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The purpose of this paper is to show that the theoretical proofs of convergence in solution of ant colony optimization (ACO) algorithms have significant values of theory and application.

This paper adapts the basic ACO algorithm framework and proves two important ACO subclass algorithms which are ACO_bs,τmin and ACO_{bs,τmin (t)}.

This paper indicates that when the minimums of pheromone trial decay to 0 with the speed of logarithms, it is ensured that algorithms can, at least, get a certain optimal solution. Even if the randomicity and deflection of random algorithms are disturbed infinitesimally, algorithms can obtain optimal solution.

This paper focuses on the analysis and proof of the convergence theory of ACO subset algorithm to explore internal mechanism of ACO algorithm.

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate reference solutions.

An adaptive quadrature algorithm which allows user control over integration accuracy, previously developed for integrating boundary value problems, is adapted to elasticity problems. The algorithm allows the development of a convergence study procedure that takes into account both integration and discretisation errors. The convergence procedure is demonstrated using an elasticity problem which has an analytical solution and is then applied to accurately solve a soft-tissue extension problem involving large deformations.

The developed convergence procedure, based on the presented adaptive integration scheme, allows the computation of accurate reference solutions for challenging problems which do not have an analytical or finite element solution.

This paper investigates the application of adaptive quadrature to solid mechanics problems in engineering analysis using the element-free Galerkin method to obtain accurate reference solutions. The proposed convergence procedure allows the user to independently examine and control the contribution of integration and discretisation errors to the overall solution error. This allows the computation of reference solutions for very challenging problems which do not have an analytical or even a finite element solution (such as very large deformation problems).

Presents a computational algorithm for the numerical integration of triaxial concrete plasticity formulations. The specific material formulation at hand is the so‐called extended leon model for concrete. It is based on the flow theory of plasticity which entails isotropic hardening as well as fracture energy‐based softening in addition to non‐associated plastic flow. The numerical algorithm resorts to implicit integration according to the backward Euler strategy that enforces plastic consistency according to the closes‐point‐projection method (generalized radial‐return strategy). Numerical simulations illustrate the overall performance of the proposed algorithm and the significant increase of the convergence rate when the algorithmic tangent is used in place of the continuum operator.

The potential for overall efficiency improvements of modern hydro power turbines is a few percent. A significant part of the losses occurs in the draft tube. To improve the efficiency by analysing the flow in the draft tube, it is therefore necessary to do this accurately, i.e. one must know how large the iterative and the grid errors are. This was done by comparing three different methods to estimate errors. Four grids (122,976 to 4,592 cells) and two numerical schemes (hybrid differencing and CCCT) were used in the comparison. To assess the iterative error, the convergence history and the final value of the residuals were used. The grid error estimates were based on Richardson extrapolation and least square curve fitting. Using these methods we could, apart from estimate the error, also calculate the apparent order of the numerical schemes. The effects of using double or single precision and changing the under relaxation factors were also investigated. To check the grid error the pressure recovery factor was used. The iterative error based on the pressure recovery factor was very small for all grids (of the order 10^–4 percent for the CCCT scheme and 10^–10percent for the hybrid scheme). The grid error was about 10 percent for the finest grid and the apparent order of the numerical schemes were 1.6 for CCCT (formally second order) and 1.4 for hybrid differencing (formally first order). The conclusion is that there are several methods available that can be used in practical simulations to estimate numerical errors and that in this particular case, the errors were too large. The methods for estimating the errors also allowed us to compute the necessary grid size for a target value of the grid error. For a target value of 1 percent, the necessary grid size for this case was computed to 2 million cells.

This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing based on Zhu and Zienkiewicz error estimation approach. If mesh adaptation only occurs at user-supplied times and results in a completely new mesh, it is necessary to stop the time-integration at these same times. In these conditions, one challenge is to find an efficient and reliable way to restart the time-integration. The authors investigate what impact grid-to-grid interpolation errors have on the relaunch of the computation.

Two restart strategies of the time-integrator were used: one based on resetting the time-step size h and time-integrator order p to default values (used in the initial startup phase), and another designed to restart with the time-step size h and order p used by the solver prior to remeshing. The authors also investigate the benefits of quadratically interpolate the solution on the new mesh. Both restart strategies were used to solve laminar incompressible Navier–Stokes and the Unsteady Reynolds Averaged Naviers-Stokes (URANS) equations.

The adaptive features of our time-integrators are excellent tools to quantify errors arising from the data transfer between two grids. The second restart strategy proved to be advantageous only if a quadratic grid-to-grid interpolation is used. Results for turbulent flows also proved that some precautions must be taken to ensure grid convergence at any time of the simulation. Mesh adaptation, if poorly performed, can indeed lead to losing grid convergence in critical regions of the flow.

This study exhibits the benefits and difficulty of assessing both spatial error estimates and local error estimates to enhance the efficiency of unsteady computations.

It is worth mentioning that in supply chain management (SCM), managerial decisions are often based on optimization of resources. Till the early 2000s, supply chain optimization problems were being addressed by conventional programming approaches such as Linear Programming, Mixed-Integer Linear Programming and Branch-and-Bound methods. However, the solution convergence in such approaches was slow. But with the advent of Swarm Intelligence (SI)-based algorithms like particle swarm optimization and ant colony optimization, a significant improvement in solution of these problems has been observed. The purpose of this paper is to present and analyze the application of SI algorithms in SCM. The analysis will eventually lead to development of a generalized SI implementation framework for optimization problems in SCM.

A structured state-of-the-art literature review is presented, which explores the applications of SI algorithms in SCM. It reviews 56 articles published in peer-reviewed journals since 1999 and uses several classification schemes which are critical in designing and solving a supply chain optimization problem using SI algorithms.

The paper revels growth of swarm-based algorithms and seems to be dominant among all nature-inspired algorithms. The SI algorithms have been used extensively in most of the realms of supply chain network design because of the flexibility in their design and rapid convergence. Large size problems, difficult to manage using exact algorithms could be efficiently handled using SI algorithms. A generalized framework for SI implementation in SCM is proposed which is beneficial to industry practitioners and researchers.

The paper proposes a generic formulation of optimization problems in distribution network design, vehicle routing, resource allocation, inventory management and supplier management areas of SCM which could be solved using SI algorithms. This review also provides a generic framework for SI implementation in supply chain network design and identifies promising emerging issues for further study in this area.

The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally.

Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions.

This work was supported by the NSF of China (No. 11971152).

This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

The purpose of this paper is to describe how emerging open standards are replacing traditional industrial networks. Current industrial Ethernet networks are not interoperable; thus, limiting the potential capabilities for the Industrial Internet of Things (IIoT). There is no forthcoming new generation fieldbus standard to integrate into the IIoT and Industry 4.0 revolution. The open platform communications unified architecture (OPC UA) time-sensitive networking (TSN) is a potential vendor-independent successor technology for the factory network. The OPC UA is a data exchange standard for industrial communication, and TSN is an Institute of Electrical and Electronics Engineers standard for Ethernet that supports real-time behaviour. The merging of these open standard solutions can facilitate cross-vendor interoperability for Industry 4.0 and IIoT products.

A brief review of the history of the fieldbus standards is presented, which highlights the shortcomings for current industrial systems in meeting converged traffic solutions. An experimental system for the OPC UA TSN is described to demonstrate an approach to developing a three-layer factory network system with an emphasis on the field layer.

From the multitude of existing industrial network schemes, there is a convergence pathway in solutions based on TSN Ethernet and OPC UA. At the field level, basic timing measurements in this paper show that the OPC UA TSN can meet the basic critical timing requirements for a fieldbus network.

This paper uniquely focuses on the specific fieldbus standards elements of industrial networks evolution and traces the developments from the early history to the current developing integration in IIoT context.

The purpose of this study is to propose an isogeometric analysis (IGA) approach for solving the Reynolds equation in textured piston ring cylinder liner (PRCL) contacts.

The texture region is accurately and conveniently expressed by non-uniform rational B-splines (NURBS) besides hydrodynamic pressure and the oil film density ratio is represented in this mathematical form. A quadratic programming method combined with a Lagrange multiplier method is developed to address the cavitation issue.

The comparison with the results solved by an analytical method has verified the effectiveness of the proposed approach. In the study of the PRCL contact with two-dimensional circular dimple textures, the solution of the IGA approach shows high smoothness and accuracy, and it well satisfies the complementarity condition in the case of cavitation presence.

This paper proposes an IGA approach for solving the Reynolds equation in textured PRCL contacts. Its novelty is reflected in three aspects. First, NURBS functions are simultaneously used to express the solution domain, texture shape, hydrodynamic pressure and oil density ratio. Second, the streamline upwind/Petrov–Galerkin method is adopted to create a weak form for the Reynolds equation that takes the oil density ratio as a first-order unknown variable. Third, a quadratic programming approach is developed to impose the complementarity conditions between the hydrodynamic pressure and the oil density ratio.

The viscous finite volume lambda formulation is presented. The suggested technique is apt to compute viscous flows with heat fluxes. The inviscid terms are evaluated by means of the non‐conservative, very accurate upwind methodology, known as the finite volume lambda formulation. The diffusive terms, on the contrary, are approximated by a central scheme. Both methods are characterized by a nominal second order accuracy in space. Efficiency is enhanced by means of a multigrid technique which directly combines each grid level with each stage of an explicit multistage time integration technique. A laminar viscous flow about a NACA 0012 airfoil and a turbulent one about a RAE 2822 airfoil have been computed as well as the two‐ and three‐dimensional turbulent flows inside the Stanitz elbow. The computed numerical results are in very good agreement with well assessed published numerical or experimental results. The suggested multigrid technique allows significant work reductions for laminar as well as for turbulent flow computations.