Search Results (166)

With the expansion of automated container terminals (ACTs), joint scheduling among multiple types of equipment has become a critical factor affecting operational efficiency. This study investigates a joint scheduling optimization problem of quay cranes (QCs) and automated guided vehicles (AGVs) by considering AGV battery swapping strategies under spare battery constraints. With the objective of minimizing the final task completion time of AGVs, a mixed-integer programming model is formulated that simultaneously accounts for task assignment, operation sequencing, battery swapping thresholds, spare battery quantity, and mutual waiting times between AGVs and QCs. To solve this problem efficiently, a hill-climbing genetic algorithm (HC-GA) is proposed. Numerical experiments under different task scales show that HC-GA outperforms the genetic algorithm (GA), simulated annealing (SA), Q-learning, and the Q-learning-based genetic algorithm (Q-GA) in key indicators. In addition, the experimental results show that a proper configuration of AGVs can improve scheduling coordination and enhance the energy utilization efficiency of AGVs. The number of spare batteries and the threshold have significant impacts on overall system performance. When both operational efficiency and equipment utilization are considered, appropriately configuring the number of spare batteries and the threshold can effectively enhance the operational efficiency of ACTs. Full article

Trade imbalances and equipment shortages are making it increasingly important to coordinate container slot allocation with empty container repositioning on liner services. This paper develops an integrated bi-objective mixed-integer model for voyage-level slot planning on a fixed cyclic route. The model jointly decides booking acceptance, inter-voyage shipment, and empty repositioning with port-level empty-inventory dynamics and leg-based vessel capacity constraints. We optimize two conflicting objectives: maximizing operational profit and minimizing empty container TEU-miles. To solve the model at practical scales, we propose a hybrid evolutionary framework, NSGA-II-RL, which uses a lightweight Q-learning controller to adapt operator and repair choices during NSGA-II evolution. Computational experiments on representative service route instances show that NSGA-II-RL produces diverse Pareto-efficient solutions and improves hypervolume relative to fixed-operator and random-control variants, revealing clear trade-offs between profitability and repositioning intensity. Full article

This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of $\mathbb{Q}$ and describe algebraic number fields through their realization as finite-dimensional $\mathbb{Q}$-algebras (via multiplication operators and matrix representations), leading naturally to the arithmetic invariants—trace, norm, and discriminant—and to the ring of integers, ideals, Dedekind domains, and the ideal class group. We then develop the classical theory of cyclotomic fields, emphasizing their Galois structure and their role in abelian extensions of $\mathbb{Q}$. Next, we discuss ramification in general extensions, including decomposition and inertia groups, the Frobenius element, and the Chebotarev density theorem. The exposition continues with a concise algebraic introduction to elliptic curves and their L-functions, and it places key conjectural links (including Birch and Swinnerton-Dyer) in context. Finally, a collection of examples highlights a common operational language between fractional calculus and number theory: Laplace and Mellin transforms turn convolution-type operators into multiplication, clarifying the appearance of $\Gamma$-factors, Dirichlet series, and zeta- and L-function structures in both settings. Full article

In the present paper, the Kantorovich modification of the Schurer type of $(\lambda ,q)$-Bernstein operators, which are associated by the shape parameter $-1\le \lambda \le 1$ and the Bézier basis function, is presented. Using Korovkin’s theorem, we establish several local and global approximation properties. Lastly, we calculate the convergence properties for the functions that belong to Peetre’s K-functional and Lipschitz maximum by using the classical modulus of continuity and second-order modulus of continuity. In the last section, graphical and numerical analysis are studied. Full article

This work addresses the increasing complexity of urban mobility by proposing an intelligent optimization and resource-allocation framework for Vehicle-to-Infrastructure (V2I) communications. The model integrates a macroscopic mobility analysis, an Integer Linear Programming (ILP) formulation for optimal Road-Side Unit (RSU) placement, and a Smart Generic Network Controller (SGNC) based on Q-learning for dynamic radio-resource allocation. Simulation results in a realistic georeferenced urban scenario with 380 candidate sites show that the ILP model activates only 2.9% of RSUs while guaranteeing more than 90% vehicular coverage. The reinforcement-learning-based SGNC achieves stable allocation behavior, successfully managing 10 antennas and 120 total resources, and maintaining efficient operation when the system exceeds 70% capacity by reallocating resources dynamically through the $\lambda$-based alert mechanism. Compared with static allocation, the proposed method improves resource efficiency and coverage consistency under varying traffic demand, demonstrating its potential for scalable V2I deployment in next-generation intelligent transportation systems. Full article

Tugboats are indispensable for ensuring the safe and efficient berthing and unberthing of large vessels, and their scheduling policies have a direct impact on port efficiency and operating costs. To overcome the limitations of conventional single-objective optimization approaches, this paper develops a multi-objective, mixed-integer linear programming (MILP) model that establishes a symmetric consideration by simultaneously minimizing total operating cost and operation time. In addition, a hybrid optimization framework that employs a Jaya algorithm integrated with Q-learning (Jaya-QL) is introduced. Its Q-learning-driven adaptive mechanism achieves a symmetric balance between global exploration and local exploitation, mitigating premature convergence in the Jaya algorithm. Experimental results show that Jaya-QL achieves average reductions of 17.5% in total cost and 0.65% in total time compared with the Artificial Bee Colony (ABC), Quantum Particle Swarm Optimization (QPSO), Ant Colony Optimization (ACO), Genetic algorithm (GA) and Jaya algorithms. Moreover, it demonstrates superior convergence accuracy and solution diversity, offering a practical and effective decision support tool for tugboat scheduling in modern port operations. Full article

Hybrid AC/DC transmission expansion planning must balance investment cost, supply reliability and AC/DC stability, which challenges conventional mathematical programming and heuristic methods. This paper proposes a multi-objective planning framework based on an improved multi-step backtracking α-Q(λ) reinforcement learning algorithm with eligibility traces and an adaptive learning factor. A tri-objective model minimises annual economic cost, expected power shortage and a comprehensive electrical index that combines electrical betweenness, commutation-failure margin and effective short-circuit ratio. The mixed-integer planning problem is reformulated as an interactive learning process, where the state encodes candidate line construction decisions, the action builds or cancels lines, and the eligibility-trace matrix is used to quantify line importance. Case studies on the Garver-6 system, the IEEE 24-bus reliability test system and a 500 kV regional hybrid AC/DC grid show that, compared with classical Q-learning, the proposed method yields lower annual cost, reduced expected power shortage and improved AC/DC stability; in the 500 kV system, the expected annual power shortage is reduced from 70,810 MWh to 28,320 MWh. Full article

Emergency scenarios in the Internet of Vehicles (IoV) face significant challenges due to the stringent requirements for ultra-reliable and low-latency communication under high-mobility conditions. This paper proposes a cooperative transmission framework for semantic communication to address these challenges. We introduce a knowledge graph-based approach to represent information as semantic triples (structured entity-relation-attribute representations), whose importance is quantified using a Zipf distribution, enabling prioritized transmission. At the physical layer, a semantic-aware cooperative communication scheme is proposed to combat fading and enhance transmission reliability. The joint optimization of the number of transmitted triples and node power allocation is formulated as a cross-layer problem. To tackle this Mixed-Integer Nonlinear Programming (MINLP) problem with a hybrid action space, we employ the Multi-Pass Deep Q-Network (MP-DQN) algorithm, which is specifically designed for problems with hybrid discrete-continuous action spaces. Simulation results demonstrate that our framework dynamically adapts to channel states and semantic value, achieving up to 85% end-to-end success rate and improving convergence speed by approximately 40% compared to conventional methods. Full article

Let $G=(V,E)$ be a finite simple graph with $p=\left|V\right|$ vertices and $q=\left|E\right|$ edges, without isolated vertices or isolated edges. A vertex magic total labeling is a bijection f from $V\cup E$ to the consecutive integers $1,2,\dots ,p+q,$ with the property that, for every vertex $u\in V$, one has $f\left(u\right)+{\sum }_{uv\in E}f\left(uv\right)=k$ for some magic constant k. The vertex magic total labeling is called E-super if furthermore $f\left(E\right)=\{1,2,\dots ,q\}$. A graph is called (E-super) vertex magic if it admits an (E-super) vertex magic total labeling. In this paper, we verify the existence of E-super vertex magic total labeling for a class of 3-regular graphs with a perfect matching, and we confirm the existence of such a labeling for general regular graphs of odd degree containing particular classes of 3-factors, which provides us with known and new examples. Note that Harary graphs are among the popular models used in communication networks. In 2012, G. Marimuthu and M. Balakrishnan raised a conjecture that if $n>4$, $n\equiv 0\left(mod4\right)$ and m is odd, then the Harary graph $H_{m,n}$ admits an E-super vertex magic labeling. Among others, we are able to verify this conjecture except for one case while $m=3$ and $n\equiv 4\left(mod8\right)$. Full article

We propose a novel optical method for performing integer division $N÷D$, based on the superposition of two transmissive masks: a dividend mask (G1) encoding N lines, and a completer mask (G2) providing blocks of D sites. The combined pattern is read in blocks, yielding quotient q and remainder r directly. This Interlaced Line Divider (ILD) provides a hardware-level analog computation of Euclidean division, with potential applications in cryptography, optical sensing, and unconventional computing. Full article

On GPU-based clusters, the training workloads of machine learning (ML) models, particularly neural networks (NNs), are often structured as Directed Acyclic Graphs (DAGs) and typically deployed for parallel execution across heterogeneous GPU resources. Efficient scheduling of these workloads is crucial for optimizing performance metrics such as execution time, under various constraints including GPU heterogeneity, network capacity, and data dependencies. DAG-structured ML workload scheduling could be modeled as a Nonlinear Integer Program (NIP) problem, and is shown to be NP-complete. By leveraging a positive correlation between Scheduling Plan Distance (SPD) and Finish Time Gap (FTG) identified through an empirical study, we propose to develop a Running Time Gap Strategy for scheduling based on Whale Optimization Algorithm (WOA) and Reinforcement Learning, referred to as WORL-RTGS. The proposed method integrates the global search capabilities of WOA with the adaptive decision-making of Double Deep Q-Networks (DDQN). Particularly, we derive a novel function to generate effective scheduling plans using DDQN, enhancing adaptability to complex DAG structures. Comprehensive evaluations on practical ML workload traces collected from Alibaba on simulated GPU-enabled platforms demonstrate that WORL-RTGS significantly improves WOA’s stability for DAG-structured ML workload scheduling and reduces completion time by up to 66.56% compared with five state-of-the-art scheduling algorithms. Full article

In this paper, we primarily use Stancu variants of Kantorovich-type operators to investigate the convergence and other associated properties of new Szász–Mirakjan operators. We compute the moments and central moments of the new Szász–Mirakjan operators by q-integers and propose their modified Kantorovich form. More specifically, we examine the convergence characteristics in the space of continuous functions. With the use of the modulus of continuity and the integral modulus of continuity, we determine the degree of convergence. Additionally, we obtain the Voronovskaja type theorems. To validate convergence, we conclude with a numerical example and graphical illustration of the operator sequences. Full article

The computation of solutions of Caputo fractional differential equations is paramount in modeling to establish its benefits over the corresponding integer order models. In the literature so far, in order to compute the solution of Caputo fractional differential equations, the solution is typically assumed to be a $C^n$ function, which is a sufficient condition for the Caputo derivative to exist. In this work, we assume the necessary condition for the Caputo derivative of order $nq,(n-1)<nq<n$, to exist, which means that we assume it to be a $C^{nq}$ function. Recently, it has been established that the Caputo derivative of order $nq$ is sequential of order $q.$ As such, we assume the fractional initial conditions. In our work, we have obtained an analytical solution for the Caputo fractional differential equation of order $nq$ with fractional initial conditions by two different methods. Namely, the approximation method and the Laplace transform method. The application of our main results is illustrated with examples. Full article

Kinetic Alfvén waves (KAWs) are investigated in an Oxygen–Hydrogen plasma with electrons following the behavior of $rq$-distribution in an upper ionosphere. We aim to study low-frequency and long wavelengths at 1700 kms in the upper ionosphere of Earth as detected by Freja satellite. The fluid model and reductive perturbation method are combined to obtain the evolutionary wave equations that can be used to describe both fractional and non-fractional KAWs in an Oxygen–Hydrogen ion plasma. This procedure is used to obtain the integer-order Korteweg–de Vries (KdV) equation and then analyze its solitary wave solution. In addition, this study is carried out to evaluate the fractional KdV (FKdV) equation using a new approach called the “Tantawy technique” in order to generate more stable and highly accurate approximations that will be utilized to accurately depict physical events. This investigation also helps locate the existence regions of the solitary waves (SWs), and in turn displays that the characteristics of KAWs are affected by a number of physical factors, such as the nonthermal parameters/spectral indices “r”, “q”, and obliqueness (characterized by $l_z$). Depending on the parameter governing the distribution, especially the nonthermality of inertialess electrons, the $rq$-distribution of electrons has a major impact on the properties of KAWs. Full article

We develop a convergence framework for Grünwald–Letnikov (GL) fractional and classical integer difference operators acting on sequences in fuzzy-paranormed (fp) spaces, motivated by data that are imprecise and contain sporadic outliers. Fuzzy paranorms provide a resolution-dependent notion of proximity, while statistical and lacunary statistical convergence downweight sparse deviations by natural density; together, they yield robust criteria for difference-filtered signals. Within this setting, we establish uniqueness of fp–${\mathsf{\Delta }}^m$ statistical limits; an equivalence between fp-statistical convergence of ${\mathsf{\Delta }}^m$ (and its GL extension ${\mathsf{\Delta }}^{\alpha }$) and fp-strong p-Cesàro summability; an equivalence between lacunary fp-${\mathsf{\Delta }}^m$ statistical convergence and blockwise strong p-Cesàro summability; and a density-based decomposition into a classically convergent part plus an fp-null remainder. We also show that GL binomial weights act as an ${\ell }^1$ convolution, ensuring continuity of ${\mathsf{\Delta }}^{\alpha }$ in the fp topology, and that nabla/delta forms are transferred by the discrete Q–operator. The usefulness of the criteria is illustrated on simple engineering-style examples (e.g., relaxation with memory, damped oscillations with bursts), where the fp-Cesàro decay of difference residuals serves as a practical diagnostic for Cesàro compliance. Beyond illustrative mathematics, we report engineering-style diagnostics where the fuzzy Cesàro residual index correlates with measurable quantities (e.g., vibration amplitude and energy surrogates) under impulsive disturbances and missing data. We also calibrate a global decision threshold ${\tau }_{\mathrm{glob}}$ via sensitivity analysis across $(\alpha ,p,m)$, where $m\in \mathbb{N}$ is the integer difference order, $\alpha >0$ is the fractional order, and $p\ge 1$ is the Cesàro exponent, and provide quantitative baselines (median/M-estimators, ${\ell }_1$ trend filtering, Gaussian Kalman filtering, and an $\alpha$-stable filtering structure) to show complementary gains under bursty regimes. The results are stated for integer m and lifted to fractional orders $\alpha >0$ through the same binomial structure and duality. Full article