Clique Finder

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

Clique Finder

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

Design and Analysis for Hypoid Gears with Ease-Off Flank Modification

An approach of ease-off flank modification for hypoid gears was proposed to improve the meshing performance of automobile drive axle. Firstly, a conjugate pinion matching with gear globally was developed based on gear meshing theory. Secondly, a modified pinion was represented by a sum of two vector functions determining the conjugate pinion and the normal ease-off deviations expressed by both predesigned transmission error function and tooth profile modification curves to change the initial contact clearance of the tooth. Thirdly, the best ease-off deviations were determined by optimizing the minimum amplitude of loaded transmission error (ALTE) based on tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA). Finally, the results show that effective contact ratios (εe) are established by clearances both teeth space and of contact elliptical, and greatly affect ALTE. The εe is a variable value with increasing loads for the tooth with modification. ALTE decreases with increasing εe. After εe reaches the maximum, ALTE increases with increasing loads. The mismatch of the best ease-off tooth is minimal, which contributes to effective reduction in ALTE, thus significantly improving drive performance.

A Single Equation to Depict Bottomhole Pressure Behavior for a Uniform Flux Hydraulic Fractured Well

Pressure transient analysis for a vertically hydraulically fractured well is evaluated using two different equations, which cater for linear flow at the early stage and radial flow in the later stage. However, there are three different stages that take place for an analysis of pressure transient, namely linear, transition and pseudo-radial flow. The transition flow regime is usually studied by numerical, inclusive methods or approximated analytically, for which no specific equation has been built, using the linear and radial equations. Neither of the approaches are fully analytical. The numerical, inclusive approach results in separate calculations for the different flow regimes because the equation cannot cater for all of the regimes, while the analytical approach results in a difficult inversion process to compute well test-derived properties such as permeability. There are two types of flow patterns in the fracture, which are uniform and non-uniform, called infinite conductivity in a high conductivity fracture. The study was conducted by utilizing an analogous study of linear flow equations. Instead of using the conventional error function, the exponential integral with an infinite number of wells was used. The results obtained from the developed analytical solution matched the numerical results, which proved that the equation was representative of the case. In conclusion, the generated analytical equation can be directly used as a substitute for current methods of analyzing uniform flow in a hydraulically fractured well.

Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination

The hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical model based on inverse problem-solving techniques to identify the HDT (noted D=) of the studied porous medium. We then showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA). The IOA is based on the numerical solution of the direct problem (which solves the convection–diffusion type transport equation) and the optimization of the error function between the simulated concentration field and that observed at the application site. The partial differential equations of the direct model were solved by high resolution of (Δx=Δy=1 m) Lattice Boltzmann Method (LBM) whose computational code is named HYDRODISP-LBM (HYDRO-DISpersion by LBM). As for the optimization step, we opted for the CMA-ES (Covariance Matrix Adaptation-Evolution Strategy) algorithm. Our choice for these two methods was motivated by their excellent performance proven in the abundant literature. The paper describes in detail the operation of the coupling of the two computer codes forming the IOA that we have named HYDRODISP-LBM/CMA-ES. Finally, the IOA was applied at the Beauvais experimental site to identify the HDT D=. The geological analyzes of this site showed that the tensor identified by the IOA is in perfect agreement with the characteristics of the geological formation of the site which are connected with the mixing processes of the latter.

A Novel Design of Morlet Wavelet to Solve the Dynamics of Nervous Stomach Nonlinear Model

The present study introduces a novel design of Morlet wavelet neural network (MWNN) models to solve a class of a nonlinear nervous stomach system represented with governing ODEs systems via three categories, tension, food and medicine, i.e., TFM model. The comprehensive detail of each category is designated together with the sleep factor, food rate, tension rate, medicine factor and death rate are also provided. The computational structure of MWNNs along with the global search ability of genetic algorithm (GA) and local search competence of active-set algorithms (ASAs), i.e., MWNN-GA-ASAs is applied to solve the TFM model. The optimization of an error function, for nonlinear TFM model and its related boundary conditions, is performed using the hybrid heuristics of GA-ASAs. The performance of the obtained outcomes through MWNN-GA-ASAs for solving the nonlinear TFM model is compared with the results of state of the article numerical computing paradigm via Adams methods to validate the precision of the MWNN-GA-ASAs. Moreover, statistical assessments studies for 50 independent trials with 10 neuron-based networks further authenticate the efficacy, reliability and consistent convergence of the proposed MWNN-GA-ASAs.

Investigation on Acoustic Versus Functional Characteristics of Porous Asphalt

The theoretical background, standards, and contract requirements of pavement friction courses involve functional (e.g., permeability) and acoustic (e.g., resistivity) characteristics. Unfortunately, their relationship is partly unknown and uncertain. This affects the comprehensiveness and soundness of the mix design of asphalt pavements. Based on the issues above, the goals of this study were confined into the following ones: 1) to investigate the relationship between acoustic and functional properties of porous asphalts; 2) to investigate, through one-layer (1L) and two-layer (2L) models, the effectiveness of the estimates of acoustic input data through mixture volumetric- and permeability-related characteristics. Volumetric and acoustic tests were performed and simulations were carried out. Equations and strategies to support a comprehensive approach were derived. Results demonstrate that even if the measured resistivity is very important, permeability-based estimates of resistivity well explain acoustic spectra. Furthermore, the distance between observed and estimated peaks of the absorption spectrum emerges as the best error function.

An Effective Antenna Array Diagnosis Method via Multivalued Neural Network Inverse Modeling Approach

Failure of element (s) in antenna arrays impair (s) symmetry and lead to unwanted distorted radiation pattern. The replacement of defective elements in aircraft antennas is a solution to the problem, but it remains a critical problem in space stations. In this paper, an antenna array diagnosis technique based on multivalued neural network (mNN) inverse modeling is proposed. Since inverse analytical input-to-output formulation is generally a challenging and important task in solving the inverse problem of array diagnosis, ANN is a compelling alternative, because it is trainable and learns from data in inverse modelling. The mNN technique proposed is an inverse modelling technique, which accommodates measurements for output model. This network takes radiation pattern samples with faults and matches it to the corresponding position or location of the faulty elements in that antenna array. In addition, we develop a new training error function, which focuses on the matching of each training sample by a value of our proposed inverse model, while the remaining values are free, and trained to match distorted radiation patterns. Thereby, mNN learns all training data by redirecting the faulty elements patterns into various values of the inverse model. Therefore, mNN is able to perform accurate array diagnosis in an automated and simpler manner.