Zainor Ridzuan Yahya

Metaheuristic optimizers are increasingly used to solve differential equations by minimizing a residual over a trial basis, but their reliability and cost relative to standard solvers are rarely quantified. This paper studies Particle Swarm Optimization (PSO) combined with cubic Bézier and clamped cubic B-spline bases, in which the initial condition is imposed exactly through the leading control point and the remaining control points minimize the sum of squared ODE residuals. The Verhulst logistic model is solved in its growth, equilibrium and decline regimes, and the study is extended to the Gompertz model, a Riccati equation and a steep logistic case. Every configuration is run with 30 independent seeds and assessed on a dense grid. A diagnostic of the originally reported 47%–60% success rate of the seven-parameter B-spline showed that particles were driven onto the bounds of the search box by unlimited velocities; limiting the velocity to 20% of the box width raised the success rate to 30/30 in all three regimes. With this correction, a numerically verified optimum of each basis is reached (1000 of 1000 multi-start least-squares runs converge to it, and its Hessian is positive definite), and the B-spline basis reduces the decline-regime maximum error from 7.6×10−3 to 2.0×10−4. A systematic study shows that the iteration budget needed for reliable convergence roughly doubles for every two to three additional control points, and that iterations are more effective than larger swarms. Against fourth-order Runge–Kutta, adaptive Runge–Kutta, Chebyshev spectral collocation and B-spline collocation with quasilinearization, PSO is several orders of magnitude less efficient on these smooth problems, and gradient-based least squares on the same basis reaches the same optimum faster and more reliably. On the steep logistic and Gompertz problems, PSO reaches the basis optimum in only 13–27 of 30 runs. PSO shows a clear advantage only for a non-smooth minimax residual objective, where it succeeds in 24–30 of 30 runs whereas Nelder–Mead and BFGS fail. The value of the framework therefore lies in its gradient-free flexibility rather than in accuracy or efficiency for smooth problems. Code, seeds and data are publicly available.

The Mahalanobis-Taguchi System (MTS) is a statistical approach used in breast cancer research to facilitate early detection and promote efficient treatment. The technique analyses mammogram images for significant features using a multivariate statistical analysis technique. It combines the Mahalanobis distance (MD) and Taguchi's method to determine the differences between benign and malignant samples. While orthogonal array (OA) has been widely used in MTS, it has been criticised for providing suboptimal results due to insufficient coverage of feature combinations during the feature optimisation process. To address this issue, the Binary Whale Optimisation Algorithm (BWOA) is proposed as an improved search algorithm for MTS. This paper aims to develop a novel hybrid method that enhances the efficiency of the Mahalanobis Taguchi System (MTS). The performance of feature selection ability due to different MTS hybrid algorithms were also compared. BWOA simulates the hunting behaviour of humpback whales and works by exploring new regions of the solution space, gradually narrowing the search space, and fine-tuning the solution. MTS-BWOA demonstrated its enhanced capability in feature optimisation compared to traditional MTS methods and has the potential to be applied in other medical imaging domains.

This paper presents an issue related to examination timetabling raised in the University of Malaysia Perlis (UniMAP). UniMAP is a distributed campus university in Perlis, North of Malaysia, which is comprised of four branch campuses that offers a total of 31 programmes at 12 schools or faculties. This study looked into an issue related to examination timetabling based on intricacy, time, and several challenges. As such, real world data were analysed by employing the Free Educational Timetable (FET) software program in the attempt to seek a solution for the issue at hand. The FET refers to an open-source and free software program can schedule timetable automatically for any learning institutes by applying an efficient and rapid algorithm meant for timetabling. Nevertheless, due to absence of solution in the literature and the employment of new dataset, the outcomes from the analyses were compared with a manual solution made available. It was discovered that the solution generated from this study appeared better in terms of its capacity of offering an examination timetable that is high in quality within a shorter period of time, as well as improved proximity cost. In conclusion, the results generated from this study have the ability to lessen the burden of the Examination Unit related to examination timetabling.

The Mahalanobis-Taguchi System (MTS) refers to a newly-developed technique based on statistics that integrates a number of mathematical concepts to be applied for classification and diagnosis purposes within systems that are comprised of multiple dimensions. The MTS has been proven to be an exceptional technique that can be employed in numerous fields. In MTS, it is essential to choose the variables in order to enhance the accuracy in classifying via orthogonal array (OA) and Signal-to-Noise (S/N) ratios. However, the penalty for over-fitting or regularization is not included in the feature selection process for the MTS classifier. Hence, this paper investigated the combination between MTS and statistical pattern recognition approach applied to automotive crankshaft remanufacturing as an automated decision-making tool for classification purposes. The outcomes revealed that MTS displayed better classification performance for both training and test datasets, besides eliminating redundant and irrelevant parameters better than the conventional approach did.

In this paper, new approximation methods for solving systems of ordinary differential equations (SODEs) by fuzzy transform (FzT) are introduced and discussed. In particular, we propose two modified numerical schemes to solve SODEs where the technique of FzT is combined with one-stage and two-stage numerical methods. Moreover, the error analysis of the new approximation methods is discussed. Finally, numerical examples of the proposed approach are confirmed, and applications are presented.

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

Breast cancer is becoming the major factor of death amongst women in the world. However, it is found that longer lifespan of this disease’s patients can be guaranteed through early detection and accurate diagnosis of this disease. When it comes to the treatment given to patients, a doctor needs to put his/her knowledge and experience in practice by specifying the source of the suspected disease (out of a list of the possible causes with similar symptoms). This is followed by confirming the diagnosis through a number of tests. Therefore, identifying the disease without receiving assistance from intelligence systems is time consuming. The objective of this study is to introduce the intelligence system which develops Random Binary Search algorithm-based feature selection in Mahalanobis Taguchi System (MTS). It is also with the purpose to validate the techniques of feature selection problems which are computationally efficient, and to apply Random Binary Search algorithm in solving medical classification problems. In this study, in order to improve the step of choosing the most useful variables, Random Binary Search (RBS) algorithm is proposed, which is incorporated between MTS. Besides being a relatively new statistical methodology where various mathematical concepts are combined, MTS is used in the field of diagnosis and classification in multidimensional systems. It is also a highly efficient method, and it has been utilized in a wide range of disciplines such as engineering, medical, financial, and more. Datasets of medical fields, which were concerning cancer, diabetes and hepatitis, were used in this study. Besides, binary class classification problems were also represented by these data sets.

In this paper, new fuzzy numerical methods based on the fuzzy transform (F-transform or FT) for solving the Cauchy problem are introduced and discussed. In accordance with existing methods such as trapezoidal rule, Adams Moulton methods are improved using FT. We propose three new fuzzy methods where the technique of FT is combined with one-step, two-step, and three-step numerical methods. Moreover, the FT with respect to generalized uniform fuzzy partition is able to reduce error. Thus, new representations formulas for generalized uniform fuzzy partition of FT are introduced. As an application, all these schemes are used to solve Cauchy problems. Further, the error analysis of the new fuzzy methods is discussed. Finally, numerical examples are presented to illustrate these methods and compared with the existing methods. It is observed that the new fuzzy numerical methods yield more accurate results than the existing methods.