Mixed Problem Research Articles

Distance Constrained Capacitated Vehicle Touting Problem For The Abuja Post Office Using Lexisearch Algorithm

Transportation problems are generally modelled as vehicle routing problems (VRPs) since they consist of minimizing the overall cost while satisfying routing constraints and customers' orderings. In this paper, the mail delivery of the Nigerian Postal Services (NIPOST) is modeled as a distance- constrained capacitated variant (DCVRP) in order to address the problem of delay in mail delivery occurring frequently experienced in NIPOST. The Lexi-search algorithm was applied and implemented on the spreadsheet solver to solve the capacitated vehicle routing problem of Abuja Post Office. The algorithm was tested on Christofides Benchmark and found to perform well with computational analyses coded in c++ and statistical analyses of goodness fit performed using R Software. The problem has been formulated as a mixed integer programming problem based on a modification of the Tompkin’s et al., model. Appropriate data was obtained from Abuja Post Office where the data is used to come up with the distance matrix. The annual cost savings for NIPOST using three vehicles is N1,950,054.66, N1,708,127.73 and N1,140,148.50 for N142, N163 and N213 per litre respectively. The annual cost savings for four vehicles, is N1,494,466.25, and therefore the purchse of a fourth vehicle will reduce delay in mail delivery though it might cost them more to aquire a new bus as already indicated. In the long run however, revenue will increase because of high patronage.

A posteriori error estimates for primal hybrid finite element methods applied to Poisson problem

This paper presents a new fully computable a posteriori error estimates for the primal hybrid finite element methods based on equilibrated flux and potential reconstructions. The reconstructed potential is obtained from a local L2 orthogonal projection of the numerical solution on a continuous function space over the mesh skeleton. The equilibrated flux is the solution of a local mixed problem with a Neumann boundary condition given by the Lagrange multipliers of the primal hybrid finite element solution. For that, a divergence-consistent finite element pair is used. The upper and lower bounds of the error estimator are proved, and numerical results illustrate the efficiency of the error indicators.

Indentation behavior of multiferroic composite materials under an axisymmetric power-law shaped indenter

Nanoindentation technique has been widely employed to characterize various material properties of multiferroic composite medium, where the indenter tip may have more general profile rather than just three common simple shapes (flat, cone and sphere). In this paper, the frictionless indentation problem of a transversely isotropic multiferroic half-space punched by an axisymmetric power-law shaped indenter is investigated. By virtue of the Hankel integral transform, the stated mixed boundary value problem is reduced to dual integral equations, which are then solved analytically. Closed-form solutions for the coupled physical fields at the surface of multiferroic half-space under the action of the power-law shaped indenters with four different electromagnetic properties are obtained, which can include the existing results in literature as special cases. The explicit analytical expressions of load-displacement relationship for the power-law shaped indenter are derived for the first time, which provide the theoretical foundation for characterizing material properties of multiferroic composite medium. The effects of the shape index and electromagnetic properties of the indenter on indentation behaviors are discussed in detail. It is found that the shape index has a significant effect on both the load-displacement relationship and the distribution of the generalized stress fields. The analytical solutions derived from this work can serve as benchmarks for experimental test and characterization of multiferroic composite materials.

Optimizing electric bus charging infrastructure deployment under two charging modes considering seasonal differences

ABSTRACT The innovations of battery and charging technologies facilitate worldwide bus electrification, which can conserve energy and reduce emissions. The emergence of wireless power transfer technology offers the potential to alleviate bus range anxiety. This paper constructs the layout models of static wireless and centralized charging stations based on the seasonal differences associated with battery capacities and passenger flow, which aims to obtain the bus charging station layout scheme of the lowest cost. Then, the heuristic algorithm is utilized to solve the layout models as the mixed linear programming problem. This study results confirm that the combined layout of static wireless and centralized charging stations is more advantageous than a single model. Finally, the required fixed cost of supporting bus system operation is explored for future capital reserves.

Deep reinforcement learning based trajectory design and resource allocation for task-aware multi-UAV enabled MEC networks

Computing tasks in the air is an important form of mobile edge computing (MEC) to improve the quality of service and enhance network coverage. In this paper, we investigate a multi-UAV cooperative computing model and massive devices access scenario in a service area without infrastructure. There are various types of ground devices with different tasks. Moreover, we consider that the UAV executing tasks of devices need to cache the content that task required. Therefore, we propose a multi-UAV enabled MEC network based on task awareness where each UAV caches some programs to execute tasks offloaded from devices. To minimize completion time, a joint UAV trajectory design, access decision and resource allocation problem is formulated. To address this intractable mixed integer non-linear programming problem, a multi-agent trajectory design and resource allocation (MATR) algorithm is proposed, where the multi-agent deep deterministic policy gradient (MADDPG) is applied. Considering the complexity of high-dimensional continuous action space, we introduce the particle swarm optimization (PSO) algorithm to jointly optimize access decisions, and computation resource allocation to reduce action space. In addition, we discuss the impact of the size of UAV cache space and the location of ground devices on the completion time. Simulation results show that the MATR algorithm can significantly reduce the completion time compared to the baselines.

Denoising of Raman Spectra Using a Neural Network Based on Variational Mode Decomposition, Empirical Wavelet Transform, and Encoder-Bidirectional Long Short-Term Memory

Raman spectroscopy has been widely applied in numerous fields including bioanalysis, disease diagnosis, and molecular recognition, owing to its unique advantages of being non-invasive, rapid, and highly specific. However, the acquisition of Raman spectral data is often susceptible to various noise interferences, such as shot noise from the internal detector and dark current noise from the instrument. As a result, the weak Raman signals typically become arduous to discern, which affects the localization and identification of characteristic spectral peaks. This study investigates variational mode decomposition (VMD), empirical wavelet transform (EWT), and integrated encoder-bidirectional long short-term memory (EBiLSTM) modules to propose a neural network algorithm for adaptive denoising of Raman spectra. By combining VMD and EWT, the Raman spectra are decomposed into several sub-sequences, which solves the problem of mode mixing between high-frequency signals and noise in empirical mode decomposition, and significantly reduces the complexity of the original Raman spectral lines. The correlation coefficient between each modal component and the original signal is calculated along with the zero-crossing rate index to categorize the noise and signal sequences. Leveraging the linear differences between the ideal spectral lines and the noisy spectral curves, an encoder-bidirectional long short-term memory (EBiLSTM) denoising network is constructed for hierarchical denoising to extract valid spectral feature information from the high-frequency components, realizing refined adaptive denoising of the Raman spectra. Industry standard objective evaluation metrics on the signal-to-noise ratio and root mean square error are utilized to conduct simulation experiments comparing state-of-the-art algorithms, including empirical mode decomposition, VMD, sliding window averaging, and wavelet thresholding. The experimental results demonstrate that the Raman spectral denoising algorithm combining variational mode decomposition and neural networks improves the denoising performance by 13.38% to 72%, exhibiting higher accuracy and reliability.

Power distribution network configuration applying the corridor method

In this paper, an optimization scheme based on the Corridor Method (CM) matheuristic is proposed for power distribution network configuration with the objective of client balancing between feeders. The problem is formulated as a mixed integer optimization problem (MIP) referring to a variant of the constrained spanning forest problem on a network. The problem is classified as NP-complete in its decision version, and the proposed matheuristic optimization approach is aimed to find high quality solutions in a short computational time on large real instances. According to the characteristics of the power distribution networks, suitable modeling solutions are adopted to retain a radial structure, satisfy power flow and voltage constraints, and reduce the reconfiguration efforts requiring a limited number of maneuvers on the electrical network. Computational experiments on different instances related to a real network have been conducted. The results demonstrated the soundness and the effectiveness of the proposed solution with respect to a baseline represented by a MIP formulation solved by a state-of-the-art commercial solver: the scalability towards large-size cases has been also considered. These results show that the proposed configuration method can effectively and efficiently solve the considered problem giving adequate support to the decision-makers.

Functional gastrointestinal disorders in adolescents during online learning

Background The COVID-19 pandemic necessitated the use of online schooling in order to comply with national and local lockdown guidelines. Online learning required students and teachers to adapt to a new method of schooling. The inability of adolescents to adapt to their environment can interfere with their psychosocial condition and become a risk factor for functional gastrointestinal disorders (FGID).
 Objective To determine the prevalence of FGID in adolescents and evaluate possible risk factors that existed during online learning.
 Methods This cross-sectional study was done in children aged 12-18 years who participated in online learning during the COVID-19 pandemic. The diagnosis of FGID was based on Rome IV criteria. Psychosocial problems were assessed using the Pediatric Symptom Checklist Questionnaire–17 (PSC-17) which includes internalization, externalization, and attention subscales. Subjects with a PSC-17 mixed subscale total score of >15 were considered as having an increased likelihood of having a behavioral health disorder. Data were collected by online questionnaires via Google Forms.
 Results Of 1,413 participants, 23% experienced FGID; of these, 32.6% had >2 FGID diagnostic criteria. Upon multivariate analysis, internalization psychosocial problems were the most common risk factors for FGID, followed by mixed subscale psychosocial problems, unstable internet connection, and not understanding of the material.
 ConclusionThe prevalence of FGID in adolescents in this study is 23%. Environmental and psychosocial conditions are interrelated as risk factors for FGID in adolescents during online learning in the COVID-19 pandemic.

Knee synovial fluid flow and heat transfer, a power law model

For the purpose of understanding, the governing system of partial differential equations for synovial fluid flow velocity and temperature distribution in the knee joint has been successfully solved for the first time. Therefore, such an article is shedding light on the convective diffusion of the viscous flow along the articular surfaces of the joints through the introduction of power-law fluids with different features of permeability, and stagnation point flow along a magnetic field. Henceforth, the frictional energy causes the knee joint’s temperature to increase. By way of filtration, heated synovial fluid reaches the articular cartilage and provides heat to the bone and cartilage. The lubricant in the joint cavity is properly mixed with this cooled fluid. A rectangular region flow and diffusion model is used to define the issue, thermal diffusion and flow inside the intra-articular gap, as well as flow and thermal diffusion within the porous matrix covering the approaching bones at the joint. Using the similarity solution approach, the linked mixed boundary value problem is addressed. The fluid has been shown to resist moving into or out of the cartilage in certain sick and/or aging synovial joints, causing the temperature to increase. By changing the values of the parameters from their usual levels, it is observed that the temperature did increase in aged and sick joints which impact cartilage and/or synovial fluid degradation.

On the non-self-adjoint and multiscale character of passive scalar mixing under laminar advection

Except in the trivial case of spatially uniform flow, the advection–diffusion operator of a passive scalar tracer is linear and non-self-adjoint. In this study, we exploit the linearity of the governing equation and present an analytical eigenfunction approach for computing solutions to the advection–diffusion equation in two dimensions given arbitrary initial conditions, and when the advecting flow field at any given time is a plane parallel shear flow. Our analysis illuminates the specific role that the non-self-adjointness of the linear operator plays in the solution behaviour, and highlights the multiscale nature of the scalar mixing problem given the explicit dependence of the eigenvalue–eigenfunction pairs on a multiscale parameter $q=2{\rm i}k\,{\textit {Pe}}$ , where $k$ is the non-dimensional wavenumber of the tracer in the streamwise direction, and ${\textit {Pe}}$ is the Péclet number. We complement our theoretical discussion on the spectra of the operator by computing solutions and analysing the effect of shear flow width on the scale-dependent scalar decay of tracer variance, and characterize the distinct self-similar dispersive processes that arise from the shear flow dispersion of an arbitrarily compact tracer concentration. Finally, we discuss limitations of the present approach and future directions.

An improved peridynamic approach for fatigue analysis of two dimensional functionally graded materials

This study investigates the fatigue behavior of functionally graded materials (FGMs) within an enhanced peridynamic (PD) framework that eliminates the need for surface and volume correction factors. FGMs offer mechanical advantages by varying material compositions and properties in one or more directions. The distribution of mechanical properties in FGMs is achieved by employing a power law. Comparative analysis is conducted between the PD predictions for reaction forces and outcomes obtained from the reference solutions for a quasi-static problem. Minimal divergence is observed between the PD and reference solutions, affirming the accuracy of the present PD formulation. Furthermore, the PD fatigue results for a Mode I Compact Tension (CT) specimen problem match the experimental findings. An experimental stop-hole problem is used to evaluate the accuracy of the PD fatigue code in mixed-mode circumstances. The load cycle determination is achieved via ABAQUS Computational Finite Element Method (CFEM) for the mixed mode problem. There is a good correlation between CFEM and the present PD outcomes. Furthermore, the effect of stop-hole existence on fatigue life in mixed mode is examined, revealing a significant retardation effect. Notably, this study adds a novel perspective by using the PD approach to investigate the fatigue analysis of FGMs and examine the impact of the stop hole on fatigue life- a component previously unexplored in the existing literature.

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System

This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.

Regularized Asymptotics of the Solution of a Singularly Perturbed Mixed Problem on the Semiaxis for the Schrödinger Equation with the Potential Q = X2

In this paper, we study the solution of a singularly perturbed inhomogeneous mixed problem on the half-axis for the Schrödinger equation in the presence of a “strong” turning point for the limit operator on time interval that do not contain focal points. Based on the ideas of the regularization method for asymptotic integration of problems with an unstable spectrum, it is shown how regularizing functions should be constructed for this type of singularity. The paper describes in detail the formalism of the regularization method, justifies the algorithm, constructs an asymptotic solution of any order in a small parameter, and proves a theorem on the asymptotic convergence of the resulting series.

DRL-Based Secure Aggregation and Resource Orchestration in MEC-Enabled Hierarchical Federated Learning

Federated learning (FL) provides a new paradigm for protecting data privacy by enabling model training at devices and model aggregation at servers. However, data information may be leaked to honest-but-curious aggregation servers by updated model parameters. The existing secure methods do not fully exploit the potentiality of data characteristics in enhancing security, which makes it impossible to optimize limited system resources overall to achieve secure, fair and efficient FL systems. In this paper, a DRL-based joint secure aggregation and resource orchestration scheme is proposed to guarantee security and fairness, and improve efficiency for hierarchical FL assisted by untrusted mobile-edge computing (MEC) servers. We formulate a joint optimization problem of data size, payment and resource orchestration, to maximize the long-term social welfare subject to secure aggregation and limited resources. Since the formulated problem is a complex mixed integer dynamic optimization problem with NP-hardness, where multiple mixed integer optimization variables are highly coupled in time-varying constraints and objective function, it is difficult to obtain its optimal solution via traditional optimization methods. Thus, we propose a hierarchical reward function-based DRL algorithm (MATD3) to guide the agents to approach the optimal policy of secure aggregation and resource orchestration. Simulation results show that the proposed algorithm MATD3 can achieve superior performance over comparison algorithms and the MEC-enabled HFL framework outperforms two-layer FL frameworks.

On global weak solutions of the Vlasov-Poisson equations with external magnetic field

We consider the first mixed problem for the system of Vlasov-Poisson equations with a given external magnetic field in a bounded domain. This problem describes the kinetics of high-temperature plasma in controlled thermonuclear fusion plants and is considered with respect to unknown functions: electric field potential, distribution functions of positively charged ions and electrons. Additionally, we assumed that the distribution functions of charged particles satisfy the condition of mirror reflection from the boundary of the domain under consideration. We prove the existence of global weak solutions of such a problem.

Discrete and mixed two-center problems for line segments

Given a set of n non-intersecting line segments L and a set Q of m points in R2; we present algorithms of the discrete two-center problem for (i) covering, (ii) stabbing and (iii) hitting the set L in (i) O(m(m+n)log2⁡n), (ii) O(m2nlog⁡n) and (iii) O(m(m+n)log2⁡n) time respectively, where the two disks are centered at two points of Q and radius of the larger disk is minimized. We also study the mixed two-center problems for (i) covering, (ii) stabbing and (iii) hitting the set L, where only one of the disks is centered at a point qi∈Q and the other disk is centered at any point in R2, and these three problems are solved in (i) O(mnlog⁡n), (ii) O(mn3log⁡n) and (iii) O(mnlog2⁡n) time, respectively. The space complexities for all these algorithms are linear.

Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

AbstractThe present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.

Generating collective counterfactual explanations in score-based classification via mathematical optimization

Due to the increasing use of Machine Learning models in high stakes decision making settings, it has become increasingly important to have tools to understand how models arrive at decisions. Assuming an already trained Supervised Classification model, post-hoc explanations can be obtained via so-called counterfactual analysis: a counterfactual explanation of an instance indicates how this instance should be minimally modified so that the perturbed instance is classified in the desired class by the given Machine Learning classification model.Most of the Counterfactual Analysis literature focuses on the single-instance single-counterfactual setting, in which the analysis is done for one single instance to provide one single counterfactual explanation. Taking a stakeholder’s perspective, in this paper we introduce the so-called collective counterfactual explanations. By means of novel Mathematical Optimization models, we provide a counterfactual explanation for each instance in a group of interest, so that the total cost of the perturbations is minimized under some linking constraints. Making the process of constructing counterfactuals collective instead of individual enables us to detect the features that are critical to the entire dataset to have the individuals classified in the desired class. Our methodology allows for some instances to be treated individually, as in the single-instance single-counterfactual case, performing the collective counterfactual analysis for a fraction of records of the group of interest. This way, outliers are identified and handled appropriately.Under some assumptions on the classifier and the space in which counterfactuals are sought, finding collective counterfactual explanations is reduced to solving a convex quadratic linearly constrained mixed integer optimization problem, which, for datasets of moderate size, can be solved to optimality using existing solvers.The performance of our approach is illustrated on real-world datasets, demonstrating its usefulness.

Face Sketch to Image Generation using Generative Adversarial Network

Numerous studies have been conducted in the area of sketch to picture conversion and they got the good outcomes, but sometimes it is not accurate that they observed the blurry boundaries, the mixing of two colors that is the color of hair and face or mixing of both. These results are of the convolution neural networks that are basic of GAN. So to overcome their drawbacks we proposed a novel generative adversarial network using conditional GAN. For that we converted the original image in sketch and both the sketch and original image as reference is applied as input. We got more realistic and sharp colored images as compared to other. We focused on the feature detection, and the results are good. For the experimentation we used the STL-10 dataset. We overcome the problem of mixing of colors and got the different colors for hair, lips, and skin using conditional GAN as compared to CNN modern with increased performance and precision.

Generalized complex variable analysis of shallow tunneling through multi-layered ground

The mechanical analysis of shallow tunnels crossing multiple ground layers is a common problem in urban underground engineering. Since the tunnel boundary intersects multiple ground layers, the challenges of mixed boundary value problem for composite boundary and the conformal mapping of irregular banding computational domain are faced in solving the multi-boundary problem. For this, a new solution strategy regarding the generalized complex variable method to calculate the mechanical responses of the multi-layered ground is proposed. The research object is divided into two independent objects including the complete multi-layered ground without tunnel and the complete tunnel boundary. Firstly, the mechanical responses of the complete multi-layered ground are solved through the superposition of multiple single-boundary contributions. Subsequently, the virtual boundary circle and its corresponding analytic functions are introduced in analyzing the tunnel boundary contribution. Finally, the solution for the stress and displacement field of the multi-layered ground is modified by superimposing the contribution of the virtual boundary circle, so that all the given boundary conditions are satisfied. The self-consistency and accuracy of the proposed method are validated by several examples. The characteristics of the displacement propagation of typical multi-layered ground patterns are analyzed based on the analytical solution. The proposed method can be used to analyze the mechanical responses of multi-layered ground with arbitrary intersections between the tunnel and ground boundaries.