Multiple Data Chain Networks

Abstract In this paper, we construct a GCCP multivariate datalink network for teaching and learning resource sharing through the Generalized Control Chaining Primary Protocol (GCCP) combined with mutual cooperative services among the physical, data link and network layers for resource sharing. The solution set is mapped to the distributed dynamic self-organizing network data links through Nash equilibrium. Attribute descriptions for the necessary digital teaching resources are provided in a P2P system for sharing resources in large-scale heterogeneous teaching environments. Finally, simulations are conducted under the Group Service Control Protocol (GCCP) for teaching resource sharing to verify the effectiveness of the scheduling and management model for digital teaching resources. According to the results, the system with a multivariate datalink network maintains an average cluster size of 5 nodes. The response time of the system increases significantly with the increase of scale when RP(k)C-Grid takes k as 10,20,30,40,50 respectively. This paper effectively manages and maintains the entire digital resource management system for teaching and learning in universities, making it more stable and efficient.

Inertia matrix identification of combined spacecraft using a deep neural network with optimized network structure

After the space robot captures the out-of-control spacecraft, they form a combined spacecraft. For the parameter identification problem of combined spacecraft with complex angular rate measurement noise, deep learning could provide a new solution, due to its ability to extract robust features from noisy data. However, the deep neural network (DNN) has substantial computing resource requirements, which restricts its application in spacecraft systems. To solve the above problems, an inertia matrix identification approach combining a structure optimization strategy of DNN is proposed to identify the inertia matrix in the presence of complex measurement noise using the DNN with optimized structure. The attitude dynamics of combined spacecraft are firstly derived, and the identification problem considering complex measurement noise is described. Based on the dynamics model, the construction process of DNN for accurately identifying the inertia matrix is proposed. A structure optimization strategy of DNN is then designed to optimize the structure of DNN for increasing computing efficiency. This strategy provides a whole set of solutions including the structure selection of the initial DNN, the redundant neurons pruning process, and the end-of-optimization condition. By combining the proposed construction process of DNN, the structure of the DNN is finally optimized by iterating the structured pruning and retraining step. The performance of the proposed DNN with optimized network structure is verified on a testing set with complex measurement noise. The results show that the proposed approach can accurately identify the inertia matrix of combined spacecraft, and meanwhile greatly improve the computing efficiency of DNN.

Critical sets of solutions of elliptic equations in periodic homogenization

AbstractIn this paper we study critical sets of solutions of second‐order elliptic equations in divergence form with rapidly oscillating and periodic coefficients. Under some condition on the first‐order correctors, we show that the ‐dimensional Hausdorff measures of the critical sets are bounded uniformly with respect to the period ε, provided that doubling indices for solutions are bounded. The key step is an estimate of “turning” of an approximate tangent map, the projection of a non‐constant solution onto the subspace of spherical harmonics of order ℓ, when the doubling index for on a sphere is trapped between and , for r between 1 and a minimal radius . This estimate is proved by using harmonic approximation successively. With a suitable L2 renormalization as well as rescaling we are able to control the accumulated errors introduced by homogenization and projection. Our proof also gives uniform bounds for Minkowski contents of the critical sets.

A multi-instance multi-label learning algorithm based on radial basis functions and multi-objective particle swarm optimization

Radial basis function (RBF) neural networks for Multi-Instance Multi-Label (MIML) directly can exploit the connections between instances and labels so that they can preserve useful prior information, but they only adopt Gaussian radial basis function as their RBF whose parameters are difficult to determine. In this paper, parameters can be obtained by multi-objective optimization methods with multi performance measures treated as objectives, specifically, parameter estimation of different RBFs by an improved multi-objective particle swarm optimization (MOPSO) is proposed where Recall rate and Precision rate are chosen to obtain the most desirable Pareto optimal solution set. Furthermore, share-learning factor is proposed to modify the particle velocity in standard MOPSO to improve the global search ability and group cooperative ability. It is experimentally demonstrated that the proposed method can estimate the reliable parameters of different RBFs, and it is also very competitive with the state of art MIML methods.

Stability analysis for set-valued inverse mixed variational inequalities in reflexive Banach spaces

This work is devoted to the analysis for a new class of set-valued inverse mixed variational inequalities (SIMVIs) in reflexive Banach spaces, when both the mapping and the constraint set are perturbed simultaneously by two parameters. Several equivalence characterizations are given for SIMVIs to have nonempty and bounded solution sets. Based on the equivalence conditions, under the premise of monotone mappings, the stability result for the SIMVIs is obtained in the reflexive Banach space. Furthermore, to illustrate the results, an example of the traffic network equilibrium control problem is provided at the end of this paper. The results presented in this paper generalize and extend some known results in this area.

Linear inverse problems with Hessian–Schatten total variation

In this paper, we characterize the class of extremal points of the unit ball of the Hessian–Schatten total variation (HTV) functional. The underlying motivation for our work stems from a general representer theorem that characterizes the solution set of regularized linear inverse problems in terms of the extremal points of the regularization ball. Our analysis is mainly based on studying the class of continuous and piecewise linear (CPWL) functions. In particular, we show that in dimension d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}, CPWL functions are dense in the unit ball of the HTV functional. Moreover, we prove that a CPWL function is extremal if and only if its Hessian is minimally supported. For the converse, we prove that the density result (which we have only proven for dimension d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}) implies that the closure of the CPWL extreme points contains all extremal points.

Collaborative Multiobjective Evolutionary Algorithms in the Search of Better Pareto Fronts: An Application to Trading Systems

Technical indicators use graphic representations of datasets by applying various mathematical formulas to financial time series of prices. These formulas comprise a set of rules and parameters whose values are not necessarily known and depend on many factors, such as the market in which they operate, the size of the time window, and so on. This paper focuses on the real-time optimization of the parameters applied for analyzing time series of data. In particular, we optimize the parameters of some technical financial indicators. We propose the combination of several Multiobjective Evolutionary Algorithms. Unlike other approaches, this paper applies a set of different Multiobjective Evolutionary Algorithms, collaborating to construct a global Pareto Set of solutions. Solutions for financial problems seek high returns with minimal risk. The optimization process is continuous and occurs at the same frequency as the investment time interval. This technique permits the application of the non-dominated solutions obtained with different MOEAs at the same time. Experimental results show that Collaborative Multiobjective Evolutionary Algorithms obtain up to 22% of profit and increase the returns of the commonly used Buy and Hold strategy and other multi-objective strategies, even for daily operations.

Sustainability-aware collaborative service composition and recommendation based on multi-attribute correlations

In the context of network collaborative manufacturing and green manufacturing, some researchers have begun to focus on collaboration-awareness or sustainability-awareness service composition separately. However, service collaboration and sustainable performance are interrelated in the service business implementation, so they should be considered simultaneously when establishing service composition to ensure efficient service delivery. In this study, a sustainability-aware collaborative service composition and service recommendation (SCSR) model is formulated, aiming to pursue maximum customer service quality, as well as the synergy effect and eco-efficiency of combined services. Given the interdependencies inherent in service attributes, DEMATEL (Decision Making Trial and Evaluation Laboratory) is presented to acquire the influential weights for aggregating multiple service attributes into the service decisions. To recommend suitable composite services for core enterprises, NSGA-II with two initialization methods and three neighborhood structures is first proposed to produce high-quality solution sets regarding service composition. Then TODIM (an acronym in Portuguese of Interactive and Multi-Criteria Decision Making) is utilized to evaluate the relative dominance of these service composition alternatives under the psychological behavior of the decision-maker. Numerous experiments demonstrate the effectiveness of the improved NSGA-II in handing the SCSR issue. Furthermore, the necessity of considering attribute interrelationships and synergy effects in service composition is verified.

The Best Compromise Solution for Multi-objective Programming Problems

This paper focuses on multi-objective optimization problems that are an important part of operations research. This part is concerned with mathematical optimization problems involving two or more interdependent objectives to be optimized simultaneously. Thus, there is not a single optimal solution for multi-objective problems, but a set of solutions that represents the compromise (Pareto-optimal, efficient, non-dominated, trade-off, or non-inferior) solutions and can be visualized as Pareto front in the objective space. The best solution of this set has the shortest distance to the ideal (utopian) solution, whereas the ideal solution optimizes all objective functions, which often cannot be found. The main contribution of this paper is to introduce some methods to find the best compromise solution. These methods depend on new calculations for the normal of objectives. They can help to reduce the overall computational distance of the searching process. Therefore, they are flexible and stable. Besides, some numerical examples are presented to demonstrate the effectiveness of proposed methods with discussing their similarities and differences. The experimental results show that the proposed methods are effective and efficient for many different multi-objective (convex and non-convex) problems.

Multiobjective Electric Vehicle Charging Network Planning Considering Chance-Constraint on the Travel Distance for Charging

Electric vehicle charging stations (EVCSs) are important infrastructures to support sustainable development of electric vehicles (EVs), by providing convenient, rapid charging services. Therefore, the planning of electric vehicle charging network (EVCN) has attracted wide interest from both industry and academia. In this paper, a multiobjective planning model for EVCN is developed, where a fixed number of EVCSs are planned in the traffic network (TN) to achieve two objectives, i.e., minimizing both average travel distance for charging (TDfC) of EVs and investment costs of EVCN. According to the random characteristics of EVs’ TDfC, its constraint is presented as a chance constraint in the developed EVCN planning model. The nondominated sorting genetic Algorithm II with the constraint domination principle (NSGA-II-CDP) is customized to solve the developed multiobjective EVCN planning model, by designing a special coding scheme, a crossover operator, and a mutation operator. Then, a maximum gradient principle of investment revenue is designed to select the optimal planning strategy from the Pareto-optimal solution set, when taking the investment return ratio as primary consideration. A 25-node TN is used to justify the effectiveness of the developed methodology.

Seismic response of deep circular tunnels subjected to P-waves: Axial and transverse compression-extension

Body waves can intersect a tunnel at various angles and thus induce complex structural responses that, at a minimum, require a comprehensive understanding of all modes of tunnel deformation due to both P- and S-waves. The majority of studies in this field have focused on a single S-wave mode, ovaling or racking (where the waves impinge on a tunnel transversely with the direction of particle movement perpendicular to the tunnel axis). Significantly less work has been devoted to the other modes. This study introduces two sets of new analytical solutions, using the soil-structure interaction approach, to predict the P-wave modes of tunnel deformation: axial compression-extension and transverse compression-extension. The solutions account for both drained and undrained loading conditions, with both no-slip and full-slip interface conditions between the tunnel lining and the ground. 2-D and 3-D numerical simulations, both static and dynamic analyses, are performed to verify the analytical solutions and determine their applicable limits. The numerical analyses also provide insights into the effects of dynamic amplification on the tunnel cross section.

Greenhouse environmental control target constrained by discrete surface curvature and multi-objective optimization algorithm

Protected greenhouse provides a suitable micro-environment for crop growth, which enhances the quality and yield of agricultural products. How to optimize the greenhouse environment is currently a pressing issue in protected agriculture. In this research, we propose a new environmental control method from the perspectives of crop photosynthesis rate and environmental control cost. The photosynthesis rate data are collected from a nested experiment of tomatoes, and these data are combined with the support vector regression algorithm to establish a photosynthesis rate model. The cost function of greenhouse environmental control is established by theoretical calculation. The non-dominated solution sets of photosynthesis rate and control cost are obtained through an improved non-dominated sorting genetic algorithm Ⅱ. To determine the optimal solution among the numerous Pareto solutions, the geometric characteristics of the photosynthetic response surface are considered to constrain the control target. Then, a discrete surface curvature method is proposed to computer the constraint region. The intersection between the Pareto solutions and the constraint region is regarded as the environmental control target. The validation experiment demonstrates that the proposed method can effectively enhance photosynthetic accumulation and reduce control cost. Compared to the traditional saturation method, this method achieves a 53% cost reduction while still obtaining 89% photosynthetic accumulation. Compared to the U-chord method, this method increases photosynthetic accumulation by 12% with only a 3% increase in cost. The research has important implications for protected agriculture production.

A new kind of double phase elliptic inclusions with logarithmic perturbation terms I: Existence and extremality results

This paper is devoted to introduce a new double phase elliptic inclusion problem (DPEI) involving nonlinear and nonhomogeneous partial differential operator which has unbalanced growth and logarithmic perturbation terms, and two multivalued functions which are defined in the domain and its boundary. The main goal of this paper is to establish the existence and extremality results to the elliptic inclusion problem under consideration. More exactly, we give the definitions of weak solutions, subsolutions and supersolutions to (DPEI). Then, under the coercive setting, an existence theorem of weak solutions to (DPEI) is obtained by employing a surjectivity theorem for pseudomonotone operators. Moreover, in the noncoercive framework, we apply the method of sub-supersolution combined with the nonsmooth calculus analysis and truncation techniques to prove that (DPEI) has at least a weak solution within an ordered interval of sub-supersolution. Finally, when the constraint set K satisfies a lattice condition, the existence of smallest and greatest elements of solution set to (DPEI) is established.

Ripple spreading algorithm: a new method for solving multi-objective shortest path problems with mixed time windows

In emergency management, the transportation scheduling of emergency supplies and relief personnel can be regarded as the multi-objective shortest path problem with mixed time window (MOSPPMTW), which has high requirements for timeliness and effectiveness, but the current solution algorithms cannot simultaneously take into account the solution accuracy and computational speed, which is very unfavorable for emergency path decision-making. In this paper, we establish MOSPPMTW matching emergency rescue scenarios, which simultaneously enables the supplies and rescuers to arrive at the emergency scene as soon as possible in the shortest time and at the smallest cost. To solve the complete Pareto optimal surface, we present a ripple spreading algorithm (RSA), which determines the complete Pareto frontier by performing a ripple relay race to obtain the set of Pareto optimal path solutions. The proposed RSA algorithm does not require an initial solution and iterative iterations and only needs to be run once to obtain the solution set. Furthermore, we prove the optimality and time complexity of RSA and conduct multiple sets of example simulation experiments. Compared with other algorithms, RSA performs better in terms of computational speed and solution quality. The advantage is especially more obvious in the computation of large-scale problems. It is applicable to various emergency disaster relief scenarios and can meet the requirements of fast response and timeliness.

On Bilevel Monotone Inclusion and Variational Inequality Problems

In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are presented. These methods are equipped with inertial terms to improve their speed of convergence. The strong convergence results of the suggested methods are proved under some standard assumptions on the control parameters. Also, strong convergence results are achieved without prior knowledge of the operator norm. Finally, the main results of this research are applied to solve bilevel variational inequality problems, convex minimization problems, and image recovery problems. Some numerical experiments to show the efficiency of our methods are conducted.

Robust multi-objective building design optimization approach using NSGA-II algorithm considering weather and occupant uncertainties

A novel methodology is presented to evaluate how real-world operational uncertainties impact multi-objective building design optimization process. NSGA-II algorithm is applied across nine distinct operational scenarios, considering diverse weather datasets and energy usage patterns to optimize energy efficiency and thermal comfort in a residential building within India's hot and dry climate. The analysis considers 382,400 possible design options for each scenario. Using (10.5–12.5) % of model evaluations, NSGA-II significantly reduces Annual Cooling Energy Demand (ACED; 46.7%–58.7%) and Cooling Set-point Unmet Hours (CSUH; 70.92%–86.93%) to identify nine Pareto–Optimal solution sets. The final robust optimal design is confirmed by selecting the most repeated parameter settings, representing the highest robustness. Low thermal transmittance walls, double-glazed windows with a 10% window-to-wall ratio (WWR), deep overhangs, and a low solar heat gain coefficient are recognized as robust optimal building components. However, Air Conditioner (AC) sizing lacks robustness in minimizing energy demand across scenarios, requiring case-specific evaluation due to its sensitivity to weather and operational variations. Further, PAWN sensitivity analysis highlighted the substantial impact of WWR (KSWWR ∼ (0.46–0.66)) and wall type (KSWall ∼ (0.31–0.46)) on ACED and CSUH in chosen climate. AC operation is more important for predicting CSUH (KSAC ∼ 0.35) than ACED (KSAC ∼ 0.10).

Machine learning for carbonate formation drilling: Mud loss prediction using seismic attributes and mud loss records

Due to the complexity and variability of carbonate formation leakage zones, lost circulation prediction and control is one of the major challenges of carbonate drilling. It raises well-control risks and production expenses. This research utilizes the H oilfield as an example, employs seismic features to analyze mud loss prediction, and produces a complete set of pre-drilling mud loss prediction solutions. Firstly, 16 seismic attributes are calculated based on the post-stack seismic data, and the mud loss rate per unit footage is specified. The sample set is constructed by extracting each attribute from the seismic trace surrounding 15 typical wells, with a ratio of 8:2 between the training set and the test set. With the calibration results for mud loss rate per unit footage, the nonlinear mapping relationship between seismic attributes and mud loss rate per unit size is established using the mixed density network model. Then, the influence of the number of sub-Gausses and the uncertainty coefficient on the model's prediction is evaluated. Finally, the model is used in conjunction with downhole drilling conditions to assess the risk of mud loss in various layers and along the wellbore trajectory. The study demonstrates that the mean relative errors of the model for training data and test data are 6.9% and 7.5%, respectively, and that R2 is 90% and 88%, respectively, for training data and test data. The accuracy and efficacy of mud loss prediction may be greatly enhanced by combining 16 seismic attributes with the mud loss rate per unit footage and applying machine learning methods. The mud loss prediction model based on the MDN model can not only predict the mud loss rate but also objectively evaluate the prediction based on the quality of the data and the model.

Physically constrained learning of MOS capacitor electrostatics

In recent years, neural networks have achieved phenomenal success across a wide range of applications. They have also proven useful for solving differential equations. The focus of this work is on the Poisson–Boltzmann equation (PBE) that governs the electrostatics of a metal–oxide–semiconductor capacitor. We were motivated by the question of whether a neural network can effectively learn the solution of PBE using the methodology pioneered by Lagaris et al. [IEEE Trans. Neural Netw. 9 (1998)]. In this method, a neural network is used to generate a set of trial solutions that adhere to the boundary conditions, which are then optimized using the governing equation. However, the challenge with this method is the lack of a generic procedure for creating trial solutions for intricate boundary conditions. We introduce a novel method for generating trial solutions that adhere to the Robin and Dirichlet boundary conditions associated with the PBE. Remarkably, by optimizing the network parameters, we can learn an optimal trial solution that accurately captures essential physical insights, such as the depletion width, the threshold voltage, and the inversion charge. Furthermore, we show that our functional solution can extend beyond the sampling domain.

Over-the-Air Computation with Quantized CSI and Discrete Power Control Levels

In this paper, an Over-the-Air Computation (AirComp) scheme for fast data aggregation is considered. Multisource data are simultaneously transmitted by single-antenna mobile devices to a single-antenna fusion center (FC) through a wireless multiple-access channel. The optimal power levels at the devices and a postprocessing scaling function at the FC are jointly derived such that mean square error of the computation is minimized. Different than the existing approaches that rely on perfect channel state information (CSI) at the FC and assume that the devices’ optimal power levels can be selected from an infinite solution set, in the present paper, it is assumed that only quantized CSI is available at the FC and that the aforementioned optimal power levels lie in a finite discrete set of solutions. To derive the optimal power levels and FC’s scaling factor, a difficult nonconvex constrained optimization problem is formulated. An efficient and robust solution to quantization errors is developed via the deep reinforcement learning framework. Numerical results verify the good performance of the proposed approach while it exhibits a significant reduction in the required feedback.

Impacts of wildfires and strategies to accelerate secondary succession: A comprehensive analysis

Wildfires pose a significant and growing threat to ecosystems, leading to loss of biodiversity, water contamination, and alteration of habitats. This paper examines the devastating impacts of wildfires, with a focus on California, and explores the natural process of secondary succession in coastal forests. It further presents a comprehensive set of solutions to accelerate this process and mitigate the effects of wildfires. Strategies include immediate interventions like mulching, controlling invasive species through geo-spatial mapping, utilizing artificial structures such as seed banks and erosion control matting, and strategic planting and seeding. The paper emphasizes the need for collaboration among governments, researchers, and communities to implement these solutions effectively. It offers a roadmap for creating resilient ecosystems that can recover more quickly and sustainably from wildfires, highlighting the importance of innovation, education, and commitment to safeguarding our natural environment.