An International Journal of Optimization and Control: Theories & Applications (IJOCTA)

List coloring based algorithm for the Futoshiki puzzle

2024-10-09T21:35:13+08:00

Given a graph G=(V, E) and a list of available colors L(v) for each vertex v\in V, where L(v) \subseteq {1, 2, ..., k}, List k-Coloring refers to the problem of assigning colors to the vertices of $G$ so that each vertex receives a color from its own list and no two neighboring vertices receive the same color. The decision version of the problem, List k-Coloring, is NP-complete even for bipartite graphs. As an application of list coloring problem we are interested in the Futoshiki Problem. Futoshiki is an NP-complete Latin Square Completion Type Puzzle. Considering Futoshiki puzzle as a constraint satisfaction problem, we first give a list coloring based algorithm for it which is efficient for small boards of fixed size. To thoroughly investigate the efficiency of our algorithm in comparison with a proposed backtracking-based algorithm, we conducted a substantial number of computational experiments at different difficulty levels, considering varying numbers of inequality constraints and given values. Our results from the extensive range of experiments indicate that the list coloring-based algorithm is much more efficient.

Early prediction of fabric quality using machine learning to reduce rework in manufacturing processes

2024-10-09T21:35:11+08:00

The increasing competition and rapid technological advancements in today's business world have raised customer expectations. People now expect quick delivery, low prices, and high-quality products. As a result, companies must adapt to this competitive environment to survive. Rework, which is a significant cost in production, increases expenses, reduces production efficiency, and can lead to customer attrition. Research shows various efforts across different sectors to reduce rework, although there is still a gap in the textile sector's fabric dyeing units. Common problems in these units include non-retentive colors, customer dissatisfaction with shades, and repeated dyeing due to environmental factors or dye vat issues. This study uses logistic regression and artificial neural networks models from machine learning to predict which fabrics will need rework, using data from a textile company in Bursa. The analysis indicates that artificial neural networks models perform better.

Witte’s conditions for uniqueness of solutions to a class of Fractal-Fractional ordinary differential equations

2024-10-09T21:35:07+08:00

In this paper, Witte's conditions for the uniqueness solution of nonlinear differential equations with integer and non-integer order derivatives are investigated. We present a detailed analysis of the uniqueness solutions of four classes of nonlinear differential equations with nonlocal operators. These classes include classical and fractional ordinary differential equations in fractal calculus. For each case, theorems and lemmas and their proofs are presented in detail.

Influence of rotation on peristaltic flow for pseudoplastic fluid: a wavy channel

2024-10-10T10:55:16+08:00

The phenomenon of rotation serves multiple purposes in cosmic and geophysical phenomena. It offers insights into the formation of galaxies and the circulation patterns of oceans. Moreover, rotational diffusion elucidates the orientation of nanoparticles within fluid mediums. Investigating the dynamics of fluid peristalsis under the influence of rotational forces holds significant relevance in addressing challenges associated with the transportation of conductive physiological fluids such as blood, polymeric materials, and saline water. This study focused on studying the impact of rotation on the peristaltic transport of non-Newtonian pseudoplastic fluids through a wavy channel. The complexity of flow equations, including the continuity and motion equations, is mathematically formulated and transformed into dimensionless nonlinear ordinary differential equations depending on the assumption of low Reynolds number and long wavelength approximation. Perturbation technique is employed to solve the problem for the stream function and the resulted system is implemented and plotted using MATHEMATICA software along with the boundary conditions. Graphical discussion is involved to utilize the impact of the emerging parameters in the flow characteristic, encompassing the velocity profile, pressure gradient, pressure rise, and trapping phenomenon. The research revealed that rotation significantly influences the fluid flow within the channel, diminishing the regressive and inhibitory impact of the fluid parameter, consequently enhancing the fluid flow within the channel.

A comparative view to H_infinity-norm of transfer functions of linear DAEs

2024-10-10T11:20:39+08:00

In this paper, bisection and extended-balanced singular perturbation methods are used to calculate the H_infinity-norm of the transfer function of a linear DAEs system for the particular case D=0. In the beginning, the approaches' algorithms and error analysis are provided separately. Next, the methods are employed to calculate the H_infinity-norms of a numerical example pertaining to an automotive gas turbine model, and the error limits are used to check the norms in the suitable range, respectively. Ultimately, every solution is compared individually with the problem's H_infinity-norm values, which are retrieved from MATLAB.

Fuzzy-PID and interpolation: a novel synergetic approach to process control

2024-10-10T12:11:48+08:00

This paper presents a novel approach for tuning a fuzzy-based proportional-integral-derivative (PID) controller to enhance the control performance of a chemical process control system. The proposed approach combines the advantages of fuzzy- PID and interpolation to achieve improved control performance. Properly tuned PID controllers can help maintain process stability, minimize deviations from setpoints, and ensure efficient operation in industrial systems. Fuzzy logic allows for the incorporation of expert knowledge and linguistic rules, enabling the controller to handle uncertain and imprecise process information. Fuzzy PID controllers combine fuzzy logic and conventional PID control to enhance control performance, particularly in systems with complex or nonlinear dynamic such as chemical plant. It dynamically adjusts the PID parameters—proportional gain (Kp), integral gain (Ki), and derivative gain (Kd)—based on error e(t) and change of error Delta e(t). Interpolation plays a crucial role in this context by filling in the gaps or handling situations not explicitly covered by the fuzzy rules. Comparative studies are conducted to evaluate the performance of the fuzzy PID controller against conventional PID controllers and other advanced control techniques. It is demonstrated that the synergy between fuzzy logic and interpolation not only enhances control performance but also offers a more intuitive and adaptable solution for addressing the complexities of modern chemical process control systems.

Global mathematical analysis of a patchy epidemic model

2024-10-14T21:35:37+08:00

The dissemination of a disease within a homogeneous population can typically be modeled and managed in a uniform fashion. Conversely, in non-homogeneous populations, it is essential to account for variations among subpopulations to achieve more precise predictive modeling and efficacious intervention strategies. In this study, we introduce and examine the comprehensive behavior of a deterministic two-patch epidemic model alongside its stochastic counterpart to assess disease dynamics between two heterogeneous populations inhabiting distinct regions. First, utilizing a specific Lyapunov function, we demonstrate that the disease-free equilibrium of the deterministic model is globally asymptotically stable. For the stochastic model, we establish that it is well-posed, meaning it possesses a unique positive solution with probability one. Subsequently, we ascertain the conditions necessary to ensure the total extinction of the disease across both regions. Furthermore, we explicitly determine a threshold condition under which the disease persists in both areas. Additionally, we discuss a scenario wherein the disease persists in one region while simultaneously becoming extinct in the other. The article concludes with a series of numerical simulations that corroborate the theoretical findings.

An Inverse recursive algorithm to retrieve the shape of the inaccessible dielectric objects

2024-10-16T09:52:32+08:00

A regularized electromagnetic iterative inverse algorithm is formulated and implemented to reconstruct the shape of 2D dielectric objects using the far-field pattern of the scattered field data. To achieve this, an integral operator that maps the unknown boundary of the object onto the far-field pattern of the scattered field is defined and solved for the unknown boundary. The addressed inverse problem has an ill-posed nature and inherits nonlinearity. To overcome these, the proposed solution is linearized via Newton and regularized by Tikhonov in the sense of least squares. Besides, the dominance of the shadow region in the inverse-imaging process is exceeded by considering the superposition of multi-incoming plane waves, leading to less computational cost and a very fast inversion process. Comprehensive numerical analyses are carried out to ascertain the algorithm's feasibility, revealing that it is very efficient and promising.

A local differential quadrature method for the generalized nonlinear Schrödinger (GNLS) equation

2024-10-16T10:22:07+08:00

A local differential quadrature method based on Fourier series expansion numerically solves the generalized nonlinear Schrodinger equation. For time integration, a Runge-Kutta fourth-order method is used. Matrix stability analysis is used to examine the method's stability. Three test problems involving the motion of a single solitary wave, the interaction of two solitary waves, and a solution that blows up in finite time, respectively, demonstrate the accuracy and efficiency of the provided method. Finally, the numerical results obtained from the presented method are compared with the exact solution and those obtained in earlier works available in the literature.

Modeling the dependency structure between quality characteristics in multi-stage manufacturing processes with copula functions

2024-10-24T18:13:54+08:00

This study is about multi-stage manufacturing processes and their control by statistical process control modeling. There are two kinds of dependence structures in a multi-stage manufacturing process: one is the dependence between the stages of the process, and the other is the dependence between the concerned quality characteristics. This study employs state-space models to demonstrate the dependency structure between the process stages and uses the Kalman filter method to estimate the states of the processes. In this setup, copula modeling is proposed to determine the dependence structure between the quality characteristics of interest. A simulation study is conducted to assess the model's accuracy. As a result, it was found that the model gives highly accurate predictions according to the mean absolute percentage error (MAPE) criteria (<10%).