Solving Procedure Research Articles

TCAS software verification using constraint programming

AbstractSafety-critical software must be thoroughly verified before being exploited in commercial applications. In particular, any TCAS (Traffic Alert and Collision Avoidance System) implementation must be verified against safety properties extracted from the anti-collision theory that regulates the controlled airspace. This verification step is currently realized with manual code reviews and testing. In our work, we explore the capabilities of Constraint Programming for automated software verification and testing. We built a dedicated constraint solving procedure that combines constraint propagation with Linear Programming to solve conditional disjunctive constraint systems over bounded integers extracted from computer programs and safety properties. An experience we made on verifying a publicly available TCAS component implementation against a set of safety-critical properties showed that this approach is viable and efficient.

Improving problem solving ability in mathematics by using a mathematical model: A computerized approach

The present study investigates the improvement of students’ mathematical performance by using a mathematical model through a computerized approach. We had developed an intervention program and 11years students worked independently on a mathematical model in order to improve their self-representation in mathematics, to self-regulate their performance and consequently to improve their problem solving ability. The emphasis of using the specific model was on dividing the problem solving procedure into stages, the concentration on the students’ cognitive processes at each stage and the self-regulation of those cognitive processes in order to overcome cognitive obstacles. The use of the computer offered the opportunity to give students general comments, hints and feedback without the involvement of their teachers. Students had to communicate with a cartoon animation presenting a human being who faced difficulties and cognitive obstacles during problem solving procedure. Three tools were constructed for pre- and post-test (self-representation, mathematical performance and self-regulation). There were administered to 255 students (11years old), who constituted the experimental and the control group. Results confirmed that providing students with the opportunity to self-reflect on their learning behavior when they encounter obstacles in problem solving is one possible way to enhance students’ self-regulation and consequently their mathematical performance.

The solution of unconfined seepage problem using Natural Element Method (NEM) coupled with Genetic Algorithm (GA)

Phreatic line detection is a major challenge in seepage problems which should be solved by iterative solving procedures. In conventional methods such as finite element method (FEM), an updating mesh is needed in each iteration where the qualities of the mesh and the nodal connectivity have significant impact on the results. The main aim of this study is to use a method not to be sensitive to mesh generation.In this study, to obtain the optimal phreatic line by the 4th degree polynomial, Natural Element Method (NEM) and Genetic Algorithm (GA) are implemented. Based on the energy principle, an objective function is defined to control the phreatic line position. In the optimization procedure, NEM is utilized to analyze the problem. NEM is a domain type mesh-free method, adapted to geometry of the problem in each iteration. Results display more convergence and flexibility of the present method in comparison with previous studies.

DEVELOPMENT OF ANALYSIS PROGRAM FOR INCOMPRESSIBLE LOOPED FLOW NETWORK USING CONSTITUTIVE TOPOLOGIC MATRIX EQUATION

Flow network which consists of a number of flow paths and their junctions is popularly used in analysis of flow and pressure distribution for complicated pipe or channel flow structure. In order to analyze flow network, it is required to resolve mass conservation equation at each junction and energy conservation equation on all independent closed loops of the flow network. Topologic matrix which reflects characteristics of network connectivity simply transforms continuity equations into linear algebraic equations. However, typical solving procedure based on topologic matrix and linear analysis includes complicated algorithm to retrieve basic closed loop for energy conservation equations. It must confront the problem of nondeterministic polynomial completion. To resolve the problem of typical flow network analysis, the theory of constitutive topologic matrix equation is known to be effective. This paper describes a program algorithm of flow network analysis based on constitutive topological matrix theory and shows user interface of the program. Additionally, comparing analysis results of developed program with commercial software is provided to prove accuracy and reliability of developed program.

Procedure for treatment of hazardous waste by MID-MIX procedure in Serbia

This paper presents adequate treatment characteristics of the problem of hazardous waste while providing a specific example of the problem. Hazardous waste being discussed here is galvanic sludge. Furthermore, not only is the hazardous waste problem within a company discussed, but also on a national level. The MID-MIX® procedure was chosen and described as an optimal solution for adequate hazardous waste treatment, as well as activities and listed documentation on a possible procedure of transporting the waste discussed here to the treatment plant. With a view to demonstrate the problem solving procedure, a flowchart has been used as a graphical representation technique of a realization of a process. Improper waste disposal, especially of hazardous waste, has a tremendously negative effect on the environment. In this particular example it impacts the agriculture, and thereby the food production. Finally, directions for future work on this subject and solutions for the hazardous waste problem on a national level are provided here. Key words: Best available technology not entailing excessive cost (BATNEEC), MID-MIX® procedure, waste management, hazardous waste, waste generator, sustainability.

Insight From Complexity: Simplified Production System Model and A Two-Staged Solving Procedure Under The Constrained Factory Space

Insight From Complexity: Simplified Production System Model and A Two-Staged Solving Procedure Under The Constrained Factory Space

Approximate functional variable separation for the porous medium equation with perturbed nonlinear source

The approximate functional variable separation for the porous medium equation with perturbed nonlinear source is studied. Complete classification of the perturbed equation which admits approximate functional separable solutions is obtained. The main solving procedure for the approximate functional variable separation approach is shown by way of examples, and the corresponding approximate functional separable solutions to the resulting equations are then constructed.

A collocation interval analysis method for interval structural parameters and stochastic excitation

Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.

An efficient parallel-operational explicit algorithm for Taylor-type model of rate dependent crystal plasticity

Low computational efficiency and instability remain the greatest obstacle for crystal plasticity model applied to industrial practice. Herein, an explicit algorithm was deduced by introducing Taylor series expansion to recast the high-order nonlinear equation (for shear strain rate of slip systems) of rate dependent crystal plasticity into a set of linear equations. By virtue of a new approach to perform constitutive update in the crystallographic system, the linear model was so built with unknowns of the increments of stress and deformation resistance of slip systems. It was then solved directly by the complete pivot Gaussian elimination method within a two-level solving procedure. Full-strain-constraints (FC) Taylor model and crystal plasticity finite element method (CPFEM) model were utilized to verify the reliability, efficiency and stability of the presented algorithm. Then, texture evolution in two typical forming processes, in-plane shear and ideal plane-strain compression, was analyzed through pole figures and orientation distribution functions (ODF). The results achieved indicated that the presented algorithm was of high efficiency, especially in parallel operation with multiple CPUs, together with acceptable accuracy in the prediction of stress–strain response and texture evolution.

Application of an Improved Trust-Region Method to Rigid-Plastic Finite Element Analysis in Strip Rolling

Rigid-plastic finite element analysis (RPFEA) is an efficient and practical method to calculate rolling parameters in the strip rolling process. To solve the system of simulations equations involved in the RPFEA, a numerous of numerical methods, including the standard Newton-Raphson method, the modified Newton-Raphson method, and etc., have been proposed by different researchers. However, the computational time of the existed numerical methods can not meet the requirement of the online application. By tracking the computational time consumption for the main components in the standard Newton-Raphson method used in finite element analysis, it was found that linear search of damping factor occupies the most of the computational time. Thus, more efforts should be put on the linear search of damping factor to speed up the solving procedure, so that the online application of RPFEA is possible. In this paper, an improved trust-region method is developed to speed up the solving procedure, in which the Hessian matrix is forced to positive definite so as to improve the condition number of matrix. The numerical experiments are carried out to compare the proposed method with the standard Newton-Raphson method based on the practical data collected from a steel company in China. The numerical results demonstrate that the computational time of the proposed method outperforms that of the standard Newton-Raphson method and can meet the requirement of online application. Meanwhile the computational values of rolling force obtained by the proposed method are in good agreement with experimental values, which verifies the validity and stability of the proposed method.

A Hybrid GA-SA Algorithm for Multi-Objective Sequencing Problem in High-Product Mix Shop-Floor

As globalization has increased in the past few years, many companies attempts to made appropriate strategic decision to meet with this challenge. The problem under study mainly focuses on minimizing overall make-span but additional objectives such as balancing the assembly line and minimizing the variation of completion time are also considered. Due to the complexity of problem solving procedure by mathematical techniques, this paper presents a new approach of hybrid GA-SA implementation in order to meet the problem objectives. A proposed hybrid GA-SA is executed to overcome the problem complexity and meet the problem objectives. In order to check the efficiency of hybrid search techniques, a comparison is done between the results obtained by hybrid GA-SA and simple GA and the results comparison validates the effectiveness of presented hybrid search techniques.

Transport phenomena in proton exchange membrane fuel cells and over-potential distribution of membrane electrode assembly

To study the coupled phenomena occurring in proton exchange membrane fuel cells, a two-phase, one-dimensional, non-isothermal model is developed. The model includes water phase change, proton transport in the membrane and electro-osmotic effect. The thinnest, but most complex layer in the membrane electrode assembly, catalyst layer, is considered an interfacial boundary between the gas diffusion layer and the membrane. Mass and heat transfer and electro-chemical reaction through the catalyst layer are formulated into equations, which are applied to boundary conditions for the gas diffusion layer and the membrane. Detail accounts of the boundary equations and the numerical solving procedure used in this work are given. The polarization curve is calculated at different oxygen pressures and compared with the experimental results. When the operating condition is changed along the polarization curve, the change of physicochemical variables in the membrane electrode assembly is studied. In particular, the over-potential diagram presents the usage of the electro-chemical energy at each layer of the membrane electrode assembly. As the fuel cell reaction becomes more limited by mass transfer, it is found that higher over-potential is uselessly concentrated on the cathode catalyst layer. The over-potential for the anode reaction was usually ignored in other studies, but the ratio of the anode over-potential to the cathode over-potential increases at a higher current condition. Water content is distributed more unevenly in the membrane, as the cell current is increased. That causes the proton conductivity of membrane to decrease and the water content to increase in the cathode side, which hampers O 2 transfer. The effect of electro-osmotic property, one of important property of membrane, on cell performance is also studied.

Design Optimization of Vehicle Control Networks

The advancement of electronic technology has made significant contributions to the safety and convenience of modern vehicles. New intelligent functionalities of vehicles have been implemented in a number of electronic control units (ECUs) that are connected to each in vehicle control networks (VCNs). However, with the rapid increase in the number of ECUs, VCNs currently face several challenges, e.g., design complexity, space constraints, system reliability, and interdependency. Considering these factors, the complexity of the VCN design problem exponentially increases, which means that the problem cannot be solved within a reasonable time using conventional optimization techniques. In this paper, we report a new methodology for the optimal design of VCNs. An analytical model was derived to examine the fundamental characteristics of the VCN design problem. Compared with the case of a conventional data network, which typically considers temporal scheduling over a fixed physical topology, the VCN design problem should also consider spatial constraints, e.g., volume, position, and weight. Moreover, the spatial constraints change during the solving procedure. Such temporal and spatial joint optimization problems with varying constraints incur extremely high computational complexity. To tackle the high complexity, this paper proposes a fast solution based on a repeated-matching method, which reduces the problem complexity from <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NNN</i> ) to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NN</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). By applying our methodology to a number of different real-world VCN design scenarios, this proposal can produce a 1% near-optimal design within a significantly reduced time.

Micro EDM deposition in air by single discharge thermo simulation

A thermo-physical model for micro electric discharge machining deposition process using finite element method (FEM) was introduced. The numerical analysis of the single spark operation of the process was carried out in FEM software ANSYS, considering the Gaussian distribution of heat flux, initial and boundary conditions, and energy distribution of different kinds of tool electrode and workpiece in material. The suitable discharge conditions for the deposition process were predicted from the transient temperature analysis. According to the results from the simulation analysis, a brass micro cylinder with approximately 200 μm in diameter and 1.2 mm in height was deposited on a steel surface, and the deposited material was close packed. The validity of the thermo-physical model and FEM solving procedure were proven through a lot of machining experiments and tests of the deposited material characters.

Application of Fuzzy Multi-Objective Linear Programming Model in a Multi-Period Multi- Product Production Planning Problem

The Multi-Period Multi-Product (MPMP) production planning, as a well known problem in literature, attempts to match production rates of individual products with fluctuated market demand over planning horizon. This study, demonstrates how the conventional MPMP Linear Programming (LP) model may fail to utilize available capacity of machines, and also a novel Multi Objective Linear Programming (MOLP) model is developed to simultaneously minimize net present value of production costs and maximize machine utilization. The proposed model consists of production constraints such as available labor, inventory, maximum subcontracting levels and also forecasted demands. The proposed MOLP model is further converted to a Fuzzy Multi Objective Linear Programming (FMOLP) model utilizing piecewise linear membership functions. The model, accommodates the Decision Maker (DM) with a more systematic decision making approach enabling the DM to adjust the search direction during the solving procedure to achieve the most satisf...

Fuzzy Approach to the Capacitated Facility Location Problem

The main objective of the paper is to devise and implement the algorithmic solution of problem of optimal location of set of facilities so that all demands of customers will be satisfied and the relevant costs of creating and maintenance of facilities are minimal. This optimization task can be modelled by capacitated facility location problem, which is the special class of integer linear programming problems. The output parameters of solution of such problems are the number of facilities actually used, the location of facilities and the assignment of individual customers to the concrete facility from the optimal set of facilities. When a distribution system is to be designed, limits on terminal capability often must be taken into account. The capacity constraints in this case and also in other problems dealing with facility locations cause the severe difficulties in exact solving procedures because the underlying mathematical models are NP-hard. One possible approach is approximate method based on Lagrangean relaxation of the capacity constraints, which has several advantageous properties. In capacitated location problems, the capacity of a facility as an upper limit of its ability to satisfy a given volume of demands cannot be precisely determined in most of practical applications. This circumstance evokes an idea to employ fuzzy approach for handling of the capacities and to utilize suggests an idea the fuzzy description in capacity constraint relaxation. The relaxed problem is exactly solvable even for real-world instances. It has been used in the heuristic method exploring the concept of measure of infeasibility.

Application of Fuzzy Multi-Objective Linear Programming Model in a Multi-Period Multi-Product Production Planning Problem

The Multi-Period Multi-Product (MPMP) production planning, as a well known problem in literature, attempts to match production rates of individual products with fluctuated market demand over planning horizon. This study, demonstrates how the conventional MPMP Linear Programming (LP) model may fail to utilize available capacity of machines, and also a novel Multi Objective Linear Programming (MOLP) model is developed to simultaneously minimize net present value of production costs and maximize machine utilization. The proposed model consists of production constraints such as available labor, inventory, maximum subcontracting levels and also forecasted demands. The proposed MOLP model is further converted to a Fuzzy Multi Objective Linear Programming (FMOLP) model utilizing piecewise linear membership functions. The model, accommodates the Decision Maker (DM) with a more systematic decision making approach enabling the DM to adjust the search direction during the solving procedure to achieve the most satisf...

Novel Approach to the Microbusinesses Logistical System Design Based on the Information Technology (Nanologistics)

AbstractThe solution of a mircobussines “knapsack problem”, i.e. article range forming one, using modern information technology is considered. The suggested approach is based on the logistical management of the material flow. The logistics is branched out to the new nanologistics branch that investigates a mircobussinessman logistics behavior. Information technology backgrounds, two logistical types of the mircobussinessmans, limitations and risks existing by the article range forming are presented and discussed. The mathematical problem definition and the problem solving procedure are shown.

A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem

This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way, the good stability properties of continuous-pressure mixed finite element approximations of the Stokes system are preserved. Estimates ensuring that each iteration can be performed in a stable way as well as a proof of the convergence of the iterative process provide a theoretical background for the application of the related solving procedure. Finally some numerical experiments are given to demonstrate the effectiveness of the approach, and particularly to compare its efficiency with an adaptation to this framework of a standard FETI-DP method.

A gradient approximation approach for adjusting temporal origin–destination matrices

The temporal demand matrix is an essential input to both on-line and off-line applications of dynamic traffic assignment (DTA). This paper presents a new method to solve the simultaneous adjustment of a dynamic traffic demand matrix, searching for a reliable solution with acceptable computational times for off-line applications and using as an input traffic counts and speeds, prior O–D matrices and other aggregate demand data (traffic demand productions by zone). The proposed solving procedure is a modification of the basic Simultaneous Perturbation Stochastic Approximation (SPSA) path search optimization method; it can find a good solution when the starting point (the seed matrix) is assumed to be “near” the optimal one, working with a gradient approximation based on a simultaneous perturbation of each demand variable.