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arithmetic optimization algorithm with cosine composite chaotic mapping in polar coordinate system for economic load dispatching problems in power systems

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APPLIED SOFT COMPUTING 2025年 175卷

作者： Li, Yi-Xuan Wang, Jie-Sheng Zhang, Si-Wen Zhang, Shi-Hui Guan, Xin-Yi Ma, Xin-Ru Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan Liaoning Peoples R China

Economic load dispatch (ELD) aims to minimize the total cost of generating electricity while satisfying load demand and different operational constraints. The arithmetic optimization algorithm (AOA) with cosine composite chaotic mapping in polar coordinate system is put forward to solve the ELD problems in the power system with the valve point effect, prohibited operation area, transmission loss and other factors. Firstly, seven polar coordinate system chaotic mappings are proposed to be embedded into the MOP and MOA parameters in the AOA. Secondly, a chaotic system based on the cosine transform is put forward. Then, the proposed cosine transform based chaotic system is combined with polar coordinate system chaotic mapping to form polar coordinate system cosine transform composite chaotic mapping. Eventually, these six polar coordinate system cosine transform composite chaotic mapping is then embedded into the MOA and MOP of the AOA to balance the algorithm's global and local search capabilities, improve the performance of the algorithm and avoid falling into the local optima. The superiority of the improved algorithm is verified by employing 12 benchmark test functions in CEC2022. Then, it is compared with the Coati optimization algorithm (COA), Prairie Dog optimization (PDO), Butterfly optimization algorithm (BOA), Reptile Search algorithm (RSA), Bat algorithm (BAT) and Osprey optimization algorithm (OOA) to verify its convergence. The ELD problem for a total demand of 2500 MW is solved by using the AOA with cosine composite chaotic mapping in polar coordinate system. The experimental results show that the improved AOA outperforms other optimization algorithms on the 12 benchmark functions in CEC2022 and the ELD problems.

关键词： Economic load dispatching arithmetic optimization algorithm Two-dimensional Chaotic mapping Cosine composite chaotic system Valve point effect

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arithmetic optimization algorithm with three-dimensional chaotic mapping in spherical coordinate system for combined economic emission dispatch problem

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APPLIED ENERGY 2025年 380卷

作者： Li, Yi-Xuan Wang, Jie-Sheng Guan, Xin-Yi Wang, Xiao-Tian Liu, Xun Zhang, Song-Bo Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan Liaoning Peoples R China

The objective of the Combined Economic Emissions Dispatch (CEED) problem is to reduce pollutant emissions by lowering the total cost of generating electricity while complying with all other constraints. The multiple objective functions of the CEED problem may be converted into a single objective by using a price penalty factor. Then it was solved with the arithmetic optimization algorithm (AOA) with three-dimensional chaotic mapping in spherical coordinate system. Firstly, five three-dimensional chaotic mappings in Cartesian coordinate system are embedded in the Mathematical optimization Accelerator (MOA) and the Mathematical optimization Probability (MOP) of the original algorithm. Secondly, 15 three-dimensional chaotic mappings in spherical coordinate system are constructed from the values of 5 three-dimensional chaotic mappings in Cartesian coordinate system through the mathematical expressions of mode length, polar angle and azimuth angle in spherical coordinate system. Then through a large number of simulation experiments, five best three-dimensional chaotic mappings in the spherical coordinate system are selected to be embedded into the two parameters (MOA and MOP) of the original algorithm to better balance the algorithm's global and local searching ability. The superiority of the improved algorithm is verified by employing 12 benchmark test functions in CEC2022. Eventually, the improved optimal algorithm (IAOA-r) to solve the power system CEED problem is tested on six generating units with four different loads (150 MW, 175 MW, 200 MW and 225 MW). The results of the improved algorithm are compared and analyzed with the results of the Reptile Search algorithm (RSA), Prairie Dog optimization (PDO), Bat algorithm (BAT), Whale optimization algorithm (WOA), Harris Hawk optimization (HHO), Rat Swarm optimization (RSO). The results demonstrate that the improved algorithm is capable of obtaining optimal fuel costs and smaller pollution emissions in every test case.

关键词： Combined economic emissions dispatch arithmetic optimization algorithm Three-dimensional chaotic mapping Spherical coordinate system

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arithmetic optimization algorithm Based on Cauchy Mutation Trigonometric Function Search to Solve Combined Economic Emission Dispatch Problem

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IEEE ACCESS 2023年 11卷 136885-136909页

作者： Li, Yun-Peng Zhang, Lin-Xuan Feng, Zheng-Jie Xinjiang Univ Sch Elect Engn Urumqi 830049 Xinjiang Peoples R China Zhejiang Jinhua Lingsheng Electron Co Ltd Jinhua 311400 Zhejiang Peoples R China

Nowadays, problems such as greenhouse effect and air pollution become increasingly prominent. The power generation process should pay attention to the fuel cost and reduce the pollution to the environment. In this paper, an arithmetic optimization algorithm (AOA) based on Cauchy mutation trigonometric function search is proposed to solve the combined economic emission dispatch (CEED) problem. The price penalty factor is used to convert multiple objective functions of CEED problem into one objective. The math optimization probability (MOP) parameter is used to control the position update of the AOA. MOP is replaced by the oscillation coefficient and Cauchy mutation, which can not only guarantee the local search accuracy but also enhance the global search capability. 6 kinds of trigonometric function search operators, sine function, hyperbolic sine, inverse hyperbolic sine, hyperbolic tangent, inverse hyperbolic tangent, are used to replace the fixed value control parameters in AOA algorithm. The algorithm still has a certain ability to jump out of the local optimal in the late running. The 23 test functions are used to verify the effect of the improved AOA method. The AOA is compared with 6 kinds of improved AOA, and the improvement method with the best effect is selected, and then compared with other intelligent optimization algorithms to verify the effectiveness of the improved strategy. In addition to improving the algorithm, the constraint of CEED problem is also treated. Five kinds of random disturbance penalty functions are proposed, which are cosine function, hyperbolic sine function, tangent function, hyperbolic tangent function and V-type function. The CEED problem of 6 units was selected for simulation experiment under 4 different load demands. The experimental data show that the arithmetic optimization algorithm based on Cauchy mutation trigonometric function search has a good effect on solving CEED problems, and the random disturbance penalty strategy is

关键词： Combined economic emission dispatch Cauchy mutation random disturbance penalty function trigonometric function search arithmetic optimization algorithm

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arithmetic optimization algorithm based on elementary function disturbance for solving economic load dispatch problem in power system

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APPLIED INTELLIGENCE 2022年第10期52卷 11846-11872页

作者： Hao, Wen-Kuo Wang, Jie-Sheng Li, Xu-Dong Wang, Min Zhang, Min Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan 114044 Peoples R China

The objective of economic load dispatch (ELD) is to minimize the overall cost of generation under the premises of meeting the load demand and satisfying different operational constraints. A new improved arithmetic optimization algorithm (AOA) based on elementary function disturbance was proposed to solve ELD problems. Math optimizer accelerated (MOA) and math optimizer probability (MOP) are two important parameters in the original AOA. Ten six elementary functions were adopted, which are sine function, tangent function, hyperbolic secant function, power function, hyperbolic cosecant function and arc-cosine function. Adding the disturbance generated by six elementary functions respectively on the original MOA and MOP parameters can effectively balance the exploration and exploitation ability of AOA, enhance the global search ability, avoid falling into local optimization, and improve the convergence speed of AOA. Then the original AOA was compared with 6 variants by using 23 benchmark functions in CEC-2005, and selected the best improved method. Next, some intelligent optimization algorithms with better performance in optimizing CEC-2005 benchmark functions are adopted to carry out the simulation experiments with the improved AOA to verify its superiority. Finally, three ELD problem cases including valve point effect, prohibited operation area, transmission loss and other factors are selected with a total demand of 1263 MW, 2500 MW and 10,500 MW respectively. The AOA based on elementary function disturbance was used to solve these three ELD problems. Experimental results show that the proposed AOA has the best performance in solving ELD problems.

关键词： Economic load dispatch arithmetic optimization algorithm Elementary function Valve point effect

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arithmetic optimization algorithm based MPPT technique for centralized TEG systems under different temperature gradients

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ENERGY REPORTS 2022年 8卷 2424-2433页

作者： Zhang, Rui Yang, Bo Chen, Nuo Kunming Univ Sci & Technol Fac Elect Power Engn Kunming 650500 Yunnan Peoples R China China Southern Power Grid EHV Transmiss Co Kunming 650217 Yunnan Peoples R China

Since centralized thermoelectric power generation (TEG) system presents multiple local maximum power points (LMPPs) at different temperature gradients (DTG), thus its optimal power harvesting is difficult to realize via conventional approaches. Therefore, an efficient arithmetic optimization algorithm (AOA) is applied to realize maximum power point tracking (MPPT) of centralized thermoelectric power generation system at different temperature gradients to improve the energy exploitation and utilization. AOA is utilized to efficiently and reliably identify unique global maximum power point (GMPP) in multiple LMPPs, which replicates the distribution mechanism of main arithmetic operators during mathematic calculation to find the best solution from a set of randomly generated candidate solutions. Compared with other well-known algorithms, AOA owns the distinctive superiorities of simple implementation structure, as well as few control parameters need to be tuning. Meanwhile, its own random and adaptive parameters selection principle greatly boost the AOA convergence performance. In addition, AOA shows strong ability to avoid falling into local optima thanks to its proper balancing between global exploration (diversification) and local exploitation (intensification). For further validation of the practicability of AOA based MPPT, two case studies are conducted, e.g., start-up test and step change of temperature. Experimental results show that AOA can achieve the optimal energy harvesting with minimal power fluctuations in comparison with the other three optimization algorithms, e.g., the energy produced by AOA is 34.44%, 6.03%, and 8.17% higher than that of perturb and observe (P&O), particle swarm optimization (PSO) and grey wolf optimization (GWO) respectively under the step change of temperature. (C) 2022 The Author(s). Published by Elsevier Ltd.

关键词： Centralized thermoelectric generation system Maximum power point tracking arithmetic optimization algorithm Different temperature gradients

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A multi-threshold image segmentation method based on arithmetic optimization algorithm: A real case with skin cancer dermoscopic images

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JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING 2025年第2期12卷 112-137页

作者： Hao, Shuhui Huang, Changcheng Chen, Yi Wang, Mingjing Liu, Lei Xu, Suling Chen, Huiling Wenzhou Univ Key Lab Intelligent Informat Safety & Emergency Zh Wenzhou 325035 Zhejiang Peoples R China Wenzhou Univ Technol Sch Data Sci & Artificial Intelligence Wenzhou 325000 Zhejiang Peoples R China Sichuan Univ Coll Comp Sci Chengdu 610065 Sichuan Peoples R China Ningbo Univ Affiliated Hosp Med Sch Dept Dermatol Ningbo 315020 Zhejiang Peoples R China

Multi-threshold image segmentation (MTIS) is a crucial technology in image processing, characterized by simplicity and efficiency, and the key lies in the selection of thresholds. However, the method's time complexity will grow exponentially with the number of thresholds. To solve this problem, an improved arithmetic optimization algorithm (ETAOA) is proposed in this paper, an optimizer for optimizing the process of merging appropriate thresholds. Specifically, two optimization strategies are introduced to optimize the optimal threshold process: elite evolutionary strategy (EES) and elite tracking strategy (ETS). First, to verify the optimization performance of ETAOA, mechanism comparison experiments, scalability tests, and comparison experiments with nine state-of-the-art peers are executed based on the benchmark functions of CEC2014 and CEC2022. After that, to demonstrate the feasibility of ETAOA in the segmentation domain, comparison experiments were performed using 10 advanced segmentation methods based on skin cancer dermatoscopy image datasets under low and high thresholds, respectively. The above experimental results show that the proposed ETAOA performs outstanding optimization compared with benchmark functions. Moreover, the experimental results in the segmentation domain show that ETAOA has superior segmentation performance under low and high threshold conditions.

关键词： meta-heuristic algorithms arithmetic optimization algorithm skin cancer multi-threshold image segmentation

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Image Registration Using the arithmetic optimization algorithm for Robotic Visual Servoing

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2025年第1期18卷 1-12页

作者： Kmich, Mohamed Harrade, Inssaf Karmouni, Hicham Sayyouri, Mhamed Askar, S. S. Abouhawwash, Mohamed Sidi Mohamed Ben Abdellah Univ Natl Sch Appl Sci Engn Syst & Applicat Lab Fes Morocco Cadi Ayyad Univ Natl Sch Appl Sci Marrakech Morocco King Saud Univ Coll Sci Dept Stat & Operat Res POB 2455 Riyadh 11451 Saudi Arabia Michigan State Univ Dept Computat Math Sci & Engn CMSE E Lansing MI 48824 USA Mansoura Univ Fac Sci Dept Math Mansoura 35516 Egypt

Visual servoing using image registration is a method employed in robotics to control the movement of a system using visual information. In this context, we propose a new intensity-based image registration algorithm (IBIR) that uses information derived from images acquired at different times or from different views to determine the parameters of the geometric transformations needed to align these images. The arithmetic optimization algorithm (AOA) is used to optimize these parameters, minimizing the difference between the images to be aligned. The proposed algorithm, Intensity-Based Image Registration via arithmetic Optimisation algorithm (IBIRAOA), is robust to image data fluctuations and perturbations and can avoid local optima. Simulation results prove the importance and efficiency of the proposed algorithm in terms of computation time and similarity of aligned images compared to other methods based on various metaheuristics. In addition, our results confirm a significant improvement in the trajectory of the wheeled mobile robot, thus reinforcing the overall effectiveness of our method in practical navigation and robotic control applications.

关键词： arithmetic optimization algorithm Image Registration Metaheuristic optimization algorithms Robotic Visual Servoing

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Sparse compressed deep echo state network with improved arithmetic optimization algorithm for chaotic time series prediction

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 259卷

作者： Wang, Hongbo Mo, Yuanbin Guangxi Minzu Univ Sch Artificial Intelligence Nanning 530006 Guangxi Peoples R China Guangxi Key Lab Hybrid Computat & IC Design Anal Nanning 530006 Guangxi Peoples R China

A sparse compressed deep echo state network (SCDESN) incorporating sparse input units, compressed sampling and principal component analysis (PCA) units is proposed in this paper, and theoretically proved the sufficient and necessary conditions to ensure the echo state characteristics of the proposed scheme. In addition, a hybrid arithmetic optimization algorithm based on matrix design strategy and boundary selection strategy (SVD-HAOA) was proposed to optimize the hyper-parameters of the SCDESN model, taking into account the characteristics of the SCDESN model. The steps and process for optimizing the hyper parameters of the SCDESN model using SVDHAOA were presented. Finally, the SCDESN model optimized by SVD-HAOA was experimentally and summarized on a classic benchmark dataset and two real-world chaotic time series. The outcomes of the simulation indicated that the suggested model surpassed alternative models in performance and enhanced computational efficiency while maintaining prediction accuracy. This model may serve as a viable alternative for real-world applications.

关键词： Echo state networks Hierarchical structure Deep learning arithmetic optimization algorithm Chaotic time series prediction

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Fuzzy Adaptive Sliding-Mode Control Optimized by an arithmetic optimization algorithm for a Quadrotor Drone With Chaotic Nonlinear Dynamics

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OPTIMAL CONTROL APPLICATIONS & METHODS 2025年第2期46卷 634-646页

作者： Mahmoodabadi, M. J. Ibrahim, M. Yousef Sirjan Univ Technol Dept Mech Engn Sirjan Iran Federat Univ Australia Sch Engn & Informat Technol Churchill Vic Australia

An optimal fuzzy adaptive sliding mode controller (OFASMC) is introduced in the present paper for stabilizing a quadrotor drone with chaotic and nonlinear dynamics. At first, control efforts related to the motor torques of the regarded quadrotor drone are determined by the sliding mode procedure as the main stabilizer. Next, using the gradient descent formulation as well as the chain derivative rule, the control gains are adapted through the system states. Then, human knowledge-based fuzzy systems are appropriately designed to set the control parameters for achieving more accurate results. The output errors and control efforts are minimized through the optimum values found for the effective coefficients of the controller by applying the arithmetic optimization algorithm (AOA). Simulation results clearly illustrate the effectiveness of the introduced strategy to stabilize the quadrotor drone system with and without external disturbances. Block diagram of theproposed optimal fuzzy adaptive sliding mode control for the quadrotor drone. image

关键词： adaptive control arithmetic optimization algorithm fuzzy system nonlinear quadrotor drone optimal control sliding mode control

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HSMAOA: An enhanced arithmetic optimization algorithm with an adaptive hierarchical structure for its solution analysis and application in optimization problems

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THIN-WALLED STRUCTURES 2025年 206卷

作者： Liu, Jingsen Zhao, Jianggui Li, Yu Zhou, Huan Henan Univ Henan Int Joint Lab Intelligent Network Theory & K Kaifeng 475004 Peoples R China Henan Univ Coll Software Kaifeng 475004 Peoples R China Henan Univ Inst Management Sci & Engn Kaifeng 475004 Peoples R China Henan Univ Business Sch Kaifeng 475004 Peoples R China

The arithmetic optimization algorithm (AOA) has recently gained significant attention as a novel meta-heuristic algorithm. However, it faces challenges such as premature convergence and entrapment in local optima when addressing complex optimization problems. To overcome these limitations, this paper proposes an enhanced AOA, termed the Self-Adaptive Hierarchical arithmetic optimization algorithm (HSMAOA). The proposed method integrates three key strategies: Firstly, a spiral-guided random walk mechanism is introduced to improve global search ability. Secondly, a novel adaptive hierarchy leader and follower mechanism is proposed, which establishes a complete multi-branch tree hierarchy with decreasing branching degrees within the population, thereby increasing information exchange among population individuals to escape local optima. Finally, a differential mutation strategy based on ranked selection is introduced to enhance candidate solution quality. HSMAOA's performance was evaluated on the CEC2022 test suite against some state-of-the-art algorithms. Results, including optimization accuracy analysis, convergence curves, and various statistical tests, demonstrate HSMAOA's superior optimization capability and robustness. In addition, tests on eight engineering structure optimization problems, including the pressure vessel design problem, the multiple disk clutch brake design problem, and the step-cone pulley problem, and so forth, further validate its effectiveness. Thus, HSMAOA shows strong competitiveness in complex optimization tasks and potential for a wide range of applications, and is an advantageous and promising alternative solution for optimization problems.

关键词： arithmetic optimization algorithm Random walk Adaptive hierarchical structure CEC2022 Engineering optimization problem

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