Partial differential equations (PDEs) are essential tools for modeling, simulation, and optimization in complex engineering systems. The main goal of this work is to present a new double integral transform, called the Double Mohand–Formable Transform (DMFT), and show how to apply it to a number of basic functions that are helpful in the engineering domain. A unified method for resolving a broad range of linear systems, boundary value issues, and initial value issues is offered by the DMFT. We present the core properties, existence conditions, and convolution theorem associated with DMFT. Furthermore, we demonstrate the usefulness of the suggested transform in practice by using it to resolve symmetric versions of the telegraph equation, thereby highlighting its effectiveness in addressing partial differential equations involving two functions with diverse characteristics.
A hyper-heuristic for the multi-depot multiple traveling salesman problems (MDMTSP) is designed based on the clustering of cities and scheduling of cities in each cluster in each iteration. The clustering of nodes for the salesmen under the balance constraint (i.e., the lower and upper bounds of nodes for each salesman) is done following the K-means clustering procedure. For each cluster, the optimal schedule for the assigned salesman is searched in some predefined iterations using a scheduling procedure. This procedure is designed using a set of schedule update rules. Different update rules are designed for this purpose using simple copy and shift operations in a pair of nodes of a schedule. The node pair is selected depending upon the position of a randomly selected node of a better schedule. A rule is selected based on its performance using the Roulette Wheel selection process as and when required. For any stagnant schedule, 3-opt operation is applied for the possible improvement. The algorithm is named hyper-heuristic with clustering-scheduling procedures (HHCSP). The performance of HHCSP is studied using different-sized TSPLIB test instances (involving up to 280 nodes and 2–10 salesmen), and its efficiency compared to a set of state-of-the-art algorithms is studied statistically. It is observed that HHCSP outperforms the other considered state-of-the-art algorithms for the MDMTSPs. The best and the average costs obtained by HHCSP for the considered instances are far better than those found by the others. Moreover, in most of the cases, the average cost is nearly equal to the mean, which implies HHCSP is efficient and consistent for the MDMTSPs. An MDMTSP with a fuzzy cost matrix is dealt with by optimizing the credibility measure of the fuzzy objective concerning a predefined fuzzy goal, and a fuzzy simulation algorithm is outlined for an estimation of the same.
Malnutrition is a medical disorder affected by deficiencies, excesses, or imbalances in nutritional components resulting from an unbalanced intake of vital nutrients compared to the body's needs. It includes both under nutrition, in which growth and development are hampered by insufficient consumption of calories, vital nutrients along with over nutrition, which is defined as an excessive calorie intake that result in obesity as well as related health problems. The study demonstrated the effectiveness of the suggested Dynamic Sailfish Optimized Advanced Support Vector Machine (DSFO-ASVM) for childhood malnutrition prediction. DSFO-ASVM addresses the specified problem and overcoming the obstacles related to the specific scenario in the examination. The proposed study utilized the publicly available Kaggle Childhood Malnutrition Health Dataset, which contains 15,000 records of children aged 1–59 months with 40 attributes, including 39 input features and one target variable representing four nutritional status categories: Normal, Underweight, Stunted, and Wasted. The preprocessed dataset using z-score normalization technique and employing the Principal Component Analysis (PCA) to extract the features. The proposed DSFO-ASVM was implemented in Python and evaluated using an 70:30 train–test split with 5-fold cross-validation, achieving 97.70
Nonlinear variants of several unconventional computing models have been developed with interesting results in real-world applications. We introduce a novel variant of the young computing paradigm of virus machines (VM): nonlinear parallel virus machines (NPVM). We provide a comprehensive overview of the architecture of NPVMs and discuss their advantages and drawbacks. NPVMs not only achieve a major leap in efficiency due to the new parallelism behavior, but now the hosts can also have a non-negative real amount of viruses. For this propose, a new type of weight in the channels between hosts is introduced where the amount of viruses consumed and replicated depends on nonlinear functions. The computational power of NPVM is established; more precisely, the computational completeness of NPVM is proved as number-generating devices. Finally, a small universal NPVM is constructed for function computing with 9 hosts and 23 instructions.
Multi-objective optimization involves the simultaneous optimization of multiple objectives, which are often conflicting. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) has emerged as a prominent and successful technique in this domain, and in recent years has garnered significant research interest due to its notable performance and its advantages in terms of addressing multi-objective optimization problems. Furthermore, there has been a growing focus on the use of this successful approach to solve real-world challenges. Despite its commendable performance, however, a closer examination of MOEA/D reveals opportunities to enhance its search capabilities and convergence speed through the incorporation of an elitist resource allocation (ERA) mechanism and a novel crossover strategy. The algorithm proposed here, called MOEA/D-ERA, incorporates these enhancements and is rigorously tested on a comprehensive suite of 40 benchmark functions alongside established state-of-the-art algorithms. The empirical findings unequivocally show that our innovations enhance the structural integrity of the MOEA/D framework and have a significant positive impact on the overall performance of the algorithm. Having demonstrated its efficacy in regard to test functions, MOEA/D-ERA is applied to address a structural multi-objective optimization problem. The proposed algorithm effectively determines a solution space consisting of optimal design inputs for an I-beam, with the objectives of minimizing both the cost and the vertical deflection as outputs. In summary, this study introduces a novel decomposition-based algorithm that incorporates an elitist selection mechanism and an innovative crossover model. To the best of our knowledge, this is the first instance in which a previously solved structural design problem has been redefined and addressed as a multi-objective problem.
