Appropriate Combination of Crossover Operator and Mutation Operator in Genetic Algorithms for the Travelling Salesman Problem

Genetic algorithms(GAs)are very good metaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems.AsimpleGAbeginswith a set of solutions represented by a population of chromosomes and then uses the idea of survival of the fittest in the selection process to select some fitter chromosomes.It uses a crossover operator to create better offspring chromosomes and thus,converges the population.Also,it uses a mutation operator to explore the unexplored areas by the crossover operator,and thus,diversifies the GA search space.A combination of crossover and mutation operators makes the GA search strong enough to reach the optimal solution.However,appropriate selection and combination of crossover operator and mutation operator can lead to a very good GA for solving an optimization problem.In this present paper,we aim to study the benchmark traveling salesman problem(TSP).We developed several genetic algorithms using seven crossover operators and six mutation operators for the TSP and then compared them to some benchmark TSPLIB instances.The experimental studies show the effectiveness of the combination of a comprehensive sequential constructive crossover operator and insertion mutation operator for the problem.The GA using the comprehensive sequential constructive crossover with insertion mutation could find average solutions whose average percentage of excesses from the best-known solutions are between 0.22 and 14.94 for our experimented problem instances.

Influence of Brownian Motion, Thermophoresis and Magnetic Effects on a Fluid Containing Nanoparticles Flowing over a Stretchable Cylinder

The influence of Brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

On Performance Characteristics of a Nonparametric Subset Selection Procedure with a Small Randomized Block Experimental Design

This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e., that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.

Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.

Modelling Foot and Mouth Disease in the Context of Active Immigrants

This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R0) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R0 α1 and α2) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.

BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX

Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

Reduced differential transform and Sumudu transform methods for solving fractional financial models of awareness

In that paper,we new study has been carried out on previous studies of one of the most important mathematical models that describe the global economic movement,and that is described as a non-linear fractional financial model of awareness,where the studies are represented at the steps following:One:The schematic of the model is suggested.Two:The disease-free equilibrium point(DFE)and the stability of the equilibrium point are discussed.Three:The stability of the model is fulfilled by drawing the Lyapunov exponents and Poincare map.Fourth:The existence of uniformly stable solutions have discussed.Five:The Caputo is described as the fractional derivative.Six:Fractional optimal control for NFFMA is discussed by clarifying the fractional optimal control through drawing before and after control.Seven:Reduced differential transform method(RDTM)and Sumudu Decomposition Method(SDM)are used to take the resolution of an NFFMA.Finally,we display that SDM and RDTM are highly identical.

Analysis of TOPSIS techniques based on bipolar complex fuzzy N-soft setting and their applications in decision-making problems

A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theory of BCFN-SS is the generalisation of two various theories,that is,bipolar complex fuzzy(BCF)and N-SS.The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time.Further,various algebraic operations,including the usual type of union,intersection,complements,and a few others types,are invented.Certain primary operational laws for BCFNSS are also invented.Moreover,a technique for order preference by similarity to the ideal solution(TOPSIS)approach is devised in the setting of BCFN-SS for managing strategic decision-making(DM)dilemmas containing BCFN-SS information.Keeping in mind the usefulness and benefits of the TOPSIS approach,two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted.To disclose the prominence and benefits of the devised work,the devised approaches with numerous prevailing work are compared.

A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

In this article,a Susceptible-Exposed-Infectious-Recovered(SEIR)epidemic model is considered.The equilibrium analysis and reproduction number are studied.The conventional models have made assumptions of homogeneity in disease transmission that contradict the actual reality.However,it is crucial to consider the heterogeneity of the transmission rate when modeling disease dynamics.Describing the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory.A numerical scheme nonstandard,finite difference(NSFD)approach is developed for the studied model and the results of numerical simulations are presented.Simulations of the constructed scheme are presented.The positivity,convergence and consistency of the developed technique are investigated using mathematical induction,Jacobean matrix and Taylor series expansions respectively.The suggested scheme preserves all these essential characteristics of the disease dynamical models.The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease.Moreover,the obtained method generates plausible predictions that can be used by regulators to support the decision-making process to design and develop control strategies.Effects of the natural immunity on the infected class are studied which reveals that an increase in natural immunity can decrease the infection and vice versa.

Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation.The governing partial differential equations(PDEs)are converted into ordinary differential equations(ODEs)using the similarity transformation.The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software.It was found that dual solutions exist for the shrinking parameter values up to a certain range.The numerical results obtained are compared,and the comparison showed a good agreement with the existing results in the literature.The governing parameters’effect on the velocity,temperature and nanoparticle fraction fields as well as the skin friction coefficient,the local Nusselt number and the Sherwood number are represented graphically and analyzed.The variation of the velocity,temperature and concentration increase with the increase in the suction and magnetic field parameters.It seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it.

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand,foot and mouth disease(HFMD),primarily caused by enterovirus 71,was reported in Taiwan in 1998.HFMD surveillance is needed to assess the spread of HFMD.The parameters we use in mathematical models are usually classical mathematical parameters,called crisp parameters,which are taken for granted.But any biological or physical phenomenon is best explained by uncertainty.To represent a realistic situation in any mathematical model,fuzzy parameters can be very useful.Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling.However,few works use fuzzy theory in building models to simulateHFMDdynamics.In this context,we examined anHFMD model with fuzzy parameters.A Non Standard Finite Difference(NSFD)scheme is developed to solve the model.The developed technique retains essential properties such as positivity and dynamic consistency.Numerical simulations are presented to support the analytical results.The convergence and consistency of the proposed method are also discussed.The proposed method converges unconditionally while the many classical methods in the literature do not possess this property.In this regard,our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Optimization of Coronavirus Pandemic Model Through Artificial Intelligence

Artificial intelligence is demonstrated by machines,unlike the natural intelligence displayed by animals,including humans.Artificial intelligence research has been defined as the field of study of intelligent agents,which refers to any system that perceives its environment and takes actions that maximize its chance of achieving its goals.The techniques of intelligent computing solve many applications of mathematical modeling.The researchworkwas designed via a particularmethod of artificial neural networks to solve the mathematical model of coronavirus.The representation of the mathematical model is made via systems of nonlinear ordinary differential equations.These differential equations are established by collecting the susceptible,the exposed,the symptomatic,super spreaders,infection with asymptomatic,hospitalized,recovery,and fatality classes.The generation of the coronavirus model’s dataset is exploited by the strength of the explicit Runge Kutta method for different countries like India,Pakistan,Italy,and many more.The generated dataset is approximately used for training,validation,and testing processes for each cyclic update in Bayesian Regularization Backpropagation for the numerical treatment of the dynamics of the desired model.The performance and effectiveness of the designed methodology are checked through mean squared error,error histograms,numerical solutions,absolute error,and regression analysis.

Intoxication Induced by Urea Containing Diets in Broiler Chickens: Effect on Weight Gain, Feed Conversion Ratio, Hematological and Biochemical Profiles

Urea as a source of cheap non-protein nitrogen is used to adulterate fish and meat meals which are basic components of broiler diets. The present study was carried out to elucidate the effects of urea on weight gain, and hematological and biochemical profiles. A total of 48 broiler chicks were randomly allotted into 4 groups, designated Groups 1, 2, 3 and 4 of 12 birds each. Birds in Groups 2, 3 and 4 were fed on diets containing urea at the levels of 1%, 2.5% and 4%, respectively. Birds in Group 1 served as control and were not exposed to urea. Experimentation period was for 3 weeks and experiment was terminated when birds were 42 days of age. Body weight of all intoxicated birds at the various intervals was significantly decreased in comparison with that of the untreated control. Compared with control, all intoxicated broilers manifested significant (P ≤ 0.05) decrease in all hematological parameters involving erythrocytic and total leucocytic counts, Hemoglobin (Hb) and Packed Cell Volume (PCV) on a dose- and time-pattern. In comparison with the control levels, biochemical profile of the intoxicated birds disclosed significant decrease in blood glucose level and significant increase in serum uric acid, urea, Alkaline Phosphatase (ALP) and Lactate Dehydrogenase (LDH) levels. Based upon the present data, it was concluded that the addition of urea to broiler diets bears serious sequences concerning the general health condition, performance, weight gain, and hematological and biochemical profiles.

Interrupted Time Series Analysis of Military and Civilian Regimes in Nigeria: A Statistical Evidence from Gross Domestic Product (GDP)

Governments influence the economy by changing the level and types of taxes, the extent and composition of spending, and the degree and form of borrowing. Governments directly and indirectly influence the way resources are used in the economy. Higher taxes, fees, and greater regulations can stymie businesses or entire industries and the resulting impact is reflected on the country’s economy status (strong or weak). The growth rate of GDP is often used as an indicator of the general health of the economy. In broad terms, an increase in real GDP is interpreted as a sign that the economy is doing well. So it is important to study and pay more attention to country’s GDP growth rate. In this paper, an intervention analysis approach was applied to Nigeria GDP data in order to evaluate the performances of military and civilian rules in the country. Data on Nigeria GDP were collected and subjected to interrupted (intervention) time series model. Based on the Alkaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and sigma2 values, the interrupted time series model ARIMA (1, 1, 0) with exogenous variables (per capita per capita GDP, intervention, year and yearAfter) was identified as the best model amongst other competing models. It was observed that the intervention (civilian rule) was significant at the 10% level of significance in increasing the Nigeria GDP by 10B US$ on the average since 2005 till 2021 while controlling for the effects of other determinants. Also, the ARIMA (1, 1, 0) forecasts indicate that the Nigeria GDP will continue increasing during the civilian rule. As a result, changing from military rule to civilian rule in Nigeria significantly increased the GDP of the country.

Interrupted Time Series Analysis of Military and Civilian Regimes in Nigeria: A Statistical Evidence from Gross Domestic Product (GDP)

Governments influence the economy by changing the level and types of taxes, the extent and composition of spending, and the degree and form of borrowing. Governments directly and indirectly influence the way resources are used in the economy. Higher taxes, fees, and greater regulations can stymie businesses or entire industries and the resulting impact is reflected on the country’s economy status (strong or weak). The growth rate of GDP is often used as an indicator of the general health of the economy. In broad terms, an increase in real GDP is interpreted as a sign that the economy is doing well. So it is important to study and pay more attention to country’s GDP growth rate. In this paper, an intervention analysis approach was applied to Nigeria GDP data in order to evaluate the performances of military and civilian rules in the country. Data on Nigeria GDP were collected and subjected to interrupted (intervention) time series model. Based on the Alkaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and sigma2 values, the interrupted time series model ARIMA (1, 1, 0) with exogenous variables (per capita per capita GDP, intervention, year and yearAfter) was identified as the best model amongst other competing models. It was observed that the intervention (civilian rule) was significant at the 10% level of significance in increasing the Nigeria GDP by 10B US$ on the average since 2005 till 2021 while controlling for the effects of other determinants. Also, the ARIMA (1, 1, 0) forecasts indicate that the Nigeria GDP will continue increasing during the civilian rule. As a result, changing from military rule to civilian rule in Nigeria significantly increased the GDP of the country.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.