Azali Saudi

Path planning for autonomous mobile robots remains a critical challenge, particularly in environments with obstacles and constraints. Efficient navigation requires a robust algorithm capable of generating smooth, collision-free trajectories while ensuring computational efficiency. This study addresses the problem of indoor mobile robot navigation by leveraging harmonic potential fields, a solution derived from Laplace’s equation, to formulate an effective path-planning strategy. Conventional numerical methods for solving Laplace’s equation, such as Successive Over-Relaxation and Accelerated Over-Relaxation, often require extensive computational resources, especially in large-scale environments. To overcome this limitation, this research introduces an improved iterative approach, the Explicit Decoupled Group Modified Accelerated Over-Relaxation (EDGMAOR) method, which enhances computational efficiency and convergence speed. The EDGMAOR method incorporates a half-sweep block approach, significantly reducing the number of computations required per iteration while maintaining accuracy. To validate the effectiveness of the proposed method, simulations were conducted in a static, enclosed environment with various configurations of obstacles. Different starting and goal positions were tested to assess the efficiency, accuracy, and computational cost of the generated paths. The results indicate that the EDGMAOR method outperforms conventional approaches by achieving faster convergence rates and reduced computational time, demonstrating its suitability for real-time robot pathfinding applications. Furthermore, the study highlights that with greater obstacles proliferation, the EDGMAOR method maintains its efficiency, as obstacle regions are automatically excluded from unnecessary computations. This characteristic makes the method particularly useful for complex indoor environments where real-time processing is crucial. In conclusion, this research establishes EDGMAOR as a practical and effective solution for solving mobile robot path-planning problems, providing a balance between computational speed, accuracy, and robustness. The findings contribute to the ongoing advancements in autonomous robotics and artificial intelligence-driven navigation systems, with potential applications in industrial automation, smart transportation, and defence sectors.

This paper presents the findings of a study that examined the effectiveness of the application of Quarter-Sweep Boosted AOR with the 9-Point Laplacian operator using the families of relaxation methods for computing the solutions of Laplace's equation to obtain the harmonic potentials+ This work is a continuation from the past study that applied the standard 5-Point Laplacian to solve path planning issue that a mobile robot faces when working in indoor environment. The robot can navigate from a given starting position to a goal position by following the safest path, ensuring it avoids any obstacles and minimizes the risk of collisions. By utilizing Laplace's equation and computing the distribution of potential values in the simulated environments, the robot can determine the safest path that avoids obstacles present in the environment. This method ensures that the robot moves along a path where the potential for collisions is minimized. The findings confirm that Quarter-Sweep Boosted AOR (QSBAOR) outperforms Half-Sweep Boosted AOR (HSBAOR) and Full-Sweep Boosted AOR (FSBAOR). QSBAOR and HSBAOR show 75% and 50% reduction respectively, compared to FSBAOR in terms of computational complexity.

The complex and invasive dynamics of brain tumours present significant clinical and computational challenges. This study aims to enhance the numerical efficiency of brain tumour growth simulation through an improved iterative solver. A two-dimensional diffusion–proliferation model of brain tumour growth is discretized using an implicit finite difference scheme to generate a large, sparse linear system. The resulting system is solved iteratively using the Kaudd Successive Over-Relaxation (KSOR) method and compared with the classical Gauss–Seidel (GS) approach in terms of convergence rate, iteration count, computation time, and numerical accuracy. Numerical experiments reveal that the KSOR method achieves up to 94.65% reduction in iterations and 86.33% faster computation compared to GS while maintaining high stability and accuracy. These findings demonstrate that integrating the implicit finite difference scheme with KSOR provides a robust and efficient numerical framework for modelling two-dimensional brain tumour dynamics. This approach offers practical implications for improving computational modelling of tumour progression, potentially supporting real-time prediction and treatment planning in biomedical and clinical applications.

This paper presents the study to examine the effectiveness of the application of Quarter Sweep Boosted TOR with the 9-Point Laplacian operator using the families of relaxation methods in the computation of Laplace equation solutions to obtain the harmonic potentials. This work is a continuation from the past study that applied the standard application 5-Point Laplacian to solve path planning issue which a mobile robot faces because of working in indoor environment. The robot can navigate from a given initial position to a goal position by following the safest path, ensuring it avoids any obstacles and minimizes the risk of collisions. By utilizing the equation of Laplace and computing the potential values’ distribution in the environments which have been simulated, the robot can determine the safest path that avoids obstacles which exists in the environment. This method ensures that the robot moves along a path where the potential for collisions is minimized. The findings confirm that QSBTOR outperforms Half Sweep Boosted TOR (HSBTOR) and Full Sweep Boosted TOR (FSBTOR). QSBTOR and HSBTOR show 73% and 50% reduction respectively, compared to FSBTOR in terms of computational complexity.

This paper presents the application of the Modified TOR (MTOR) method, implemented using CUDA, for solving Poisson's equation through the iterative Finite Difference (FD) method. The study aims to provide a detailed description of the MTOR method for solving Partial Differential Equations (PDEs) on both standard and rotated meshes, employing CUDA for parallel processing. The MTOR method uses a red-black ordering strategy during iteration; consequently, the calculation of red cells utilizes the updated values of their four neighbouring black cells, and vice versa. To evaluate the performance of these iterative methods, robot path planning and image blending problems were tested. Our results highlight the advantages of employing parallel methods on Graphics Processing Units (GPUs) in terms of iterations and computational time, compared to their sequential counterparts. In the path planning simulation, the parallel implementations exhibited over 20 times faster execution compared to their corresponding sequential versions. Similarly, in the image blending problem, the parallel implementations achieved more than a 6-fold improvement in speed compared to the sequential methods.

Quantum networks facilitate communication among quantum devices, playing a crucial role in enabling applications beyond the reach of classical networks. However, creating a quantum network that supports reliable long-distance entanglement distribution remains a significant challenge. Unlike classical networks, connections in quantum networks are established through entanglement generation. Effective communication between quantum devices requires a routing strategy that efficiently manages the establishment of entanglement. In addition to fidelity, the quality of communication is also determined by the capacity of the generated entanglement. Therefore, we proposed a capacity allocation scheduling scheme based on a metaheuristic approach, namely a Genetic Algorithm (GA), to ensure efficient capacity allocation for multiple communication paths within each communication request. Simulations were conducted in four different scenarios, and the results were compared to an existing capacity allocation scheduling algorithm, Progressive Filling (PF), to verify the effectiveness of the proposed scheme. The average capacity utilisation, U and weighted throughput, F results indicate that PF outperforms GA in a scenario with four communication requests, while GA performs better in scenarios involving six, eight, and ten communication requests. Specifically, the improvement in average capacity utilisation ranges from 8% to 46%, and the improvement in weighted throughput ranges from 24% to 94%. These results suggest that GA can serve as a valuable reference for designing optimal routing and capacity allocation schemes in more complex networks with multiple communication requests.

In recent years, there has been an increasing interest in the study of path planning algorithms for autonomous robot systems. The current study aims to examine the simulation performance of path planning using the Successive Overrelaxation (SOR) method and the log-space Gauss-Seidel (LGS) method. The simulation addresses the numerical solution of a boundary value problem for Laplace's equation, utilising Log-space mapping and adhering to Dirichlet boundary conditions within a closed region. The experiment done in both sparse and dense environments shows the benefits of the iterative methods. The paths generated by the SOR and LGS approach are compared using specific numerical examples in smooth trajectory planning. The comparative analysis suggests that the LGS iterative method effectively addresses the issue of achieving high precision in the numerical computation of the gradient of harmonic potentials for generating safe paths in dense environments with narrow corridors and difficult regions. The simulation results also indicate that the LGS employed in this study exhibits faster convergence. Although it has a slower execution time, it is successful in dense environments compared to the SOR method.

The quantum internet facilitates communication between quantum devices, making its development essential for advancing quantum technologies. However, realizing a fully functional quantum internet requires overcoming several challenges, including establishing efficient routing mechanisms to ensure effective communication. This study proposes a capacity allocation scheduling scheme based on a Genetic Algorithm (GA) to address the issue of non-uniform edge capacity utilization within a practical routing process. However, it is essential to note that the performance of the GA scheduling scheme is influenced by its control parameters, highlighting the need for parameter tuning. In this paper, we conducted simulations to examine how epochs and population sizes impact the GA scheduling performance, specifically in maximizing average capacity utilization and weighted throughput . The configurations were simulated under six and ten communication requests across two topology structures to assess their response to variations in problem characteristics. The simulation results were then compared with an existing capacity allocation scheduling method, Progressive Filling (PF). Our findings reveal that GA outperforms PF in all scenarios and topology structures. Additionally, we deduce that 30 epochs and a population size of 50 are adequate for optimizing average capacity utilization and weighted throughput .

This paper is considering a semi-approximate approach in investigating the Burgers’ problem. The process of the discretization of Burgers’ problem has taken place which it starts with the second-order finite difference in the discretize process together with the linearization part by using the semi-approximate implicit scheme in a way to achieve the approximation equation, thus generating the corresponding linear system equations. Besides, the Gauss-Seidel (GS), Successive Over-Relaxation (SOR) and explicit group (EG) iterative method has combined together with the SOR iterative method, namely as 4-point EGSOR (4EGSOR) has been introduced in this study for resolving the linear system. To assess the proficiency of the suggested methods on the approximation equation, the numerical test has been conducted by considering three parameters, which are computational time, iteration number and maximum absolute error. The findings indicate that the 4EGSOR method outperforms both SOR and GS iterative methods.