Sine-cosine Function Research Articles

Multiple elite strategy enhanced RIME algorithm for 3D UAV path planning

With the wave of artificial intelligence sweeping the world in recent years, UAVs is widely used in various fields. UAV path planning has attracted much attention from scientists as an essential part of UAV work. In order to design an efficient and reasonable 3D UAV path planning program, recent researchers have invented and improved many algorithms. This paper proposes an elite RIME algorithm for 3D UAV path planning. First, we propose an elite reverse learning population selection strategy based on piecewise mapping to enhance the population diversity of the algorithm for better exploration. Second, this paper proposes a stochastic factor-controlled elite pool exploration strategy so that the algorithm is difficult to enter the local optimum and can better explore the global optimum. Then, this paper proposes a hard frost puncture exploitation strategy based on the sine–cosine function so that the algorithm can find the global optimum faster during the exploitation process. Meanwhile, in order to test the performance of the algorithm proposed in this paper, we compare it with 13 other intelligent optimization algorithms that are classical and popular nowadays on 52 test functions in three test sets, CEC2017, CEC2020, and CEC2022, and obtain competitive results. Finally, we applied it to the 3D UAV path planning problem in three different terrain scenarios, and the ELRIME algorithm achieved good results in all of them. Especially in the 7-peak model, the ELRIME algorithm improves the performance of the RIME algorithm by a factor of two. In the 9-peak model, the average value aspect also reduce the cost by 91 compared to the RIME algorithm, and more importantly, it has the smallest fluctuation in 30 runs, which is among the most stable of all the compared algorithms. In the 12-peak model, its stability is also significantly enhanced, and in terms of worst-case cost, it improves the cost by 340 compared to RIME.

Power Series Expansions of Real Powers of Inverse Cosine and Sine Functions, Closed-Form Formulas of Partial Bell Polynomials at Specific Arguments, and Series Representations of Real Powers of Circular Constant

In this paper, by means of the Faà di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and inverse cosine functions, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes power series expansions for real powers of the inverse cosine (sine) functions and the inverse hyperbolic cosine (sine) functions. By comparing different series expansions for the square of the inverse cosine function and for the positive integer power of the inverse sine function, the author not only finds infinite series representations of the circular constant π and its real powers, but also derives several combinatorial identities involving central binomial coefficients and the Stirling numbers of the first kind.

Conditions for the existence of soliton solutions: An analysis of coefficients in the generalized Wu–Zhang system and generalized Sawada–Kotera model

Abstract Exploring nonlinear equations and systems with predetermined coefficient values constrains the depth of understanding of the dynamics inherent in various applications and phenomena represented by such equations. On the contrary, exploration of nonlinear models with free coefficients offers avenues for improved development and ongoing refinement. In light of this, this study aimed to reassess the Wu–Zhang (WZ) system and Sawada–Kotera (SK) model by introducing arbitrary coefficients. Our goal is to identify the constraints necessary to ensure the existence of soliton solutions. Through the application of two distinct approaches, namely, the sine–cosine function method and tanh–coth expansion method, we systematically examine the conditions that facilitate the emergence of solitons within the WZ system and SK model. The insights gained from this analysis are supported by the presentation of 2D and 3D plots, providing a visual depiction of the propagation characteristics exhibited by the obtained solutions. The findings of the current work on conditions for the existence of soliton solutions for both generalized Wu–Zhang and generalized Sawada–Kotera models are novel and presented here for the first time.

Classification feature selection and dimensionality reduction based on logical binary sine-cosine function arithmetic optimization algorithm

Arithmetic optimization algorithm (AOA) is a meta-heuristic algorithm inspired by mathematical operations. AOA has been diffusely used for optimization issues on continuous domains, but few scholars have studied discrete optimization problems. In this paper, we proposed Binary AOA (BAOA) based on two strategies to handle the feature selection problem. The first strategy used S-shaped and V-shaped shift functions to map continuous variables to discrete variables. The second strategy was to combine four logical operations (AND, OR, XOR, XNOR) on the basis of the transfer function, and constructed a parameter model based on the sine and cosine function. An enhanced logic binary sine–cosine function arithmetic optimization algorithm (LBSCAOA) was proposed to realize the position update of variables. Its purpose was to improve the algorithm's global search capabilities and local exploitation capabilities. In the simulation experiments, 20 datasets were selected to testify the capability of the proposed algorithm. Since KNN had the advantages of easy understanding and low training time complexity, this classifier was selected for evaluation. The performance of the improved algorithm was comprehensively evaluated by comparing the average classification accuracy, the average number of selected features, the average fitness value and the average running time. Simulation results showed LBSCAOA with V-Shaped “V4” stood out among many improved algorithms. On the other hand, LBSCAOA with V-Shaped “V4” was used as a representative to compare with other typical feature selection algorithms to verify its competitivenes.

Optimal design of hybrid renewable energy sources with battery storage using an efficient weighted mean of vectors algorithm

An improved algorithm called mINFO is developed, based on the modification of the original weIghted meaN oF vectOrs Optimizer (INFO). In this article, to enhance the original INFO method, an improved version called mINFO is presented by incorporating the sine-cosine function and balancing exploration/exploitation strategy through the control randomization parameter. This suggested mINFO algorithm is applied to obtain the optimal size design of two hybrid renewable power sources (HRPS), the first configuration consists of the photovoltaic (PV)/biomass system (BS)/fuel cells (FC) and the second configuration consists of the PV/BS/battery storage units. This HRPS are designed to generate the power needed to meet the loads supply on the campus of Aswan University in the Sahary region of Aswan city, Egypt. The proposed mINFO approach is developed to avoid the weaknesses of the original INFO method by enhancing the balance between the exploration and exploitation phases and preventing the conventional INFO method from getting stuck in local minima. In order to prove the efficiency and robust search capabilities of the developed mINFO algorithm, the mINFO algorithm is tested by using 10 IEEE CEC’20 test suites and its results are compared with the original INFO method and other well-known optimization algorithms. The proposed mINFO algorithm achieved the first rank in terms of the Friedman mean rank-sum test over F2, F3, F4, F6, F9, and F10, and the second rank after the original INFO algorithm over F1 and F7. Boxplot analysis is also used to show the features of data distribution. For the majority of functions, the boxplots generated by the mINFO algorithm have the narrowest ranges of values out of all comparison algorithms. As a result, for the majority of test functions, the mINFO algorithm shows more promise than its competitors. The main objectives of the suggested HRPS are to minimize energy cost (EC), excess energy (EXE), and maximize the power system's reliability (LPSP). By applying the mINFO algorithm to find the optimal sizing for the two configurations proposed in this study and by comparing the mINFO results with other algorithms such as the original INFO, Particle Swarm optimization (PSO), Runge Kutta optimization (RUN), Sooty Tern Optimization Algorithm (STOA), and Gray Wolf optimization (GWO). The proposed mINFO method shows the best results for the two suggested configurations compared to the other algorithms used by studying the systems for 100 iterations and 50 times run. For the PV/BS/battery units, the best optimal solution has achieved after 36 iterations with the lowest EC with 0.11676275 $/kWh, net present cost (NPC) with 3,420,036 $, EXE with 0.090282 and LPSP with 0.0419687649, while for the PV/BS/FC units, the optimal solution has achieved after 11 iterations with the minimal EC with 0.17996701 $/kWh, NPC with 5,271,318 $, EXE with 0.150022 and LPSP with 0.07598679.

Refined Fractional-Order Fault-Tolerant Coordinated Tracking Control of Networked Fixed-Wing UAVs Against Faults and Communication Delays via Double Recurrent Perturbation FNNs.

This article investigates the fault-tolerant coordinated tracking control problem for networked fixed-wing unmanned aerial vehicles (UAVs) against faults and communication delays. By supplementing the commonly used Gaussian functions in the fuzzy neural networks (FNNs) with sine-cosine functions and constructing two kinds of recurrent loops within the FNN architecture, double recurrent perturbation FNNs are cleverly designed to learn the unknown terms containing faults and uncertainties. Then, adaptive laws are designed for double recurrent perturbation FNNs. Moreover, by assimilating fractional-order calculus into the sliding-mode surfaces and the control signals, refined transient-state and steady-state adjustment performances can be obtained. It is shown by Lyapunov stability analysis that all fixed-wing UAVs can coordinately track their desired trajectories and the tracking errors are uniformly ultimately bounded. Comparative simulation results are provided to show the effectiveness of the proposed control strategy.

Necessary conditions for convex-periodic, elliptic-periodic, inclined-periodic, and rogue wave-solutions to exist for the multi-dispersions Schrodinger equation

In this study, we revisit the modified Schrödinger equation, which incorporates multiple dispersion terms, including linear, nonlinear, and random dispersion. We establish the essential constraints on the model’s parameters to ensure the presence of complex-valued solutions. Subsequently, we employ effective and explicit techniques such as the extended tanh-coth expansion, rational sine-cosine functions, and rational sinh-cosh functions to derive innovative types of periodic solutions for the proposed model. These solutions demonstrate unique physical properties applicable to various complex media, such as surface water waves, optical fiber pulses, and plasma waves.

CALCULUS OPERATORS AND SPECIAL FUNCTIONS ASSOCIATED WITH KOHLRAUSCH–WILLIAMS–WATTS AND MITTAG-LEFFLER FUNCTIONS

In this paper, many important formulas of the subtrigonometric, subhyperbolic, pretrigonometric, prehyperbolic, supertrigonometric, and superhyperbolic functions sin Wiman class are developed for the first time. The subsine, subcosine, subhyperbolic sine, and subhyperbolic cosine associated with Kohlrausch–Williams–Watts (KWW) function and their scaling-law ODEs are proposed. The supersine, supercosine, superhyperbolic sine, and superhyperbolic cosine functions associated with Mittag-Leffler (ML) function and their fractional ODEs are obtained. The conjectures for the supercosine functions containing ML function are presented in detail.

Practical Exploration of Big Data Technology in Improving the Efficiency of English Education Resource Allocation and Utilization

Abstract In order to make full use of educational big data for English education resource allocation and utilization, this paper is based on the standard Bottle Sheath Optimization Algorithm, which generates a random number through the sine-cosine function to update the random positions of individual Bottle Sheaths to improve the randomness and population diversity of the leader search process, improve the Bottle Sheath position updating method, and enhance the algorithm’s ability to perform global search. This paper develops a resource allocation model that can be employed for English education resource allocation. For the vast majority of single-peak and multi-peak functions, the success rate of SCSSA’s solution is 100%, and the performance of SCSSA’s search is significantly better than that of the comparison algorithms (p<0.05), and all of its convergence curves have the fastest decline. After using the model for allocation, the student-teacher ratio of the five districts and counties was improved, with a cumulative decrease of 86.72% in the student-teacher ratio, and the gap in the student-teacher ratio between districts and counties was reduced. However, the model’s optimization effect on the allocation of English books is limited, suggesting that further support of human and financial resources is needed in the allocation process.

Novel Optical bi-directional solutions to the new dual-mode derivative nonlinear Schrödinger equation

In recent times, a novel category of nonlinear physical models known as dual-mode nonlinear equations has emerged. These equations include various real-valued dual-mode equations linked to widely-known single-mode equations like KdV, mKdV, Schrödinger and Burger’s. Extensive research has been conducted to establish and investigate these equations. This study presents a novel dual-mode derivative nonlinear Schrödinger equation that incorporates new parameters for dissipative effects, nonlinearity, and interaction phase velocity. Various methods such as the tanh-coth scheme, extended exponential method, Kudryashov-scheme and the sine-cosine function methods are employed to investigate the solutions of the model. The obtained solutions are illustrated through graphical 2D and 3D and to demonstrate their dynamics and shapes. Furthermore, the interaction of the dual-waves is correlated with changes in the phase-velocity parameter. This model describes propagation of two simultaneously directional waves instead of as in standard Schrödinger equation. For the propagation of solitons in nonlinear optics, the solutions found in this study have important significance. All the resulting solutions can help to comprehend the underlying mechanisms for numerous nonlinear phenomena in diverse domains, including nonlinear optics, plasma physics, Bose–Einstein condensates and others.

Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model

Recently, two fourth-order integrable equations were established by Wazwaz using the Boussinesq model. Tian and Zhang subsequently demonstrated that both equations are potential forms of the Ito model. This study investigates the dynamics of these equations using three effective schemes: the modified rational sine-cosine functions, Kudryashov-expansion, and the Hirota bilinear forms The study reports novel findings, including the observation that although these equations were derived from the same model, one propagates as a single-wave while the other propagates as a bi-wave. Additionally, some solutions of one equation can be obtained from the solutions of the other equation. These results are expected to be highly significant in the study of propagation solitary wave-solutions for nonlinear equations.

Multi-Drone Optimal Mission Assignment and 3D Path Planning for Disaster Rescue

In a three-dimensional (3D) disaster rescue mission environment, multi-drone mission assignments and path planning are challenging. Aiming at this problem, a mission assignment method based on adaptive genetic algorithms (AGA) and a path planning method using sine–cosine particle swarm optimization (SCPSO) are proposed. First, an original 3D digital terrain model is constructed. Second, common threat sources in disaster rescue environments are modeled, including mountains, transmission towers, and severe weather. Third, a cost–revenue function that considers factors such as drone performance, demand for mission points, elevation cost, and threat sources, is formulated to assign missions to multiple drones. Fourth, an AGA is employed to realize the multi-drone mission assignment. To enhance convergence speed and optimize performance in finding the optimal solution, an AGA using both the roulette method and the elite retention method is proposed. Additionally, the parameters of the AGA are adjusted according to the changes in the fitness function. Furthermore, the improved circle algorithm is also used to preprocess the mission sequence for AGA. Finally, based on the sine–cosine function model, a SCPSO is proposed for planning the optimal flight path between adjacent task points. In addition, the inertia and acceleration coefficients of linear weights are designed for SCPSO so as to enhance its performance to escape the local minimum, explore the search space more thoroughly, and achieve the purpose of global optimization. A multitude of simulation experiments have demonstrated the validity of our method.

Location controllable rogue wave and mixed interaction solutions on the sine-cosine function period background for the Heisenberg ferromagnetic equation

Location controllable rogue wave and mixed interaction solutions on the sine-cosine function period background for the Heisenberg ferromagnetic equation

Quasi discreteness analysis of a two dimensional ferromagnetic spin system

By introducing bilinear and anisotropic interactions in a model based on a square lattice of ferromagnetism, we learn about the influence of excitations with nonlinearity in intrinsic localized modes (ILMS) and modulational instability. Equations of motion are constructed in the semi-classical limit by pairing Glauber’s coherent state representation with the Dyson-Maleev form of spin operators. A Cubic Nonlinear Schrödinger (CNLS) equation is obtained using an intensive method of quasi-discreteness analysis mixed with a method of multiple scales. We also analyze the bright envelope solitons and intrinsically localized modes using a Sine-Cosine function approach. Stability conditions are obtained using Modulational Instability analysis.

Application of chaos assisted sine cosine algorithm on wind–solar integrated hydrothermal scheduling problem

AbstractIn recent times, renewable energy sources are essential for generating low‐cost, pollution‐free power. Since the last two decades, hydrothermal coordination system has been used to fulfill the demand power. The traditional generating model's two biggest flaws are high generation cost and excessive fossil fuel emission. In the proposed work, generation process of traditional hydrothermal scheduling (HTS) has been improved by integrating wind–solar energy. To overcome current issues of HTS, that is, excessive emission and generation cost, hydrothermal–solar–wind scheduling (HTSWS) problem has been introduced where two wind and two solar power generating units have been considered with four hydro and three thermal power generating units. Here, effective performance of low cost‐emission based proposed HTSWS has been examined by using chaos‐based sine cosine algorithm (SCA) (CSCA). Chaos has been used in sine cosine function of SCA to improve searching process for finding global optimal results. The proposed CSCA has been used to investigate three separate situations of standard HTS and recommended HTSWS problems including generation cost, emission, and combined cost‐emission. The cost of generation and emissions from conventional HTS can be reduced by 11% and 68%, respectively, by the suggested renewable energy source‐based generation model. The results of several case studies of proposed HTSWS and standard HTS reveal that wind–solar energy is effective in the HTS issue, and chaos assists in the SCA to improve its optimization process. In this study, effectiveness and robustness of the CSCA have been demonstrated by comparing the CSCA‐based results to existing methods for the challenges under consideration.

Enhanced chimp optimization algorithm for high level synthesis of digital filters

The HLS of digital filters is a complex optimization task in electronic design automation that increases the level of abstraction for designing and scheming digital circuits. The complexity of this issue attracting the interest of the researcher and solution of this issue is a big challenge for the researcher. The scientists are trying to present the various most powerful methods for this issue, but keep in mind these methods could be trapped in the complex space of this problem due to own weaknesses. Due to shortcomings of these methods, we are trying to design a new framework with the mixture of the phases of the powerful approaches for high level synthesis of digital filters in this work. This modification has been done by merging the chimp optimizer with sine cosine functions. The sine cosine phases helped in enhancing the exploitation phase of the chimp optimizer and also ignored the local optima in the search area during the searching of new shortest paths. The algorithms have been applied on 23-standard test suites and 14-digital filters for verifying the performance of the algorithms. Experimental results of single and multi-objective functions have been compared in terms of best score, best maxima, average, standard deviation, execution time, occupied area and speed respectively. Furthermore, by analyzing the effectiveness of the proposed algorithm with the recent algorithms for the HLS digital filters design, this can be concluded that the proposed method dominates the other two methods in HLS digital filters design. Another prominent feature of the proposed system in addition to the stated enhancement, is its rapid runtime, lowest delay, occupied area and lowest power in achieving an appropriate response. This could greatly reduce the cost of systems with broad dimensions while increasing the design speed.

A Simplified Sine Cosine Algorithm for the Solution of Optimal Reactive Power Dispatch

In this article, a simplified sine cosine algorithm (SSCA) is applied to solve the optimal reactive power dispatch (ORPD) issues by estimating the control variables. This algorithm uses sine cosine functions and generates number of random solutions to obtain the best solution by fluctuating inwards or outwards. The SSCA is implemented in the ORPD problem to find the best control variables to achieve minimum power loss and maximum net savings. Furthermore, the efficacy of SSCA is validated with other recently used algorithms considering three case studies, i.e., IEEE-30, -57, and -118 bus test system. The results show that the SSCA approach finds more precise and superior ORPD solutions. A comparison among SSCA and other methods proves the robustness of SSCA to attain the solution with faster convergence. The statistical analysis is performed to justify the effectiveness of SSCA by yielding minimum operating cost and maximum net savings as compared to other techniques considered in this study.

Application of Sine Cosine Egret Swarm Optimization Algorithm in Gas Turbine Cooling System

Gas turbine cooling system is a typical multivariable, strongly coupled, nonlinear, and uncertain MIMO system. In order to solve the control problem of pressure, flow, and temperature of the system, an intelligent approach is necessary and more appropriate. The current system control mainly depends on the experience of the staff, which exists problems such as high labor intensity, low work efficiency and low control accuracy. Lack of accurate models make parameters tune difficultly, and ordinary control methods are difficult to control complex gas turbine cooling system. In this paper, the system transfer function model is built based on the field data obtained under different working conditions and system identification method. The diagonal matrix decoupling method is used to weaken the correlation between variables and achieve independent control among variables. When optimizing the parameters of the controller, Sine Cosine Egret Swarm Optimization Algorithm is proposed. Egret Swarm Optimization Algorithm is composed of Sit-And-Wait strategy, random walk, and encirclement strategy. The sit-and-wait strategy is prone to premature convergence, which makes the optimized parameters unsuitable for gas turbine cooling system. Sine Cosine Algorithm is introduced to randomly use the sine-cosine function for the pseudo-gradient of the weights of the observation equation, thus expanding the search range of the population. Friedman tests prove that the deviation of SE-ESOA is within the allowable range. The results show that the result of Sine Cosine Egret Swarm Optimization Algorithm is more stable and accurate, and it is more suitable for gas turbine cooling system, which solve the pressure, flow, and temperature control problems of complex systems.

Disentangling the influence of temperature and season on weekly birth rates in Vienna, Austria

Background: Before examining other environmental predictors of weekly birth- and conception rates, we set out to investigate seasonal and meteorological predictors in a time series of births given by Viennese women between 1999 and 2019. Methods: We extracted week of birth and duration of gestation in weeks to calculate number of conceptions and of births per week. For both outcomes (birth and conception numbers) we first applied negative binomial regression models. But, when we saw that over-dispersion was negligible, we reverted to Poisson regression models. As predictors, we included a linear term, sine-cosine functions with a wave-length of one year, and another one with a wavelength the average duration of a lunar cycle. In addition, we included temperature as a linear and a quadratic term. Results: On average 341.4 births and 344.1 conceptions occurred per week. The number of births and conceptions increased over the years and within each year seasonal variation was visible. Birth numbers according to the annual sine-cosine model were lowest in January and February and highest in July and August. The number of conceptions were lowest in May and highest in November. Adding another sine-cosine function for the lunar cycle did not improve the model fit much. Nevertheless, that parameter was still significant, with the highest birth numbers occurring roughly between the waxing crescent and the first quarter moon, and the highest conception numbers conceptions occurring at the full moon. Extremer temperatures (both hot and cold) decreased conception numbers and increased birth numbers. Conclusion: While the effects of temperature and the annual variation resembled our expectations, the lunar influence was unexpected. This latter finding should be treated with care, because it was not hypothesis driven. KEYWORDS: annual & lunar cycle, births, temperature, births, conceptions

New interesting optical solutions to the quadratic–cubic Schrodinger equation by using the Kudryashov-expansion method and the updated rational sine–cosine functions

New interesting optical solutions to the quadratic–cubic Schrodinger equation by using the Kudryashov-expansion method and the updated rational sine–cosine functions