Search Results (11)

In this paper, an emission- and reliability-aware stochastic optimization model is proposed for the economic planning of electric bus parking lots (EBPLs) with photovoltaic (PV) and wind-turbine (WT) resources in an 85-bus radial distribution network. The model simultaneously minimizes operating, emission, and energy-loss costs while increasing system reliability, measured by energy not supplied (ENS), and uses a fuzzy decision-making approach to determine the final solution. To address optimization challenges, a new multi-objective entropy-guided Sinh–Cosh Optimizer (MO-ESCHO) is proposed to efficiently mitigate premature convergence and produce a well-distributed Pareto front. Also, a hybrid forecasting architecture that combines MO-ESCHO and artificial neural networks (ANN) is proposed for accurate prediction of PV and WT power and network loading. The framework is tested across five cases, progressively incorporating EBPL, demand response (DR), forecast information, and stochastic simulation of uncertainties using a new hybrid Unscented Transformation–Cubature Quadrature Rule (UT-CQR) method. Comparative analyses against conventional methods confirm superior performance in achieving better objective values and ensuring computational efficiency. The outcomes indicate that the combination of EBPL with RES reduces operating costs by 5.23%, emission costs by 27.39%, and ENS by 11.48% compared with the base case with RES alone. Moreover, incorporating the stochastic model increases operating costs by 6.03%, emission costs by 5.05%, and ENS by 7.94% over the deterministic forecast case, reflecting the added complexity of uncertainty. The main contributions lie in coupling EBPLs and RES under uncertainty and proposing UT-CQR, which exhibits robust system performance with reduced variance and lower computational effort compared with Monte Carlo and cloud-model approaches. Full article

To address the issues of low convergence accuracy, poor population diversity, and susceptibility to local optima in the Red-billed Blue Magpie Optimization Algorithm (RBMO), this study proposes a multi-strategy improved Red-billed Blue Magpie Optimization Algorithm (SWRBMO). First, an adaptive T-distribution-based sinh–cosh search strategy is used to enhance global exploration and speed up convergence. Second, a neighborhood-guided reinforcement strategy helps the algorithm avoid local optima. Third, a crossover strategy is also introduced to improve convergence accuracy. SWRBMO is evaluated on 15 benchmark functions selected from the CEC2005 test suite, with ablation studies on 12 of them, and further validated on the CEC2019 and CEC2021 test suites. Across all test sets, its convergence behavior and statistical significance are analyzed using the Wilcoxon rank-sum test. Comparative experiments on CEC2019 and CEC2021 demonstrate that SWRBMO achieves faster convergence and higher accuracy than RBMO and other competitive algorithms. Finally, four engineering design problems further confirm its practicality, where SWRBMO outperforms other methods by up to 99%, 38.4%, 2.4%, and nearly 100% in the respective cases, highlighting its strong potential for real-world engineering applications. Full article

Three-dimensional (3D) path planning is a crucial technology for ensuring the efficient and safe flight of UAVs in complex environments. Traditional path planning algorithms often find it challenging to navigate complex obstacle environments, making it challenging to quickly identify the optimal path. To address these challenges, this paper introduces a Nutcracker Optimizer integrated with Hyperbolic Sine–Cosine (ISCHNOA). First, the exploitation process of the sinh cosh optimizer is incorporated into the foraging strategy to enhance the efficiency of nutcracker in locating high-quality food sources within the search area. Secondly, a nonlinear function is designed to improve the algorithm’s convergence speed. Finally, a sinh cosh optimizer that incorporates historical positions and dynamic factors is introduced to enhance the influence of the optimal position on the search process, thereby improving the accuracy of the nutcracker in retrieving stored food. In this paper, the performance of the ISCHNOA algorithm is tested using 14 classical benchmark test functions as well as the CEC2014 and CEC2020 suites and applied to UAV path planning models. The experimental results demonstrate that the ISCHNOA algorithm outperforms the other algorithms across the three test suites, with the total cost of the planned UAV paths being lower. Full article

This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to convert the physical model into ordinary differential equations. Utilizing extended rational sinh–cosh and sine–cosine techniques, we derive an abundant soliton solution for the transformed system. By plugging these explicit solutions back into the wave transformation, we obtain dark and singular soliton solutions for the Hirota equation. The dynamic evolution of dark soliton profiles is then demonstrated, with a focus on varying physically significant parameters such as wave frequency, strength of third-order dispersion, and wave number. Furthermore, a comprehensive analysis is examined to elucidate how the dark and singular soliton profiles undergo deformation in the background influenced by these arbitrary parameters. The findings presented in this study offer valuable insights that could potentially guide experimental manipulation of dark solitons in optical fibers. Full article

The Dung beetle optimization (DBO) algorithm, devised by Jiankai Xue in 2022, is known for its strong optimization capabilities and fast convergence. However, it does have certain limitations, including insufficiently random population initialization, slow search speed, and inadequate global search capabilities. Drawing inspiration from the mathematical properties of the Sinh and Cosh functions, we proposed a new metaheuristic algorithm, Sinh–Cosh Dung Beetle Optimization (SCDBO). By leveraging the Sinh and Cosh functions to disrupt the initial distribution of DBO and balance the development of rollerball dung beetles, SCDBO enhances the search efficiency and global exploration capabilities of DBO through nonlinear enhancements. These improvements collectively enhance the performance of the dung beetle optimization algorithm, making it more adept at solving complex real-world problems. To evaluate the performance of the SCDBO algorithm, we compared it with seven typical algorithms using the CEC2017 test functions. Additionally, by successfully applying it to three engineering problems, robot arm design, pressure vessel problem, and unmanned aerial vehicle (UAV) path planning, we further demonstrate the superiority of the SCDBO algorithm. Full article

This paper outlines a study into the exact solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation that is used to illustrate the ferromagnetic materials of magnetic ordering by applying two recent techniques, namely, the Sardar-subequation method and extended rational sine–cosine and sinh–cosh methods. Abundant exact solutions such as the bright soliton, dark soliton, combined bright–dark soliton, singular soliton and other periodic wave solutions expressed by the generalized trigonometric, generalized hyperbolic, trigonometric and hyperbolic functions are obtained. The numerical results are illustrated in the form of 3D plots, 2D contours and 2D curves by choosing proper parametric values to interpret the physical behavior of the model. The obtained results in this work are expected to provide a rich platform for constructing the soliton solutions of PDEs in physics. Full article

In this study, the dispersal caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using the nonlinear longitudinal wave equation (LWE), a mathematical physics problem. Using the generalized exp-function method, we investigate the families of solitary wave solutions of one-dimensional nonlinear LWE. Using the computer program Wolfram Mathematica 10, these new exact and solitary wave solutions of the LWE are derived as trigonometric function, periodic solitary wave, rational function, hyperbolic function, bright and dark solitons solutions, sinh, cosh, and sech² function solutions of the LWE. These solutions represent the electrostatic potential and pressure for LWE as well as the graphical representation of electrostatic potential and pressure. Full article

Sharp bounds for $\frac{cosh\left(x\right)}{x},\frac{sinh\left(x\right)}{x}$, and $\frac{sin\left(x\right)}{x}$ were obtained, as well as one new bound for $\frac{e^x+arctan\left(x\right)}{\sqrt{x}}$. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral. Full article

Let $I_p\left(x\right)$ be the modified Bessel function of the first kind of order p. The upper and lower bounds in the form of simple rational functions about $cosht$ and $(sinht)/t$ for the function $I_0\left(x\right)$ are obtained. The corresponding inequalities for the Toader-Qi mean do not match those in the existing literature. Full article

While browsing through the famous book of Bierens de Haan, we came across a table with some very interesting integrals. These integrals also appeared in the book of Gradshteyn and Ryzhik. Derivation of these integrals are not listed in the current literature to best of our knowledge. The derivation of such integrals in the book of Gradshteyn and Ryzhik in terms of closed form solutions is pertinent. We evaluate several of these definite integrals of the form ${\int }_0^{\infty }\frac{{(a+y)}^k-{(a-y)}^k}{e^{by}-1}dy$, ${\int }_0^{\infty }\frac{{(a+y)}^k-{(a-y)}^k}{e^{by}+1}dy$, ${\int }_0^{\infty }\frac{{(a+y)}^k-{(a-y)}^k}{sinh\left(by\right)}dy$ and ${\int }_0^{\infty }\frac{{(a+y)}^k+{(a-y)}^k}{cosh\left(by\right)}dy$ in terms of a special function where k, a and b are arbitrary complex numbers. Full article

Let $I_v\left(x\right)$ be he modified Bessel function of the first kind of order v. We prove the double inequality $\sqrt{\frac{sinht}{t}{cosh}^{1/q}\left(qt\right)}<I_0\left(t\right)<\sqrt{\frac{sinht}{t}{cosh}^{1/p}\left(pt\right)}$ holds for $t>0$ if and only if $p\ge 2/3$ and $q\le \left(ln2\right)/ln\pi$ . The corresponding inequalities for means improve already known results. Full article