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The arithmetic optimization algorithm

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2021年 376卷 113609-113609页

作者： Abualigah, Laith Diabat, Ali Mirjalili, Seyedali Elaziz, Mohamed Abd Gandomi, Amir H. Amman Arab Univ Fac Comp Sci & Informat Amman 11953 Jordan New York Univ Abu Dhabi Div Engn Abu Dhabi 129188 U Arab Emirates NYU Tandon Sch Engn Dept Civil & Urban Engn Brooklyn NY 11201 USA Torrens Univ Australia Ctr Artificial Intelligence Res & Optimisat Brisbane Qld Australia Yonsei Univ YFL Yonsei Frontier Lab Seoul South Korea Zagazig Univ Dept Math Fac Sci Zagazig Egypt Wuhan Univ Technol Sch Comp Sci & Technol Wuhan Peoples R China Univ Technol Sydney Fac Engn & Informat Technol Ultimo NSW 2007 Australia

This work proposes a new meta-heuristic method called arithmetic optimization algorithm (AOA) that utilizes the distribution behavior of the main arithmetic operators in mathematics including (Multiplication (M), Division (D), Subtraction (S), and Addition (A)). AOA is mathematically modeled and implemented to perform the optimization processes in a wide range of search spaces. The performance of AOA is checked on twenty-nine benchmark functions and several real-world engineering design problems to showcase its applicability. The analysis of performance, convergence behaviors, and the computational complexity of the proposed AOA have been evaluated by different scenarios. Experimental results show that the AOA provides very promising results in solving challenging optimization problems compared with eleven other well-known optimization algorithms. Source codes of AOA are publicly available at http://***/matlabcentral/fileexchange/8474 and https://***/projects. (C) 2020 The Author(s). Published by Elsevier B.V.

关键词： arithmetic optimization algorithm AOA algorithm optimization Meta-heuristics Heuristic Artificial Intelligence Grey Wolf Optimizer Whale optimization algorithm Genetic algorithm Particle Swarm optimization Benchmark Computational Intelligence

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The application of arithmetic optimization algorithm in solving the optimal reactive power dispatch problem

Measurement: Digitalization

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Measurement: Digitalization 2025年

作者： Tanmay Das Ranjit Roy Kamal Krishna Mandal Department of Power Engineering Jadavpur University Salt Lake Campus Kolkata India Department of Electrical and Electronics Engineering SRM University Sonipat Haryana India

The optimal reactive power dispatch problem (ORPD) is a crucial tool in optimizing power flow by minimizing line losses. This problem is solved by finding optimal solutions to control variables to minimize power loss in lines. The paper introduces the arithmetic optimization algorithm (AOA), a new optimization technique not yet introduced in the ORPD problem study. This unique metaheuristic approach, inspired by mathematical operators, balances exploration and exploitation to optimize control parameters. Although not a nature-inspired technique, it has demonstrated superior solution quality compared to many other methods, as reported in the literature. The AOA has demonstrated superior solution quality compared to other methods when tested on two test bus systems, the IEEE 30 bus system and the IEEE 300 bus system. It has acquired solutions with a significant reduction in the power loss to almost 18.92% for the IEEE 30 bus system and 17.57% for the IEEE 300 bus system. The AOA’s superior performance in resolving the ORPD issue was validated through statistical tests like the Kolmogorov-Smirnov normality test and the Kruskal-Wallis non-parametric rank test, along with the computational complexity test. The study also confirmed that the AOA not only optimized the ORPD problem but also improved the overall voltage profile for both test bus systems.

关键词： arithmetic optimization algorithm mathematical arithmetic operators optimal reactive power dispatch optimization problem power loss voltage profile

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A symbiosis of arithmetic optimizer with slime mould algorithm for improving global optimization and conventional design problem

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JOURNAL OF SUPERCOMPUTING 2022年第5期78卷 6234-6274页

作者： Chauhan, Sumika Vashishtha, Govind Kumar, Anil St Longowal Inst Engn & Technol Dept Elect & Instrumentat Engn Longowal 148106 India St Longowal Inst Engn & Technol Dept Mech Engn Precis Metrol Lab Longowal 148106 India Wenzhou Univ Coll Mech & Elect Engn Wenzhou 325035 Peoples R China

An arithmetic optimizer algorithm (AOA) is hybridized with slime mould algorithm (SMA) to address the issue of less internal memory and slow convergence at local minima which is termed as HAOASMA. Lens opposition-based learning strategy is also integrated with the hybrid algorithm which enhances the population diversity of the hybrid optimizer to accelerate the convergence. The local best (P-best) and global best (g(best)) of SMA initializes the AOA's search process. The Pbest obtained from AOA again initializes the SMA to further exploit the search space. In this way, the developed hybrid algorithm utilizes the exploitation and exploration capabilities of SMA and AOA, respectively. The developed HAOASMA has been compared on twenty-three benchmark functions at different dimensions with basic SMA, AOA and six renowned meta-heuristic algorithms. The HAOASMA has also been applied to classical engineering design problems. The performance of HAOASMA is significantly superior compared to basic SMA, AOA and other meta-heuristic algorithms.

关键词： arithmetic optimization algorithm Slime mould algorithm Lens opposition-based learning Global optimization Hybridization

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Optimal power flow using a hybridization algorithm of arithmetic optimization and aquila optimizer

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 235卷

作者： Ahmadipour, Masoud Othman, Muhammad Murtadha Bo, Rui Javadi, Mohammad Sadegh Ridha, Hussein Mohammed Alrifaey, Moath Univ Teknol MARA Coll Engn Sch Elect Engn Shah Alam 40450 Selangor Malaysia Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA Inst Syst & Comp Engn Technol & Sci INESC TEC Porto Portugal Univ Putra Malaysia UPM Fac Engn Dept Elect & Elect Engn Adv Lightning Power & Energy Res ALPER Serdang 43400 Selangor Malaysia Univ Al Mustansiriyah Dept Comp Engn Baghdad Iraq Univ Putra Malaysia Fac Engn Dept Mech & Mfg Engn Serdang 43400 Selangor Malaysia

In this paper, a hybridization method based on arithmetic optimization algorithm (AOA) and Aquila optimizer (AO) solver namely, the AO-AOA is applied to solve the Optimal Power Flow (OPF) problem to independently optimize generation fuel cost, power loss, emission, voltage deviation, and L index. The proposed AO-AOA algorithm follows two strategies to find a better optimal solution. The first strategy is to introduce an energy parameter (E) to balance the transition between the individuals' procedure of exploration and exploitation in AOAOA swarms. Next, a piecewise linear map is employed to reduce the energy parameter's (E) randomness. To evaluate the performance of the proposed AO-AOA algorithm, it is tested on two well-known power systems i.e., IEEE 30-bus test network, and IEEE 118-bus test system. Moreover, to validate the effectiveness of the proposed (AO-AOA), it is compared with a famous optimization technique as a competitor i.e., Teaching-learning-based optimization (TLBO), and recently published works on solving OPF problems. Furthermore, a robustness analysis was executed to determine the reliability of the AO-AOA solver. The obtained result confirms that not only the AO-AOA is efficient in optimization with significant convergence speed, but also denotes the dominance and potential of the AO-AOA in comparison with other works.

关键词： arithmetic optimization algorithm Aquila optimizer Map of piecewise linear Optimal power flow optimization

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Levy arithmetic algorithm: An enhanced metaheuristic algorithm and its application to engineering optimization

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 241卷

作者： Barua, Sujoy Merabet, Adel St Marys Univ Div Engn Halifax NS Canada St Marys Univ Div Engn 923 Robie St Halifax NS B3H 3C3 Canada

Levy arithmetic algorithm is an upgraded metaheuristic optimization approach proposed to enhance the arithmetic optimization algorithm using the Levy random step. arithmetic optimization algorithm addresses diverse optimization problems by employing arithmetic operators. However, its linear search capability might hinder attaining optimal solutions, which leads to stagnation. In this study, the Levy arithmetic algorithm is introduced by combining the arithmetic optimization algorithm and the Levy random step to enhance search capabilities and minimize computational demands for improved outcomes. The evaluation encompassed ten CEC2019 benchmark functions, four established real-world engineering problems, and the Economic Load Dispatch of microgrids with renewable energy integration. Using evaluation metrics such as standard deviation and mean, along with hypothesis tests, the study conducts a thorough comparison between the performance of the proposed algorithm and that of the conventional arithmetic optimization algorithm. The results show that the Levy arithmetic algorithm achieves optimization with a minimized number of evaluations in terms of standard deviation and mean, compared to the arithmetic optimization algorithm. Additionally, the proposed method was compared with various well-known and recent metaheuristics algorithms, and the Levy arithmetic algorithm consistently demonstrates superior performance, especially in contrast to the arithmetic optimization algorithm.

关键词： arithmetic optimization algorithm Levy arithmetic algorithm Metaheuristic algorithm CEC Benchmarks Engineering Problems Microgrid ELD

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Adaptive hybrid optimization algorithm for numerical computing in engineering applications

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ENGINEERING optimization 2025年第4期57卷 845-883页

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

A novel hybrid arithmetic optimization algorithm (HAOA) is proposed to address the inherent constraints of traditional numerical computing techniques, including increased computational complexity and excessive reliance on gradient information. First, the Latin hypercube sampling initialization strategy is used to generate higher quality initial candidate solutions. Then, the strategy is used to expand the advantages of leading individuals, boost the local search ability and improve the computational accuracy of the algorithm. Finally, the adaptive t-distribution mutation perturbation strategy is adopted to randomly perturb the position of the current optimal solution, aiming to prevent the algorithm from falling into a local optimal solution. The performance of HAOA is examined in comparison to alternative algorithms using the CEC 2022 data set and Bayesian validation is applied to comprehensively validate the superiority of the HAOA. Numerical experimental results demonstrate that HAOA achieves more accurate extremal and integral results, and has a high solution speed.

关键词： Numerical computing engineering problem arithmetic optimization algorithm Latin hypercube sampling optimal neighbourhood

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Software defect prediction using wrapper-based dynamic arithmetic optimization for feature selection

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CONNECTION SCIENCE 2025年第1期37卷

作者： Anand, Kunal Jena, Ajay Kumar Das, Himansu Askar, S. S. Abouhawwash, Mohamed KIIT Deemed Univ Sch Comp Engn Bhubaneswar 751024 Odisha India King Saud Univ Coll Sci Dept Stat & Operat Res Riyadh Saudi Arabia Michigan State Univ Dept Anim Sci E Lansing MI USA Mansoura Univ Fac Sci Dept Math Mansoura Egypt

Software Defect Prediction (SDP) empowers the creators to diagnose and unscramble defects in the introductory legs of the software evolution process to reduce the effort and cost invested in creating high-quality software. Feature Selection (FS) is critical to pinpoint the most pertinent features for defect prediction. This paper intends to employ a peculiar wrapper-based FS mode, dubbed DAOAFS, rooted on the dynamic arithmetic optimization algorithm (DAOA). Subsequently, this work evaluates the competence of the proposed FS mode using ten benchmark NASA datasets on four supervised learning classifiers, namely NB, DT, SVM, and KNN using accuracy and error curve as the standard performance measure metrics. This paper also correlates the proposed FS mode's conduct with existing FS techniques based on widely utilized meta-heuristic approaches such as GA, PSO, DE, ACO, FA, and SWO. This work employed Friedman and Holm test to ratify the proposed FS mode's statistical connotation. The investigatory outcomes supported the assertion that the recommended DAOAFS mode was effective in enhancing the efficacy of the defect forecasting model by achieving the highest mean accuracy of 94.76%. The findings also revealed that the proposed approach established its supremacy over the other studied FS techniques with bettered veracity in most instances.

关键词： Software defect prediction machine learning feature selection classification algorithm wrapper approach arithmetic optimization algorithm

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arithmetic optimization for Coinciding Diabetic Retinopathy and Diabetic Macular Edema Grading based on Self-Attention Convolutional Neural Network

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2024年第PartB期95卷

作者： Devi, T. M. Karthikeyan, P. Syed Ammal Engn Coll Dept Comp Sci & Engn Madurai Rameswaram Rd Landai Tamil Nadu India Thiagarajar Coll Engn Dept Informat Technol V3JJ VJ3 Thiruparankundram Tamil Nadu India

This paper proposes a Self-Attention Convolutional Neural Network (SACNN) optimized with arithmetic optimization algorithm (AOA) for coinciding Diabetic Retinopathy (DR) and Diabetic Macular Edema Grading (DMEG) (SACNN-AOA-DR-DMEG). Initially, the input image is collected from 2 openly available benchmark datasets, namely Messidor and ISBI 2018 IDRiD. Then the input image is pre-processing using Altered Phase Preserving Dynamic Range Compression (APPDRC) for reducing noise from the imageries. SACNN receives the pre-processed imageries. The SACNN has three modules: (i) plane attention module, (ii) depth attention module, (iii) Attention Fusion Module. DR and DME features are extracted by plane attention module and depth attention module of SACNN. Attention Fusion Module receives extracted characteristics for categorizing and grading DR and DME disorders. SACNN does not adopt any optimization techniques to guarantee accurate DR and DME grading disorders. That's why, arithmetic optimization algorithm (AOA) is deemed to optimize the SACNN weight parameters. The proposed technique is implemented in Python. The proposed SACNN-AOA-DR-DMEG method provides 11.18%, 18.99% and 23.76% higher accuracy for diabetic retinopathy grading;11.52%, 29.62% and 20.38% higher accuracy for DMEG;33.39%, 22%, 39.26% lower computation time on Messidor data compared with the existing methods, such as AMGNN-DR-DMEG, LCNN-DR-DMEG, and FFN-DR-DMEG respectively.

关键词： arithmetic optimization algorithm Messidor dataset Self -attention convolutional neural network

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Optimized FOPID controller for nuclear research reactor using enhanced planet optimization algorithm

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ALEXANDRIA ENGINEERING JOURNAL 2024年 97卷 267-282页

作者： Abdelfattah, Hany Aseeri, Ahmad O. Abd Elaziz, Mohamed Suez Univ Fac Technol & Educ Elect Dept Suez 41522 Egypt Prince Sattam Bin Abdulaziz Univ Coll Comp Engn & Sci Dept Comp Sci Al Kharj 11942 Saudi Arabia Zagazig Univ Fac Sci Dept Math Zagazig 44519 Egypt Galala Univ Fac Comp Sci & Engn Suze 435611 Egypt Ajman Univ Artificial Intelligence Res Ctr AIRC Ajman 346 U Arab Emirates Lebanese Amer Univ Dept Elect & Comp Engn Byblos 135053 Lebanon Middle East Univ MEU Res Unit Amman 11831 Jordan

Nuclear reactor control is pivotal for the safe and efficient operation of nuclear power plants, facilitating the regulation of reactor reactivity. This study introduces an optimized fractional-order proportional-integral-derivative (FOPID) controller tailored for maintaining reactivity levels in nuclear power plants, particularly during load-following operations. The controller adjusts the position of control rod to regulate power output effectively. We enhance FOPID controller's performance using a modification of Planet optimization algorithm (POA-M), leveraging the strengths of the arithmetic optimization algorithm (AOA) to improve its exploitation capabilities. We evaluate the efficacy of POA-M-FOPID controller against traditional techniques, including POA, AOA, and Particle Swarm optimization (PSO). We assess its performance using the Egyptian Testing Research Reactor (ETRR-2) as a case study. Our results demonstrate that the POA-M-FOPID controller outperforms alternative algorithms across various control metrics, exhibiting superior resilience and efficiency. Notably, the utilization of the POA-M-FOPID controller yields remarkable improvements in reactor power performance, achieving significantly reduced settling time (25.27 sec) and maximum overshoot (0.67 %) compared to conventional FOPID controllers incorporating POA, AOA, and PSO methods. These findings underscore the effectiveness of POA-MFOPID in enhancing nuclear reactor control systems, offering potential benefits for broader nuclear power industry in terms of safety, stability, and operational efficiency.

关键词： Planet optimization algorithm arithmetic optimization algorithm Particle swarm optimization algorithm fractional-order proportional-integral-deriva tive (FOPID) controller

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Evaluation of driven piles' load capacity by optimization-based prediction algorithms

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INTERNATIONAL JOURNAL OF INTERACTIVE DESIGN AND MANUFACTURING - IJIDEM 2025年第5期19卷 3277-3288页

作者： Xiao, Lili Du, Kun Xian FanYi Univ Coll Art & Design Xian 710105 Shaanxi Peoples R China China Northwest Architectural Design & Res Inst Co Xian 710018 Shaanxi Peoples R China

In geotechnical engineering, a variety of models-both theoretical and empirical-have been put forward to calculate the load capacity of deep footings. In the present instance, physical hypotheses and the construction of estimations utilizing mathematical concepts are the main driving forces behind the models. The research findings are directly applicable to geotechnical engineering practice. Engineers and practitioners involved in foundation design, construction, and evaluation can use the developed models to estimate the load capacity of driven piles more accurately. The load capacity of driven piles (Qt) using an experimental dataset has been estimated in the current essay using two-hybrid radial basis function (RBF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$RBF$$\end{document}) and multilayer perceptron (MLP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$MLP$$\end{document}) neural networks optimized with an arithmetic optimization algorithm (AOA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$AOA$$\end{document}). To ameliorate the modeling of the best network efficiency, the AOA method was used to identify the main components of each model (ARBF and AMLP). By raising the value of R2 from 0.9653 to 0.9931 for the train portion as well as from 0.9516 to 0.9884 for the test portion, with increases of around 2.78% as well as 3.68% each, the AMLP model outperforms the ARBF network among the two constructed systems. The comparis

关键词： Bearing capacity Driven piles Deep foundation Estimation Artificial neural network arithmetic optimization algorithm

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