The rising global demand for oil has driven the offshore industry toward deep and ultra-deepwater exploration. Drillships are critical in these operations due to their high mobility and adaptability to challenging environments. Station-keeping is paramount for safe operations, as drifting beyond thresholds can result in severe economic losses and environmental disasters. This study presents a novel approach to drillship station-keeping by leveraging artificial intelligence (AI) to locally control the dynamic positioning (DP) system, thereby eliminating reliance on global positioning systems or internet-based systems. A numerical model of a drillship was developed, and simulations across multiple sea states generated a comprehensive database to train an AI controller. The system focuses on key degrees of freedom: surge, sway, and yaw. Positional changes detected by the onboard inertial navigation system are analyzed to calculate displacement, representing the vessel’s response to external forces. The trained AI matches these responses to database entries, calculates the required thrust force, and applies it through DP thrusters to restore the vessel’s position. The results showed that the AI controller achieves high precision in station-keeping across various sea states, confirming its robustness and reliability. The key novelty of this method lies in its onboard, localized control system, which enhances operational independence and safety by eliminating external dependencies while significantly reducing the risk of positional loss in ultra-deepwater environments. By combining advanced numerical simulations with AI tools, this study introduces an innovative, safer, and more efficient solution for maintaining drillship stability in demanding marine conditions.

This paper presents a MILP model for one dimensional cutting stock (CSP) problems that considers the most commonly used objectives all together. These are the minimization of the trim loss which is the leftover that is not large enough to be reused in the future, minimization of the total cutting cost and number of bars involved. We carried out computational experiments in order to find out the limitations of our model and to compare it with the most commom linear cutting software on the market.

An option is a financial contract or a derivative security entitling the owner to trade a certain quantity of a particular asset having a certain cost on or before a certain date. Therefore, in the last few years, not only mathematicians but also financial engineers have paid a great deal of attention to pricing options. Applying the fractal structure in the processes of stochasticity led to both fractional calculus (FC) and fractional partial differential equations (FPDEs) being associated with the stochastic models in financial theory. Thus, the beginning of the 20th century witnessed the use of stochastic processes to model the financial market. By studying the price behavior of assets, a model was presented, which is known as the Black-Scholes equation. The main focus of the present paper is the time-fractional Black-Scholes (TFB-S) model. The difficulty or impossibility of providing an analytical solution for the aforesaid equation has made numerical solutions more helpful or even the only option. In this work, using the Crank-Nicolson scheme, a numerical solution with an implicit discrete design is demonstrated. We use the Fourier analysis method to investigate the stability of the implicit discrete design and demonstrate that the proposed method is unconditionally stable. The truncation error is checked. We also show that the numerical scheme suggested to solve the TFB-S model is convergent. This method is the second order in space and 2 − β order in time, where 0 < β < 1 is the order of the time-fractional derivative. Finally, the accuracy as well as the efficiency considered for the method are evaluated by providing three examples and comparing them with previous works. Finally, the method’s accuracy and efficiency are assessed through three examples, with results compared to previous studies. Additional advantages of the method include its high computational speed, ease of implementation, and the reliability of obtaining an approximate solution, supported by stability proof.

We consider a multiple item Economic Lot Sizing problem where the demands for items depend on their stock quantities. The objective is to find a production plan such that the resulting stock levels (and hence demands) maximize total profit over a finite planning horizon. The single item version of this problem has been studied in the literature, and a polynomial time algorithm has been proposed when there are no bounds on production. It has also been proven that the single item version is NP -hard even when there are constant (i.e., time-invariant) finite capacities on production. We extend this single item model by considering multiple items and production capacities. We propose a Lagrangian relaxation method to find an initial solution to the problem. This solution is a hybrid solution obtained by combining two distinct solutions generated in the process of solving the Lagrangian dual problem. Starting with this initial solution, we then implement a Tabu Search algorithm to find better solutions. The performance of the proposed solution method is compared with the performance of a standard commercial software that works on a mixed integer programming formulation of the problem. We show that our solution approach finds better solutions within a predetermined time limit in general.

Combining metaheuristics with exact methods improves solution quality by efficiently exploring promising regions and refining the obtained solutions. This paper introduces a novel hybrid approach that combines exact methods and metaheuristics to address the Traveling Tournament Problem (TTP) in sports scheduling. The TTP, a critical aspect of sports management, aims to create a tournament schedule that minimizes the total travel distance of participating teams, which is essential for controlling league management costs and maximizing revenue. However, its complex optimization requirements and tournament structure make it highly challenging to solve efficiently. Our hybrid approach combines exact methods with the Biogeography-Based Optimization (BBO) metaheuristic to tackle both the TTP and its variant, the Unconstrained Traveling Tournament Problem (UTTP). We introduce a novel relaxation technique to enhance the efficiency of the Integer Linear Programming (ILP) formulation for the TTP. This technique involves fixing the schedule for a subset of teams and employing an ILP solver to optimize the schedule for the remaining teams. This relaxation technique is seamlessly integrated into the BBO operators. We evaluate the effectiveness of our method using publicly available benchmark instances and compare it with existing techniques for both TTP and UTTP. Our experimental results demonstrate that the proposed approach achieves competitive solution quality. It outperforms prior methods on UTTP for the US National Baseball League NL16 instances and some prominent methods when applied to TTP.

Challenging and time-consuming tasks performed by humans can today be performed faster and more efficiently by robot manipulators with the development of technology. Robotic manipulators are flexible, can fit in small spaces, and are very effective for tasks that require high precision. They are widely used in the production lines of factories (handling, assembly, welding, etc.) and in fields that require manpower, such as medicine and engineering. Since it is used in tasks that require precision, its control is also important. Sliding modal control (SMC), one of the robust control methods, is a control method used in nonlinear systems because it can be applied to unstable systems, is easy to design and, has high accuracy against parameter uncertainties. However, it produces an unstable control signal within a certain range and this discontinuous control signal causes cracking in the system, which causes damage to the system elements. Especially in recent years, one of the most recent and successful methods used to reduce the chattering effect, which is the biggest problem in the SMC approach, is the fractional order design of the sliding surface. In the fractional order SMC (FOSMC) method, the derivative expression in the sliding surface is defined using the system variable’s error to be controlled and the derivative of the error is computed fractionally. In this paper, Caputo FOSMC (CFOSMC), defined with 3 different sliding surfaces using the Caputo fractional operator, is compared with classical SMC for controlling a 2-degree of-freedom (2-DOF) robot manipulator. According to the results obtained from simulation comparisons, it is observed that approach 3 gives better results than the other two approaches and classical SMC in terms of overshoot, settling and error value for some derivative orders.

This paper describes a new and powerful way to solve optimal control problems (OCPs) on a multi-strain COVID-19 model for strategies related to vaccination and amplification. We call it the collocation method with a flood-based metaheuristic optimizer (FBMO). We use a collocation method with Laguerre polynomials and their derivative operational matrices to turn the OCP into a nonlinear programming (NLP) problem. To address the NLP, the research employs the FBMO to determine the control variables u_i for i = 1, 2, and 3, representing isolation, vaccination efficacy, and treatment enhancement, in conjunction with the state function of the multi-strain COVID-19 model. These strategies are executed within an SVI_cI_vR-type control model for COVID-19 in Morocco, designed to control the outbreak of multi-strain disease. The paper’s primary aim is to achieve a high-quality optimal solution for the given OCP, thereby contributing to the advancement of efficient strategies for managing the COVID-19 pandemic.

This paper presents a Parallel Late Acceptance Hill-Climbing (PLAHC) algorithm for solving binary-encoded optimization problems, with a focus on the Uncapacitated Facility Location Problem (UFLP) and the Maximum Cut Problem (MCP). The experimental results on various benchmark problem instances demonstrate that PLAHC significantly improves upon the sequential implementation of the standard Late Acceptance Hill-Climbing method in terms of solution quality and computational efficiency. For UFLP instances, an 8-thread implementation with a history list length of 50 achieves the best results, while for MCP instances, a 4-thread implementation with a history list length of 100 is the most effective configuration. The speedup analysis shows performance improvements ranging from 3.33x to 10.00x for UFLP and 2.72x to 9.20x for MCP as the number of threads increases. The performance comparisons to the state-of-the-art algorithms illustrate that PLAHC is highly competitive, often outperforming existing sequential methods, indicating the potential of exploiting parallelism to improve heuristic search algorithms for complex optimization problems.

An End-of-Day process is a batch job that includes a sequence of programs, wherein tasks are completed automatically at times specified by a scheduler. The efficient allocation of resources for the timely execution of tasks allows a company to reduce the overall time needed for the completion of the work and improve customer satisfaction by delivering orders on time. This paper presents a case study of a Turkish bank with the objective of minimizing the duration of the end-of-day process through the optimization of work scheduling and resource allocation. This problem is modeled as a multi-mode resource-constrained project scheduling problem, optimally resolved by mixed-integer programming, and approximated via simulated annealing heuristic. The scheduler in this paper can also be used to assess the importance of scheduling and crashing tasks, along with the sufficiency of the infrastructure to optimize the End-of-Day process.

This paper focuses on the nature of the traveling wave solutions of the singular perturbed (sixth-order) Boussinesq equation, which is important for the physical relationships of water waves and shows strong interactions. Most studies of this equation have been analyzed by numerical methods and it has been observed that analytical solutions are limited. This has formed the main motivation for an analytical method, the Kudryashov method, for the generation of traveling wave solutions. One of the important goals of this work is to analyze the wave propagation phenomena in detail. For this purpose, the model has been extended by adding parameters to the diffusion term, which can illuminate shallow fluid layers and nonlinear atomic phenomena. This model aims to provide a deeper understanding of the motion of waves and the behavior of fluids, as well as its solution by the analytical method. To deepen the physical discussion, the responses of the solution are simulated for different values of the diffusion coefficient and the parameter associated with the wave velocity.

This paper proposes a simplified frequency based tuning method for Second-order Linear Active Disturbance Rejection Control (SLADRC). By employing a 2-DOF structure for the controller, the challenge of optimizing numerous tuning parameters for complex systems is addressed. By considering the phase margin (PM) as one of the design specifications, an admissible region is mapped onto the Nyquist plot to identify the permissible bound for gain crossover frequencies (ω_gc), from the known system frequency points. Distinct controllers with unique performance characteristics can be designed within the comprehensive set of design specifications (PM and ω_gc). Subsequently, the optimal tuning parameter values are determined by identifying the design specifications that yield the desired response and the minimum ITSE. Two distinct approaches are proposed for selecting suitable design specifications: an iterative method and a heuristic-based method. These approaches rely on graphical analysis of time-domain performance metrics and robustness analysis using the disk margin. While the heuristic approach offers faster computation, the iterative method generally provides more accurate results. The reliability and versatility of the proposed tuning technique are validated on five distinct benchmark systems. The systems with time delay and unstable dynamics explains the detailed tuning procedure in performance study. In comparative study, time delay with integrating system, pure integrating system and nonminimum phase with higher order systems are considered, provides equivalent performance with reduced computational effort. Additionally, it is experimentally verified through a real-time speed control of a rotary servo system, achieving an ITSE of 16.2 and a disk margin of 1.332, confirming its practical applicability.

Optimal control problem of a Caputo fractional state-dependent delay system is discussed in this paper. Both Dirichlet and Neumann fractional optimal control problems are studied. Using a linear continuous operator, the delay system is converted to an equivalent system not involving explicit delay term. The existing results for the unique solution of the fractional system associated with the optimal control problem are attained by the application of Lax-Milgram Theorem. Optimality conditions, both necessary and sufficient for the fractional Dirichlet and Neumann problems with the quadratic objective function, are obtained. Interpreting the first-order optimality condition of Euler-Lagrange along with the corresponding adjoint system involving the right Caputo derivative, the optimality system is derived. Initially, the first-order Euler-Lagrange optimality condition is used along with the corresponding adjoint system to derive the optimality system. Subsequently, adjoint equations and Hamiltonian maximization conditions are derived using duality and variational analysis.