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Application of empirical wavelet transform, particle swarm optimization, gravitational search algorithm and long short-term memory neural network to copper price forecasting

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PORTUGUESE ECONOMIC JOURNAL 2025年第1期24卷 151-169页

作者： Kim, Yong-Hyong Ham, Song-Jun Ri, Chong-Sim Kim, Won-Hyok Ri, Wi-Song Kim Il Sung Univ Fac Finance Dept Accounting Pyongyang North Korea Artificial Intelligence Inst Korea Comp Ctr Pyongyang North Korea

Copper is one of the main non-ferrous metals which are closely associated with important industries, such as equipment manufacturing, electrical wiring, and construction;and thus, copper price is becoming an important impact factor on the performance of related economies. This paper aims to develop a hybrid method for forecasting the copper price by combining empirical wavelet transform (EWT), particle swarm optimization (PSO), gravitational search algorithm (GSA) and long short term memory neural network (LSTM), which is denoted as EWT-PSO-GSA-LSTM in this study. The forecasting performance of the proposed hybrid method was verified by time series data of the copper closing price in the London Metal Exchange (LME). The results of this study have shown that the proposed EWT-PSO-GSA-LSTM method outperformed other forecasting methods in terms of several performance criteria, such as the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), and the Diebold-Mariano (DM) test. For the daily copper price time series, the EWT-PSO-GSA-LSTM method had the smallest RMSE, MAE and MAPE values (0.007, 0.013 and 1.358, respectively) compared to LSTM, EWT-LSTM, PSO-LSTM and EWT-PSO-LSTM methods. Furthermore, all the DM values of our proposed method were below -2.61 and the p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} values were smaller than 1%, indicating that the proposed method performed the best in forecasting the copper price at the 99% confidence level. Given the present results, it can be concluded that it is possible to improve the copper price forecasting method by combining the EWT, PSO, GSA and LSTM models.

关键词： Copper price forecasting Long-short term memory neural network Particle swarm optimization gravitational search algorithm Empirical wavelet transform C22 C45 C53 C61 L61

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A cluster based routing for maximizing the lifetime of underwater wireless sensor network using gravitational search algorithm

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RESULTS IN ENGINEERING 2025年 25卷

作者： Shyamsundar, R. Harshavarthan, M. Thangavelu, Shankar Vellore Inst Technol Sch Elect Engn Vellore India

Underwater Wireless Sensor Networks (UWSN) is a type of Wireless Sensor Network that branches from Ad Hoc networks. This type of network is designed to investigate and explore underwater environments and oceans. The UWSN network interconnects multiple sensory devices, forming a temporary communication network that forwards the data. Due to the attenuation issue, UWSN uses an acoustic modem for transmission and reception. The energy depletion of UWSN is comparatively higher than Terrestrial Wireless Sensor Networks (TWSN) as it uses an acoustic modem, and the channel mitigations in UWSN are of a higher order than TWSN. Due to this, extensive research is being undertaken worldwide to increase the lifetime of a UWSN network. This paper focuses on the clustering-based routing of the devices using the gravitational search algorithm. The proposed algorithm works in four phases: exploration phase, clustering phase, routing phase, and transmission phase. Also, the proposed algorithm works well for higher and lower node densities. The proposed GSA shows 33.06 %, 11.77 %, and 57.2 % improvements compared to EECMR, EERBLC, and conventional LEACH, respectively. The proposed GSA has been compared with competitive meta-heuristic algorithms, including Particle Swarm Optimization, Whale Optimization algorithm, and Moth Flame Optimizer.

关键词： Underwater wireless sensor networks Clustering Network topology gravitational search algorithm Optimization load balancing

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gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity

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INFORMATION SCIENCES 2013年 247卷 154-173页

作者： David, Radu-Codrut Precup, Radu-Emil Petriu, Emil M. Radac, Mircea-Bogdan Preitl, Stefan Politehn Univ Timisoara Fac Automat & Comp Dept Automat & Appl Informat RO-3000223 Timisoara Romania Univ Ottawa Sch Elect Engn & Comp Sci Ottawa ON K1N 6N5 Canada

This paper proposes the design of fuzzy control systems with a reduced parametric sensitivity making use of gravitational search algorithms (GSAs). The parametric variations of the processes lead to sensitivity models. Objective functions expressed as integral quadratic performance indices, which depend on the control error and squared output sensitivity functions are suggested. GSAs are employed to minimize the objective functions in the appropriately defined optimization problems. This paper also suggests a GSA with improved search accuracy. The new GSA is characterized by the modification of the denominator in the expression of the force acting on an agent from the other agent;the denominator depends not only on the Euclidian distance between the two agents but also on the position of the latter: A design method for Takagi-Sugeno proportional-integral fuzzy controllers (PI-FCs) is proposed. The PI-FCs are dedicated to a class of processes characterized by second-order linear or linearized models with an integral component. Two discrete-time sensitivity models of the fuzzy control systems are derived. An example dealing with the angular position control of direct current (DC) servo system laboratory equipment validates the new controller design. A set of real-time experimental results illustrates the fuzzy control system performance. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Fuzzy control gravitational search algorithm Optimization Parametric sensitivity Real-time experiments Takagi-Sugeno proportional-integral fuzzy controllers

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gravitational search algorithm for coordinated design of PSS and TCSC as damping controller

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Journal of Central South University 2012年第4期19卷 923-932页

作者： M.Eslami H.Shareef A.Mohamed M.Khajehzadeh Department of Electrical Electronic and Systems EngineeringUniversity Kebangsaan MalaysiaBangi 43600SelangorMalaysia

A newly developed heuristic global optimization algorithm, called gravitational search algorithm （GSA）, was introduced and applied for simultaneously coordinated designing of power system stabilizer （PSS） and thyristor controlled series capacitor （TCSC） as a damping controller in the multi-machine power system. The coordinated design problem of PSS and TCSC controllers over a wide range of loading conditions is formulated as a multi-objective optimization problem which is the aggregation of two objectives related to damping ratio and damping factor. By minimizing the objective function with oscillation, the characteristics between areas are contained and hence the interactions among the PSS and TCSC controller under transient conditions are modified. For evaluation of effectiveness and robustness of proposed controllers, the performance was tested on a weakly connected power system subjected to different disturbances, loading conditions and system parameter variations. The cigenvalues analysis and nonlinear simulation results demonstrate the high performance of proposed controllers which is able to provide efficient damping of low frequency oscillations.

关键词： gravitational search algorithm power system stabilizer thyristor controlled series capacitor tuning

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gravitational search algorithm-based dynamic economic dispatch by estimating transmission system losses using A-loss coefficients

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TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES 2016年第5期24卷 3769-3781页

作者： Chinasamy Hemparuva, Ram Jethmalani Simon, Sishaj Pulikottil Kinattingal, Sundareswaran Panugothu, Srinivasa Rao Nayak Natl Inst Technol Tiruchirappalli Tamil Nadu India

Dynamic economic dispatch (DED) is an important problem in power system generation, operation, planning, and control. The objective of the DED problem is to schedule power generation for the online units over a time horizon, satisfying the unit and ramp rate constraints. Here, valve point loading effects that cause nonsmoothness of the objective function is also considered while solving the DED. The accuracy of the solution not only depends on the optimal scheduling of generating units, but it also lies in accuracy while estimating transmission system losses. Generally, B-loss coefficients are used in estimating transmission losses. However, in the literature, A-loss coefficients are found to be at par with B-loss coefficients in estimating transmission system losses. Therefore, in this paper, the performance in estimating the transmission system losses using A-loss coefficients are investigated through the solution of the DED problem. Here, a recently evolved heuristic search technique called the gravitational search algorithm is used for solving the DED. The feasibility of the proposed method is tested and validated on standard benchmark test systems such as the IEEE 30-bus system, IEEE 39-bus system, and IEEE 118-bus system. All simulations are carried out using SCILAB 5.4 (***), which is open-source software.

关键词： A-loss coefficients gravitational search algorithm dynamic economic dispatch

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gravitational search algorithm using CUDA: a case study in high-performance metaheuristics

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JOURNAL OF SUPERCOMPUTING 2015年第4期71卷 1277-1296页

作者： Zarrabi, Amirreza Samsudin, Khairulmizam Karuppiah, Ettikan K. Univ Putra Malaysia Fac Engn Dept Comp & Commun Syst Engn Serdang 43400 Selangor Malaysia MIMOS Berhad Kuala Lumpur 5700 Malaysia

Many scientific and technical problems with massive computation requirements could benefit from the graphics processing units (GPUs) using compute unified device architecture (CUDA). gravitational search algorithm (GSA) is a population-based metaheuristic which can be effectively implemented on GPU to reduce the execution time. Nonetheless, the performance improvement depends strongly on the process used to adapt the algorithm into CUDA environment. In this paper, we discuss possible approaches to parallelize GSA on graphics hardware using CUDA. An in-depth study of the computation efficiency of parallel algorithms and capability to effectively exploit the architecture of GPU is performed. Additionally, a comparative study of parallel and sequential GSA was carried out on a set of standard benchmark optimization functions. The results show a significant speedup while maintaining results quality which re-emphasizes the utility of CUDA-based implementation for complex and computationally intensive parallel applications.

关键词： gravitational search algorithm Graphic processing units CUDA

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gravitational search algorithm Based Optimal Reactive Power Dispatch for Voltage Stability Enhancement

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2012年第9期40卷 956-976页

作者： Roy, P. K. Mandal, B. Bhattacharya, K. Dr BC Roy Engn Coll Dept Elect Engn Durgapur 713206 W Bengal India Kalyani Govt Engn Coll Dept Elect Engn Kalyani W Bengal India Jadavpur Univ Dept Elect Engn Kolkata 700032 W Bengal India

In this article, an efficient and reliable optimization procedure based on the behaviors of swarm in nature, namely the gravitational search algorithm, is proposed for solving multi-objective optimal reactive power dispatch problems, which minimizes transmission loss while maintaining the quality of voltages. The gravitational search algorithm is based on Newton's law of gravity and interaction of masses. In the proposed algorithm, the searcher agents which are a collection of masses interact with each other using Newton's laws of gravity and motion. In order to investigate the performance of the proposed scheme, multi-objective optimal reactive power dispatch problems are solved. This new gravitational search algorithm method is tested on IEEE 57-bus and IEEE 118-bus power systems. Results obtained by the gravitational search algorithm are compared with two versions of genetic algorithms, three versions of differential evolution algorithms, four versions of particle swarm optimization algorithms and the seeker optimization algorithm It is observed from the test results that the proposed gravitational search algorithm approach converges to better solutions much faster than the earlier reported approaches.

关键词： biogeography-based optimization evolutionary programming gravitational search algorithm law of gravity law of motion optimal reactive power dispatch voltage stability margin

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gravitational search algorithm for Microseismic Source Location in Tunneling: Performance Analysis and Engineering Case Study

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ROCK MECHANICS AND ROCK ENGINEERING 2019年第10期52卷 3999-4016页

作者： Ma, Chunchi Jiang, Yupeng Li, Tianbin Chengdu Univ Technol State Key Lab Geohazard Prevent & Geoenvironm Pro Chengdu 610059 Sichuan Peoples R China Univ Sydney Sch Civil Engn Sydney NSW 2006 Australia

Microseismic source location (MSL) provides crucial information for the interpretation of rock mass stability and early warning of rock mass hazards. The accuracy of MSL mainly depends on the formation of the sensor array, the multi-velocity model, and the locating algorithm. Especially, the choice of algorithm plays a decisive role, which requires both optimal accuracy and efficiency for searching the global optimal solution. In this paper, an advanced heuristic algorithm, gravitational search algorithm (GSA), is applied for MSL in tunnel engineering. A standard framework of the GSA-based searching process is first built. Its accuracy, stability, and speed of convergence are rigorously compared and analyzed with particle swarm optimization and simplex algorithm using synthetic and real microseismic data. Four types of equivalent velocity models are combined with the searching algorithm to further discuss the applicability and performance of GSA in different situations. The studies show that for all the cases, GSA has the highest speed of convergence with the best accuracy. Locating errors are controlled within 10 m, which fulfills the requirement of engineering accuracy. A representative case study is conducted using microseismic data prior to a major rockburst in a twin-tube highway tunnel. The calculated cluster of seismic events using GSA-based algorithm well matches the actual unstable areas. This work indicates that GSA is an optimal algorithm for microseismic source location and rockburst warning in tunneling.

关键词： Microseismic source location gravitational search algorithm Velocity models Rockburst warning Tunnel engineering

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gravitational search algorithm and K-means for simultaneous feature selection and data clustering: a multi-objective approach

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SOFT COMPUTING 2019年第6期23卷 2083-2100页

作者： Prakash, Jay Singh, Pramod Kumar ABV Indian Inst Informat Technol & Management Gwa Computat Intelligence & Data Min Res Lab Gwalior MP India

Clustering is an unsupervised classification method used to group the objects of an unlabeled data set. The high dimensional data sets generally comprise of irrelevant and redundant features also along with the relevant features which deteriorate the clustering result. Therefore, feature selection is necessary to select a subset of relevant features as it improves discrimination ability of the original set of features which helps in improving the clustering result. Though many metaheuristics have been suggested to select subset of the relevant features in wrapper framework based on some criteria, most of them are marred by the three key issues. First, they require objects class information a priori which is unknown in unsupervised feature selection. Second, feature subset selection is devised on a single validity measure;hence, it produces a single best solution biased toward the cardinality of the feature subset. Third, they find difficulty in avoiding local optima owing to lack of balancing in exploration and exploitation in the feature search space. To deal with the first issue, we use unsupervised feature selection method where no class information is required. To address the second issue, we follow pareto-based approach to obtain diverse trade-off solutions by optimizing conceptually contradicting validity measures silhouette index (Sil) and feature cardinality (d). For the third issue, we introduce genetic crossover operator to improve diversity in a recent Newtonian law of gravity-based metaheuristic binary gravitational search algorithm (BGSA) in multi-objective optimization scenario;it is named as improved multi-objective BGSA for feature selection (IMBGSAFS). We use ten real-world data sets for comparison of the IMBGSAFS results with three multi-objective methods MBGSA, MOPSO, and NSGA-II in wrapper framework and the Pearson's linear correlation coefficient (FM-CC) as a multi-objective filter method. We employ four multi-objective quality measures converge

关键词： Feature selection Data clustering Multi-objective optimization gravitational search algorithm

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gravitational search algorithm-based optimal control of archimedes wave swing-based wave energy conversion system supplying a DC microgrid under uncertain dynamics

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IET RENEWABLE POWER GENERATION 2017年第6期11卷 763-770页

作者： Hasanien, Hany M. Ain Shams Univ Elect Power & Machines Dept Fac Engn Cairo 11517 Egypt

This study presents a novel application of the gravitational search algorithm (GSA) to optimally control a wave energy conversion (WEC) system under different operating conditions. In the WEC system, the generator side converter controls the d-axis and q-axis current of the generator for minimising the generator power losses and extracting the maximum real power from the WEC system, respectively. The DC-DC converter is implemented to maintain the terminal voltage of the DC microgrid. The control of both converters relies on the proportional-integral controllers, which are optimally designed by the GSA through a simulation-based optimisation approach. In that manner, the integral of squared error criteria is used as an objective function. The validity of the WEC system model is verified by comparing its simulation results with the experimental results that extracted from a field test. The effectiveness of the proposed controller is tested when the system is subjected to different operating conditions such as a DC microgrid load disturbance, a temporary DC fault condition, and an irregular wave condition. Moreover, the effectiveness of the proposed controller is compared with that by using the genetic algorithm. The simulation results of the system are extensively carried out using PSCAD/EMTDC program.

关键词： search problems distributed power generation optimal control power generation control power convertors PI control genetic algorithms gravitational search algorithm-based optimal control archimedes wave swing-based wave energy conversion system DC microgrid uncertain dynamics gravitational search algorithm wave energy conversion system generator side converter WEC system DC-DC converter simulation-based optimisation approach proportional-integral controllers squared error criteria DC microgrid load disturbance DC fault condition genetic algorithm PSCAD EMTDC program

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