Problem Domain Research Articles

A Novel Approach to Combinatorial Problems: Binary Growth Optimizer Algorithm

The set-covering problem aims to find the smallest possible set of subsets that cover all the elements of a larger set. The difficulty of solving the set-covering problem increases as the number of elements and sets grows, making it a complex problem for which traditional integer programming solutions may become inefficient in real-life instances. Given this complexity, various metaheuristics have been successfully applied to solve the set-covering problem and related issues. This study introduces, implements, and analyzes a novel metaheuristic inspired by the well-established Growth Optimizer algorithm. Drawing insights from human behavioral patterns, this approach has shown promise in optimizing complex problems in continuous domains, where experimental results demonstrate the effectiveness and competitiveness of the metaheuristic compared to other strategies. The Growth Optimizer algorithm is modified and adapted to the realm of binary optimization for solving the set-covering problem, resulting in the creation of the Binary Growth Optimizer algorithm. Upon the implementation and analysis of its outcomes, the findings illustrate its capability to achieve competitive and efficient solutions in terms of resolution time and result quality.

A novel investigation of Casson fluid flow over an infinite plate with constant temperature by constructing the absorbing boundary conditions

Casson fluid has been widely used in blood, honey, chocolate, and various polymer fluids, for which the investigation of its underlying flow and heat transfer mechanisms in complex environments is of vital significance. In this paper, the Casson fluid flow over an infinite moving plate with constant temperature is studied, which leads to a coupled system of the velocity and temperature fields. To treat the infinite coupled system more accurately, the artificial boundary conditions in terms of fractional derivatives are developed using the Laplace transform, which transfers the problem in the infinite domain to a model in the bounded domain. The finite difference method is applied to solve the new bounded coupled system. Furthermore, three numerical experiments are presented to demonstrate the validity and accuracy of the transferred model and the numerical scheme. The influence of some important physical parameters on the velocity and temperature fields is also explored. The main findings are that the viscosity of the Casson fluid decreases with an increasing Grashof number leading to an accelerated flow, the thermal conductivity diminishes as the Prandtl number increases resulting in a weakened thermal effect within the flow, and the velocity at the fixed position decreases as the Casson parameter increases.

Towards an ITU Standard for DLT Energy Consumption

Towards an ITU Standard for DLT Energy Consumption

Activation Functions for Neural Networks: Application and Performance-based Comparison

Past decade has seen explosive growth of Deep Learning (DL) algorithms based on Artificial Neural Networks (ANNs) and its applications in vast emerging domains to solve real world complex problems. The DL architecture uses Activation Functions (AFs), to perform the task of finding relationship between the input feature and the output. Essential building blocks of any ANN are AFs which bring the required non-linearity of the output in the Output layer of network. Layers of ANNs are combinations of linear and nonlinear AFs. Most extensively used AFs are Sigmoid, Hyperbolic Tangent (Tanh), Rectified Linear Unit (ReLU) etc to name a few. Choosing an AF for a particular AF depends on various factors such as Nature of Application, Design of ANN, Optimizers used in the network, Complexity of Data etc. This paper presents a survey on most widely used AFs along with the important consideration while selecting an AF on a specific problem domain. A broad guideline on selecting an AF based on the literature survey has been presented to help researchers in employing suitable AF in their problem domain.

Research on vehicle path planning of automated guided vehicle with simultaneous pickup and delivery with mixed time windows

AbstractThe authors investigate new Automated Guided Vehicle (AGV) Routing Problem with Simultaneous Pickup and Delivery with Mixed Time Windows (VRPSPDMTW) in smart workshops, a variation of the classic Vehicle Routing Problem (VRP). A mixed time window vehicle routing model was developed for simultaneous deliveries. This model reduces the cost of AGVs used and distribution cost, along with time window penalties. To address this complex challenge, a Hybrid Adaptive Genetic Algorithm using Variable Neighbourhood Search (AGA‐VNS) is proposed. This algorithm enhances the genetic algorithm's local search capabilities while preserving solution diversity, thereby improving both efficiency and quality of solutions. Comprehensive computational experiments are conducted, which include both VRPSPDTW test benchmark and real‐world smart factory instance studies. The outcomes reveal that the AGA‐VNS algorithm outperforms both professional solver software and advanced heuristic methods significantly. Moreover, the newly developed mixed time window model is more aligned with the requirements of real‐world production processes compared to the traditional time window model. Thus, this research not only presents novel insights into the domain of vehicle routing problems but also demonstrates its significant applicability and potential in the background of intelligent workshops.

Nonlinear elliptic problem in exterior domains: exact boundary behavior of blow-up positive solutions

Nonlinear elliptic problem in exterior domains: exact boundary behavior of blow-up positive solutions

Collaborative Solutions to Software Architecture Challenges Faced by IT Professionals

Software architecture serves as a crucial link between problem and solution domains in software systems. However, reliance on graphical artifacts for architecture design has limitations, especially in abstract analysis. To overcome these constraints, Architecture Description Languages (ADLs) offer a more formal approach. Yet, our research reveals that ADLs face numerous challenges, as identified through interviews, surveys, and community interactions. By mining content from various sources, including mailing lists and forums, we comprehensively explore the concerns of software engineers. Employing content mining, topic modeling, and grounded theory, we compile a database of real-world issues and solutions in software architecture. Comparing our findings with existing literature, we identify 17 primary issues faced by practitioners. We also compare our results with language models to ascertain areas of agreement and disagreement. Finally, we propose solutions for each identified issue to aid future analysts.

Asymptotic analysis of particle cluster formation in the presence of anchoring sites

The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples of such assemblies include lipid rafts, and postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, thus localizing them at specific spatial positions. Hence, PSDs play a key role in determining the strength of synaptic connections and their regulation during learning and memory. Recently, a two-dimensional (2D) diffusion-mediated aggregation model of PSD formation has been developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a stationary distribution consisting of multiple clusters, whose average size can be determined using an effective mean-field description of the particle concentration around each anchored cluster. In this paper, we derive corrections to the mean-field approximation by applying the theory of diffusion in singularly perturbed domains. The latter is a powerful analytical method for solving two-dimensional (2D) and three-dimensional (3D) diffusion problems in domains where small holes or perforations have been removed from the interior. Applications range from modeling intracellular diffusion, where interior holes could represent subcellular structures such as organelles or biological condensates, to tracking the spread of chemical pollutants or heat from localized sources. In this paper, we take the bounded domain to be the cell membrane and the holes to represent anchored clusters. The analysis proceeds by partitioning the membrane into a set of inner regions around each cluster, and an outer region where mean-field interactions occur. Asymptotically matching the inner and outer stationary solutions generates an asymptotic expansion of the particle concentration, which includes higher-order corrections to mean-field theory that depend on the positions of the clusters and the boundary of the domain. Motivated by a recent study of light-activated protein oligomerization in cells, we also develop the analogous theory for cluster formation in a three-dimensional (3D) domain. The details of the asymptotic analysis differ from the 2D case due to the contrasting singularity structure of 2D and 3D Green’s functions.Graphical abstract2D model of diffusion-based protein cluster formation in the presence of anchoring cites and particle recycling. a A set of N anchoring sites at positions xj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{x}}_j$$\\end{document}, j=1,…,N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=1,\\ldots ,N$$\\end{document}, in a bounded domain Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document}. b Diffusing particles accumulate at the anchoring sites resulting in the formation of particle aggregates or clusters Uj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {U}}}_j$$\\end{document}. c The clusters are dynamically maintained by a combination of lateral diffusion outside the clusters and particle recycling

Enacted institutions, participatory sense-making and social norms

This paper argues that institutions are higher-level autonomous systems enacted by patterns of participatory sense-making. Therefore, unlike in the standard equilibrium theory, institutions are not themselves thought of as behavioural patterns. Instead, they are problem domains that these patterns have brought forth. Moreover, these are not merely any patterns, but only those devoted to maintaining a specific strategy of problem solving, called the strategy of ‘letting be’. The latter refers to, following Hanne de Jaegher, a balance between underdetermination and overdetermination of individual behaviour by a collective. Such an understanding of institutions becomes an option once a hybrid ‘equilibrium + rules’ theory of institutions, such as the one proposed by Frank Hindriks, is supplemented with insights from enactivism. In this light, drawing a connection between these two areas is the additional, meta-theoretical goal of this paper. This connection is beneficial, I argue, in particular since it allows for a satisfactory, in-depth account of the normative character of institutions as well as their local character.

Predicting underwater acoustic transmission loss in the SOFAR channel from ray trajectories via deep learning.

Predicting acoustic transmission loss in the SOFAR channel faces challenges, such as excessively complex algorithms and computationally intensive calculations in classical methods. To address these challenges, a deep learning-based underwater acoustic transmission loss prediction method is proposed. By properly training a U-net-type convolutional neural network, the method can provide an accurate mapping between ray trajectories and the transmission loss over the problem domain. Verifications are performed in a SOFAR channel with Munk's sound speed profile. The results suggest that the method has potential to be used as a fast predicting model without sacrificing accuracy.

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.

A novel multi-strategy ameliorated quasi-oppositional chaotic tunicate swarm algorithm for global optimization and constrained engineering applications

Over the last few decades, a number of prominent meta-heuristic algorithms have been put forth to address complex optimization problems. However, there is a critical need to enhance these existing meta-heuristics by employing a variety of evolutionary techniques to tackle the emerging challenges in engineering applications. As a result, this study attempts to boost the efficiency of the recently introduced bio-inspired algorithm, the Tunicate Swarm Algorithm (TSA), which is motivated by the foraging and swarming behaviour of bioluminescent tunicates residing in the deep sea. Like other algorithms, the TSA has certain limitations, including getting trapped in the local optimal values and a lack of exploration ability, resulting in premature convergence when dealing with highly challenging optimization problems. To overcome these shortcomings, a novel multi-strategy ameliorated TSA, termed the Quasi-Oppositional Chaotic TSA (QOCTSA), has been proposed as an enhanced variant of TSA. This enhanced method contributes the simultaneous incorporation of the Quasi-Oppositional Based Learning (QOBL) and Chaotic Local Search (CLS) mechanisms to effectively balance exploration and exploitation. The implementation of QOBL improves convergence accuracy and exploration rate, while the inclusion of a CLS strategy with ten chaotic maps improves exploitation by enhancing local search ability around the most prospective regions. Thus, the QOCTSA significantly enhances convergence accuracy while maintaining TSA diversification. The experimentations are conducted on a set of thirty-three diverse functions: CEC2005 and CEC2019 test functions, as well as several real-world engineering problems. The statistical and graphical outcomes indicate that QOCTSA is superior to TSA and exhibits a faster rate of convergence. Furthermore, the statistical tests, specifically the Wilcoxon rank-sum test and t-test, reveal that the QOCTSA method outperforms the other competing algorithms in the domain of real-world engineering design problems.

Prismatic-element SBPML coupled with SBFEM for 3D infinite transient wave problems

In this paper, an enhanced prismatic-element scaled boundary perfectly matched layer (SBPML) is developed, which is a novel time-domain artificial boundary method for 3D infinite wave problems. The SBPML permits the utilization of an artificial boundary with general geometry and can consider planar physical surfaces and interfaces extending to infinity. Moreover, this enhancement enables the seamless integration with surface meshes of arbitrary polygonal faces (such as triangles, quadrangles, pentagons, heptagons, octagons, etc.) at the truncation boundaries. The interior domain can be modelled by polyhedrons formulated by the scaled boundary finite element method (SBFEM). The geometric shape of the SBPML elements in the proposed method, within the local coordinate system, takes the form of a regular prism with regular polygonal top and bottom faces. Consequently, it is referred to as the Prismatic-element SBPML. Local scaled boundary coordinates based on the polygonal shape function are firstly introduced into the truncated infinite domain to describe its general geometry properties and provide the coupled capabilities with arbitrary polygonal face meshes at the truncation boundaries of numerical models. Then, a complex stretching function from PML is applied to radial direction of the local scaled boundary coordinates to map the physical space onto the complex space, resulting in a SBPML domain. Upon spatial discretization, the proposed method is formulated using a 2nd-order mixed displacement-stress unsplit-field formulation, allowing seamless coupling with FEM and SBFEM originally designed for the interior computational domain. Finally, three benchmark examples of wave propagation problems in unbounded domains and two soil-structure interaction problems of engineering problems are presented to demonstrate the accuracy and robustness of the Prismatic-element SBPML.

Fundamental solutions and critical Lane-Emden exponents for nonlinear integral operators in cones

In this article we study the fundamental solutions or “α-harmonic functions” for some nonlinear positive homogeneous nonlocal elliptic problems in conical domains, such asF(u)=0inCω,u=0inRN∖Cω, where ω is a proper C2 domain in SN−1 for N≥2, Cω:={x:x≠0,|x|−1x∈ω} is the cone-like domain related to ω, and F is an extremal fully nonlinear integral operator. We prove the existence of two fundamental solutions that are homogeneous and do not change signs in the cone; one is bounded at the origin and the other at infinity.As an application, we use the fundamental solutions obtained to prove Liouville type theorems in cones for supersolutions of the Lane-Emden-Fowler equation in the formF(u)+up=0inCω,u=0inRN∖Cω. We also prove a generalized Hopf type lemma in domains with corners. Most of our results are new even when F is the fractional Laplacian operator.

Semi-analytic PINN methods for boundary layer problems in a rectangular domain

Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary layers are responsible for the stiffness of solutions, which leads to large computational errors, if not properly handled. It is well-known that the classical numerical methods as well as the Physics-Informed Neural Networks (PINNs) require some special treatments near the boundary, e.g., using extensive mesh refinements or finer collocation points, in order to obtain an accurate approximate solution especially inside of the stiff boundary layer. In this article, we modify the PINNs and construct our new semi-analytic SL-PINNs suitable for singularly perturbed boundary value problems. Performing the boundary layer analysis, we first find the corrector functions describing the singular behavior of the stiff solutions inside boundary layers. Then we obtain the SL-PINN approximations of the singularly perturbed problems by embedding the explicit correctors in the structure of PINNs or by training the correctors together with the PINN approximations. Our numerical experiments confirm that our new SL-PINN methods produce stable and accurate approximations for stiff solutions.

Adaptive Deep Fourier Residual method via overlapping domain decomposition

The Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural network (VPINN). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based on minimizing the dual norm of the weak residual of a PDE, which is equivalent to minimizing the energy norm of the error. To compute the dual norm of the weak residual, the DFR method employs an orthonormal spectral basis of the test space, known for rectangles or cuboids for multiple function spaces.In this work, we extend the DFR method with ideas of traditional domain decomposition (DD). This enables two improvements: (a) to solve problems in more general polygonal domains and (b) to develop an adaptive refinement technique in the test space using a Döfler marking algorithm. In the former case, we retain the desirable equivalence between the employed loss function and the H1 error under non-restrictive assumptions, numerically demonstrating adherence to explicit bounds in the case of the L-shaped domain problem. In the latter, we show how refinement strategies lead to potentially significant improvements against a reference, classical DFR implementation with a test function space of significantly lower dimensionality, allowing us to better approximate singular solutions at a more reasonable computational cost.

A non-boundary-fitted-grid method, based on compact integrated-RBF approximations, for solving differential problems in multiply-connected domains

This paper presents a new non-boundary-fitted-grid numerical technique for solving partial differential equations (PDEs) in multi-hole domains. A multiply-connected domain is converted into a simply-connected domain of rectangular or non-rectangular shape that is discretised using a Cartesian grid. Compact radial basis function (RBF) stencils, which are constructed through integration rather than the conventional differentiation, are used to discretise the field variables. The imposition of inner boundary conditions is conducted by means of body forces that are derived from satisfying the governing equations and prescribed boundary conditions in small subregions. Salient features of the proposed method include: (i) simple pre-processing (Cartesian grid), (ii) high rates of convergence of the solution accuracy with respect to grid refinement achieved with compact integrated-RBF stencils, where both nodal function and derivative values are included in the approximations, (iii) the system matrix kept unchanged for the case of moving holes, and (iv) no interpolation between Lagrange and Euler meshes required. Several linear and nonlinear problems, including rotating-cylinder flows and buoyancy-driven flows in eccentric and concentric annuli, are simulated to verify the proposed technique.

Exploring Quaternion Neural Network Loss Surfaces

This paper explores the superior performance of quaternion multi-layer perceptron (QMLP) neural networks over real-valued multi-layer perceptron (MLP) neural networks, a phenomenon that has been empirically observed but not thoroughly investigated. The study utilizes loss surface visualization and projection techniques to examine quaternion-based optimization loss surfaces for the first time. The primary contribution of this research is the statistical evidence that QMLP models yield smoother loss surfaces than real-valued neural networks, which are measured and compared using a robust quantitative measure of loss surface “goodness” based on estimates of surface curvature. Extensive computational testing validates the effectiveness of these surface curvature estimates. The paper presents a comprehensive comparison of the average surface curvature of a tuned QMLP model and a tuned real-valued MLP model on both a regression task and a classification task. The results provide strong support for the improved optimization performance observed in QMLPs across various problem domains.

Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction

The aim of this work is to characterize the asymptotic behaviour of the first eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and Neumann) boundary conditions in cylindrical domains when the length of the cylindrical domains tends to infinity. This generalises an earlier work of Chipot et al. (Asymptot. Anal. 85(3–4) (2013) 199–227) where the linear case p = 2 is studied. Asymptotic behavior of all the higher eigenvalues of the linear case and the second eigenvalues of general case (using topological degree) for such problems is also studied.

ANALYSIS OF CALCULATION METHODS FOR PROGRESSIVE COLLAPSE OF SINGLE-STOREY FRAME INDUSTRIAL BUILDINGS AND SEARCH FOR OPPORTUNITIES TO IMPROVE THE ACCURACY OF CALCULATIONS

The issues of analysing the progressive collapse of buildings have become an inseparable part of design. However, design standards still do not provide clear criteria for the calculation algorithm in the analysis of instantaneous collapse of building structures. The article discusses the problems and uncertainties of formulating the problem of analysing the instantaneous collapse of structures. To illustrate the uncertainty of applying applying building analysis methods to progressive collapse in accordance with the requirements of various standards, examples of calculations of existing one-storey frame industrial buildings are given. SCAD Office and LIRA-SCAD software packages are used for the analysis. The results of the solution of the dynamic problem in the time domain are compared with the setting of different times of redistribution of the reaction and the results of the quasi-static calculation with different dynamic coefficients. A comparison is made between the theoretical results of predicting disproportionate destruction and the actual collapse of the structures of the industrial building that was damaged by missile strikes. The presence of important discrepancies in the calculation results and their causes are analyzed. The purpose of the article is to analyze the main features that arise when designing (reinforced) structures of industrial buildings, taking into account the possibility of their local destruction. Conclusion. The article considers some problems that must be solved during the design or reconstruction of industrial buildings, the operation of which may be associated with one or another local destruction of the bearing structures. Prospective constructive ways of effectively solving these problems are presented.