sine cosine algorithm
در نشریات گروه فنی و مهندسی-
International Journal of Optimization in Civil Engineering, Volume:14 Issue: 3, Summer 2024, PP 385 -422
The sine-cosine algorithm is concerned as a recent meta-heuristic method that takes benefit of orthogonal functions to scale its walking steps through the search space. The idea is utilized here in a different manner to develop a modified sine-cosine algorithm (MSCA). It is based on the controlled perturbation about current solutions by applying a novel combination of sine and cosine functions. The desired transition from exploration to exploitation phases mainly relies on such a term that provides continued fluctuations within a dynamic amplitude. Performance of the proposed algorithm is further evaluated on a set of thirteen test functions with unimodal and multimodal search spaces, as well as on engineering and structural problems in a variety of discrete, continuous and mixed discrete-continuous types. Numerical simulations show that MSCA can find the best literature results for such benchmarks problems. Additional fair comparisons, declare competitive performance of the proposed method with other meta-heuristic algorithms and its enhancement with respect to the standard sine-cosine algorithm.
Keywords: Sine-Cosine Algorithm, Computational Intelligence, Meta-Heuristic Method, Function Optimization, Constrained Problem -
برنامه ریزی توان تولیدی واحدها جهت تامین تقاضای بار ساعتی، یکی از مسائل مهم در مدیریت تولید و بهره برداری از سیستم های قدرت می باشد. در این مقاله، مسئله توزیع بهینه بار با در نظر گرفتن تلفات شبکه انتقال، ملاحظات و محدودیت های عملی نیروگاه های حرارتی از قبیل نرخ افزایشی و کاهشی تولید، نواحی ممنوعه تولید، اثر شیر بخار با ترکیب منابع تجدید پذیر شامل مزارع بادی و واحدهای خورشیدی مطرح شده است. منابع انرژی تجدید پذیر به دلیل عدم استفاده از سوخت های سوختی باعث کاهش آلودگی های زیست محیطی شده اما این منابع، دارای عدم قطعیت و ماهیت تصادفی در تولید می باشند. از طرف دیگر منابع بادی و خورشیدی جزء منابع راه اندازی سریع و منابع حرارتی جزء منابع حرارتی راه اندازی کند محسوب می شوند. در نظر گرفتن موارد ذکر شده به صورت توام، مساله توزیع بهینه بار را پیچیده می نماید که در این مقاله برای تعیین میزان مشارکت منابع تولیدی مختلف در تامین بار، از روش جدیدی مبتنی بر الگوریتم سینوس کسینوس، استفاده شده است. به منظور بررسی کارآیی روش پیشنهادی، نتایج شبیه سازی و مطالعات عددی روی یک سیستم نمونه شامل 6 واحد حرارتی، 5 واحد بادی و 13 واحد خورشیدی پیاده سازی شده و با دیگر روش های هوشمند مقایسه شده است. نتایج مطالعات عددی ضمن داشتن سرعت و دقت مناسب، برتری روش پیشنهادی را نسبت به سایر روش ها نشان می دهد.کلید واژگان: توزیع بهینه، الگوریتم سینوس کسینوس، بهینه سازی، منابع انرژی تجدید پذیرDynamic production power planning to meet hourly load demand is one of the important issues in production management and operation of power systems. In this article, the problem of optimal load dispatch considering transmission network losses, considerations and practical limitations of thermal power plants such as increasing and decreasing ramp rates, prohibited production areas, steam valve effect with the combination of renewable resources including wind farms and solar units has been raised. Renewable energy sources have reduced environmental pollution due to the non-use of fossil fuels, but these sources have uncertainty and random nature in production. On the other hand, wind and solar sources are considered to be part of fast start-up sources and thermal sources are considered to be part of slow start-up thermal sources. Considering the mentioned cases together complicates the problem of optimal load distribution, in this article, a new method based on the sine-cosine algorithm is used to determine the contribution of different production sources in the load supply. To solve this problem, which has non-convex cost functions, a new method based on the sine-cosine algorithm has been used. In order to evaluation the effectiveness of the proposed method, simulation results and numerical studies on a sample system including 6 thermal units, 5 wind units and 13 solar units have been implemented and compared with other metaheuristic algorithms. The results of numerical studies show the superiority of the proposed method over other methods while having the appropriate speed and accuracy.Keywords: Optimal Dispatch, Sine Cosine Algorithm, Optimization, Renewable Energy Sources
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In this study, optimal energy management is addressed in the residential building. The residential building is equipped with renewable energies including wind turbines (WT) and photovoltaic (PV) systems. Stochastic programming is used to model the uncertainty of renewable energy resources. To manage these uncertainties and reduce the total daily cost of energy, the load control program is adopted. In this respect, five different types of loads are modeled in the building, including interruptible, uninterruptible, constant-energy, constant-power and movable loads. The above charges are properly adjusted and shipped to minimize energy costs and address the uncertainties of renewable energy by hybrid sine cosine shuffled frog leaping algorithm. The residential building is considered as later active in the network, which transfers energy from network to the building and vice versa. The simulation results show that the proposed model can efficiently harness all the energy possible from WT-PV systems, manage uncertainties, minimize total daily costs and operate as an island. All of these objectives are achieved by optimal load distribution and control within the proposed load control program.Keywords: Sine Cosine Algorithm, Shuffled Frog Leaping Algorithm, Renewable Energy, Residential Building, Energy Management
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A New Model-based Bald Eagle Search Algorithm with Sine Cosine Algorithm for Data ClusteringJournal of Advances in Computer Engineering and Technology, Volume:7 Issue: 3, Summer 2021, PP 177 -186
Clustering is one of the most popular techniques in unsupervised learning in which data is divided into different groups without any prior knowledge, and for this reason, clustering is used in various applications today. One of the most popular algorithms in the field of clustering is the k-means clustering algorithm. The most critical weakness of k-means clustering is that it is sensitive to initial values for parameterization and may stop at local minima. Despite its many advantages, such as high speed and ease of implementation due to its dependence on the initial parameters, this algorithm is in the optimal local configuration and does not always produce the optimal answer for clustering. Therefore, this paper proposes a new model using the Bald Eagle Search (BES) Algorithm with the Sine Cosine Algorithm (SCA) for clustering. The evaluation of the proposed model is based on the number of iterations, convergence, number of generations, and execution time on 8 UCI datasets. The proposed model is compared with Flower Pollination Algorithm (FPA), Crow Search Algorithm (CSA), Particle Swarm Optimization (PSO), and Sine-Cosine Algorithm (SCA). The results show that the proposed model has a better fit compared to other algorithms. According to the analysis, it can be claimed that the proposed model is about 10.26% superior to other algorithms and also has an extraordinary advantage over k-means.
Keywords: Clustering, Bald Eagle Search Algorithm, Sine-Cosine Algorithm, K-means -
نشریه مهندسی عمران و محیط زیست دانشگاه تبریز، سال پنجاه و سوم شماره 1 (پیاپی 110، بهار 1402)، صص 199 -210خاک های غیراشباع حدود 40 درصد از خاک های سطح زمین را پوشانده و در اکثر پروژ ه های مهندسی ژیومکانیک به چنین خاک های برخورد می شود. تعیین مقاومت برشی خاک های غیراشباع براساس اصل تنش موثر به منظور استفاده در این گونه پروژه ها، مستلزم انجام آزمایش های نسبتا وقت گیر، پرهزینه و پیچیده است. از طرفی به دلیل تغییرات در خصوصیات خاک هر منطقه استفاده از روش های تجربی به منظور تخمین تنش موثر خاک های غیراشباع از دقت کم تری برخوردار بوده و با خطا همراه است. به منظور برآورد صحیح مقاومت برشی خاک های غیراشباع، هدف از نگارش این مقاله کاربرد روش های جدید هوشمند برای تخمین پارامتر تنش موثر، با استفاده از دو الگوریتم بهینه سازی هوشمند گرگ خاکستری، (Grey wolf optimization) و سینوس- کسینوس، (Sine cosine algorithm) می باشد. در این مدل ها از پارامترهایی نظیر: مقدار ورودی هوا، مقدار آب حجمی در شرایط باقی مانده و اشباع، شیب منحنی مشخصه آب- خاک، فشار محدودکننده خالص و مکش به عنوان پارامترهای ورودی و از پارامتر تنش موثر به عنوان خروجی استفاده شده است. در انتها برای صحت و ارزیابی مدل های پیش بینی از شاخص های ضریب همبستگی مربع (R2)، میانگین درصد خطای مطلق، (Mean Absolute Percentage Error)، شمول واریانس، (Variance accounted for)، مجذور میانگین خطای مربع، (Root mean squared error) و میانگین خطای مربع، (Mean squared error) استفاده شده است. نتایج مدل سازی نشان می دهد که استفاده از دو الگوریتم بهینه سازی هوشمند گرگ خاکستری و سینوس- کسینوس دقت و کارایی قابل قبولی را در تخمین پارامتر تنش موثر برای خاک های غیراشباع دارد.کلید واژگان: پارامتر تنش موثر، خاک غیراشباع، تخمین غیرمستقیم، الگوریتم گرگ خاکستری، الگوریتم سینوس- کسینوسJournal of Civil and Environmental Engineering University of Tabriz, Volume:53 Issue: 1, 2023, PP 199 -210Compacted soils, which are commonly used in geotechnical engineering projects, such as earth dams, highways, embankments, and airport runways, are mostly unsaturated. To achieve a safe design in all these projects, the stress state variable in soil plays a significant role. Any proposed model for the stress state variable should express its independence from the soil properties. In saturated soils, the e effective stress is taken into account as the stress state variable. Some researchers have attempted to find the stress state variable for unsaturated soils the same as that for saturated soils with only one variable; however, they have noticed that the soil properties have been involved in the proposed models (Bishop, 1959; Escario and Saez, 1986; Khalili and Khabbaz, 1998; Lu and Likos, 2004; Rahnema et al., 2019). The purpose of this paper is to apply new intelligent methods to accurately estimate the effective stress parameter, using two gray wolf optimization (GWO) and sine-cosine (SCA) optimization algorithms.Keywords: Effective stress parameter, Unsaturated soil, indirect estimation, gray wolf algorithm, sine-cosine algorithm
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International Journal of Optimization in Civil Engineering, Volume:13 Issue: 1, Winter 2023, PP 17 -38
Colliding Bodies Optimization (CBO) is a population-based metaheuristic algorithm that complies physics laws of momentum and energy. Due to the stagnation susceptibility of CBO by premature convergence and falling into local optima, some meritorious methodologies based on Sine Cosine Algorithm and a mutation operator were considered to mitigate the shortcomings mentioned earlier. Sine Cosine Algorithm (SCA) is a stochastic optimization method that employs sine and cosine based mathematical models to update a randomly generated initial population. In this paper, we developed a new hybrid approach called hybrid CBO with SCA (HCBOSCA) to obtain reliable structural design optimization of discrete and continuous variable structures, where a memory was defined to intensify the convergence speed of the algorithm. Finally, three structural problems were studied and compared to some state of the art optimization methods. The experimental results confirmed the competence of the proposed algorithm.
Keywords: Colliding Bodies Optimization, Sine Cosine Algorithm, Structural Design, Discrete, Continuous Optimization, Metaheuristic Algorithms -
Scientia Iranica, Volume:27 Issue: 3, May-Jun 2020, PP 1467 -1480Economic Load Dispatch (ELD) is an important part of cost minimization procedure in power system operation. Different derivative and probabilistic methods are used to solve ELD problems. This paper proposes a powerful Sine Cosine Algorithm (SCA) to explain the ELD issue including equality and inequality restrictions. The main aim of ELD is to satisfy the entire electric load at minimum cost. The SCA is a population based probabilistic method which guides its search agents that are randomly placed in the search space, towards an optimal point using their fitness function and also keeps a track of the best solution achieved by each search agent. SCA is being used to solve the ELD problem with their high exploration and local optima escaping technique. This algorithm confirms that the promising areas of the search space are exploited to have a smooth transition from exploration to exploitation using sine and cosine functions. Simulation results prove that the proposed algorithm surpasses other existing optimization techniques in terms quality of solution obtained and computational efficiency. The final results also prove the robustness of the SCA.Keywords: Economic Load Dispatch, optimization, Prohibited operating zone, Sine Cosine Algorithm, Valve-point loading
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Journal of Operation and Automation in Power Engineering، سال هشتم شماره 1 (Winter-Spring 2020)، صص 75 -85
باتری خودروهای الکتریکی توانایی افزایش تعادل بین تقاضای بار و واحد های تولید توان را دارد. به منظور مدیریت رفتار تصادفی صاحبان خودروها و افزایش مشارکت آنها در بازار خدمات جانبی، تجمیع کننده ی خودروهای الکتریکی به کار گرفته می شود. حضور تجمیع کننده ها می تواند منجربه بروز تاخیرهای متغیر با زمان در سیستم کنترل بار فرکانس شود. اثرات این تاخیرها بایستی در طراحی کنترل کننده سیستم LFC در نظر گرفته شود. با توجه به وابستگی اثربخشی کنترل کننده به مقادیر پارامترهای آن، این پارامترها بایستی به گونه ای طراحی شوند که سیستم LFC عملکرد مطلوبی را در حضور تاخیرهای متغیر با زمان داشته باشد. از این رو، الگوریتم سینوس کسینوس برای تنظیم ضرایب کنترل کننده FOPID استفاده می شود. همچنین، برخی ارزیابی ها پیرامون عملکرد سیستم LFC توسط شاخص IAE ارائه می شود. شبیه سازی ها در هر دو سیستم LFC تک و دو ناحیه ای شامل تجمیع کننده خودروهای الکتریکی با تاخیرهای متغیر با زمان انجام می شود. طبق نتایج، کنترل کننده پیشنهادی دارای نوسانات فرکانسی کمتری در مقایسه با سایر کنترل کننده های ارائه شده در مطالعات موردی می باشد. خروجی به دست آمده می تواند به عنوان راه حلی برای ارزیابی عملکرد کنترل کننده پیشنهادی در کاهش نوسانات فرکانسی سیستم LFC دارای تاخیر در نظر گرفته شود.
کلید واژگان: تجمیع کننده خودروی الکتریکی، تاخیر متغبر با زمان، کنترل کننده PID مرتبه کسری، الگوریتم سینوس کسینوس، کنترل بار فرکانسJournal of Operation and Automation in Power Engineering, Volume:8 Issue: 1, Winter-Spring 2020, PP 75 -85The EVs battery has the ability to enhance the balance between the load demand and power generation units. The EV aggregators to manage the random behaviour of EV owners and increasing EVs participation in the ancillary services market are employed. The presence of aggregators could lead to time-varying delay in load frequency control (LFC) schemes. The effects of these delays must be considered in the LFC controller design. Due to the dependency of controller effectiveness on its parameters, these parameters should be designed in such a way that the LFC system has desired performance in the presence of time-varying delay. Therefore, a Sine Cosine Algorithm (SCA) is utilized to adjust the fractional-order PID (FOPID) controller coefficients. Also, some evaluations are performed about the proposed LFC performance by integral absolute error (IAE) indicator. Simulations are carried out in both single and two area LFC system containing EV aggregators with time-varying delay. According to results, the proposed controller has fewer frequency variations in contrast to other controllers presented in the case studies. The obtained output could be considered as a solution to evaluate the proposed controller performance for damping the frequency oscillations in the delayed LFC system.
Keywords: Electric vehicle aggregator, Time-varying delay, Fractional-order PID, Sine cosine algorithm, Load frequency control -
International Journal of Optimization in Civil Engineering, Volume:9 Issue: 2, Spring 2019, PP 195 -212This paper proposes a modified sine cosine algorithm (MSCA) for discrete sizing optimization of truss structures. The original sine cosine algorithm (SCA) is a population-based metaheuristic that fluctuates the search agents about the best solution based on sine and cosine functions. The efficiency of the original SCA in solving standard optimization problems of well-known mathematical functions has been demonstrated in literature. However, its performance in tackling the discrete optimization problems of truss structures is not competitive compared with the existing metaheuristic algorithms. In the framework of the proposed MSCA, a number of worst solutions of the current population is replaced by some variants of the global best solution found so far. Moreover, an efficient mutation operator is added to the algorithm that reduces the probability of getting stuck in local optima. The efficiency of the proposed MSCA is illustrated through multiple benchmark optimization problems of truss structures.Keywords: discrete optimization, sizing optimization, truss structures, metaheuristic, sine cosine algorithm
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