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بهینهسازی گرگ خاکستری با قیود نامعین برای حل غیر محدب مسائل مهندسی | ||
| مدل سازی در مهندسی | ||
| دوره 23، شماره 83، دی 1404، صفحه 145-155 اصل مقاله (686.13 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22075/jme.2025.34751.2704 | ||
| نویسندگان | ||
| سمیه ابراهیم زاده1؛ سید کاظم علوی پناه* 1؛ سارا عطارچی1؛ وحید محبوب2 | ||
| 1گروه سنجش از دور و سیستم اطلاعات جغرافیایی، دانشکدة جغرافیا، دانشگاه تهران، تهران، ایران | ||
| 2گروه مهندسی نقشهبرداری، دانشکده مهندسی، دانشگاه گلستان، علی آباد کتول، ایران | ||
| تاریخ دریافت: 25 تیر 1403، تاریخ بازنگری: 24 اسفند 1403، تاریخ پذیرش: 17 فروردین 1404 | ||
| چکیده | ||
| در این مقاله یک روش فراابتکاری بهبود یافته برای حل یک نوع از چالش برانگیزترین مسائل غیرخطی موسوم به مسائل غیرمحدب پیشنهاد شده است. در این نوع از مسائل، ما با بیش از یک کمینه روبرو هستیم که همهی آنها منجر به جواب صحیح نمیشوند. این روش مبتنی بر تجهیز الگوریتم فراابتکاری گرگ خاکستری با قیود نامعین براساس روش دیپیلو و گریپو است. اگرچه اشکال مختلفی از الگوریتم گرگ خاکستری در چند سال اخیر ارائه شدهاند، هیچ یک از آنها قیود نامعین را به شکلی که در اینجا ارائه میشود، در نظر نمیگیرند. مزیت اصلی الگوریتم پیشنهادی در کاربردهای مهندسی، حل مسائل بهینهسازی غیرمحدب است که در آن روشهای تحلیلی ممکن است در کمینه محلی گیر کنند، در حالی که الگوریتم مذکور در کمینهی جهانی به جواب میرسد. ضمنا در مقایسهی با برخی روشهای فرابتکاری شناخته شده، الگوریتم مذکور به تکرار کمتری نیاز دارد. با چهار تابع آزمون ریاضی و یک مثال ژئودتیکی، کارایی روش پیشنهادی ارزیابی میشود. | ||
| کلیدواژهها | ||
| مسئلهی غیر محدب؛ قیود نامعین؛ بهینه سازی؛ الگوریتم گرگ خاکستری | ||
| عنوان مقاله [English] | ||
| Grey Wolf Optimization with Inequality Constraints for Non-Convex Optimization with Application to Engineering Science | ||
| نویسندگان [English] | ||
| Somayeh Ebrahimzadeh1؛ Seyed Kazem َAlavipanah1؛ Sara Attarchi1؛ Vahid Mahboub2 | ||
| 1Department of Remote Sensing and GIS, Faculty of Geography, University of Tehran, Tehran, Iran | ||
| 2Department of Surveying Engineering, Faculty of Engineering, Golestan University, Aliabad Katoul, Iran | ||
| چکیده [English] | ||
| Here, an improved meta-heuristic method is proposed to solve one of the most challenging nonlinear problems known as non-convex problems. In this type of problem, we are faced with more than one minimum, all of which do not lead to the correct solution. This method is based on equipping the grey wolf meta-heuristic algorithm with inequality constraints. Although various forms of the grey wolf algorithm have been proposed in the last few years, none of them included inequality constraints, especially in the form presented here. The main advantage of the proposed algorithm in engineering applications is solving non-convex optimization problems where analytical methods may get stuck in a local minimum, while the aforementioned algorithm is located in a global minimum. With two mathematical test functions and one geodetic example, the efficiency of the proposed approach is evaluated. | ||
| کلیدواژهها [English] | ||
| Non-convex problem, Optimization, Inequality constraints, Grey wolf algorithm | ||
| مراجع | ||
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[1] Mahboub, Vahid. "L1-norm optimization of problems with arbitrary column rank by Whale method and its improved algorithm for outlier detection." Earth Science Informatics (2024): 1-11. [2] Bonabeau, Eric, Marco Dorigo, and Guy Theraulaz. Swarm Intelligence: from Natural to Artificial Systems. Oxford University Press, 1999. [3] Dorigo, Marco, Mauro Birattari, and Thomas Stutzle. "Ant colony optimization." IEEE Computational Intelligence Magazine 1, no. 4 (2006): 28-39. [4] Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis. "Grey wolf optimizer." Advances in Engineering Software 69 (2014): 46-61. [5] Deb, Kalyanmoy, and Soumil Srivastava. "A genetic algorithm based augmented Lagrangian method for constrained optimization." Computational Optimization and Applications 53 (2012): 869-902. [6] Long, Wen, Ximing Liang, Yafei Huang, and Yixiong Chen. "An effective hybrid cuckoo search algorithm for constrained global optimization." Neural Computing and Applications 25 (2014): 911-926. [7] Brajevic, Ivona. "Crossover-based artificial bee colony algorithm for constrained optimization problems." Neural Computing and Applications 26 (2015): 1587-1601. [8] Niu, Ben, Jingwen Wang, and Hong Wang. "Bacterial-inspired algorithms for solving constrained optimization problems." Neurocomputing 148 (2015): 54-62. [9] Mahboub, Vahid. "A direct approach for L1-norm minimisation." Survey Review (2023): 1-5. [10] Mahboub, V., S. Ebrahimzadeh, A. Baghani, A. Rastegar, and M. Zanganeh. "L1-norm optimisation of rank deficient GNSS networks by an improved Grey Wolf method." Survey Review 56, no. 399 (2024): 582-588. [11] Mahboub, Vahid. "A modified grey wolf algorithm with applications to engineering." Journal of Modeling in Engineering 22, no. 76 (2024): 189-195. [12] Boyd, Stephen, and Lieven Vandenberghe. Convex optimization. Cambridge University Press, 2004. [13] Mahboub, Vahid, and Mohammad Ali Sharifi. "On weighted total least-squares with linear and quadratic constraints." Journal of geodesy 87 (2013a): 279-286. [14] Mahboub, Vahid, and Mohammad Ali Sharifi. "Erratum to: On weighted total least-squares with linear and quadratic constraints." Journal of Geodesy 87 (2013b): 607-608. [15] Overton, Michael L. "Large-scale optimization of eigenvalues." SIAM Journal on Optimization 2, no. 1 (1992): 88-120. [16] Jarre, Florian. "Some aspects of nonlinear semidefinite programming." In System Modeling and Optimization XX: IFIP TC7 20 th Conference on System Modeling and Optimization July 23–27, 2001, Trier, Germany 20, pp. 55-69. Springer US, 2003. [17] Arrow, Kenneth Joseph, Leonid Hurwicz, Hirofumi Uzawa, Hollis Burnley Chenery, Selmer Johnson, and Samuel Karlin. Studies in Linear and Non-Linear Programming. Vol. 2. Stanford: Stanford University Press, 1958. [18] Mosheyev, Leonid, and Michael Zibulevsky. Penalty/Barrier Multiplier Algorithm for Semidefinite Programming: Dual Bounds and Implementation. Research Report 1, Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa, Israel, 1996. [19] Kočvara, Michal, and Michael Stingl. "On the solution of large-scale SDP problems by the modified barrier method using iterative solvers." Mathematical Programming 109 (2007): 413-444. [20] Di Pillo, Gianni, and Luigi Grippo. "A new augmented Lagrangian function for inequality constraints in nonlinear programming problems." Journal of Optimization Theory and Applications 36 (1982): 495-519. [21] Metropolis, Nicholas, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. "Equation of state calculations by fast computing machines." The journal of chemical physics 21, no. 6 (1953): 1087-1092. [22] Surjanovic, Sonja, and Derek Bingham. "Virtual library of simulation experiments: test functions and datasets." Simon Fraser University, Burnaby, BC, Canada, Accessed May 13 (2013): 2015. [23] Mahboub, Vahid, Mohammad Saadatseresht, and Alireza A. Ardalan. "A solution to dynamic errors-in-variables within system equations." Acta Geodaetica et Geophysica 53 (2018): 31-44. [24] Mahboub, Vahid, Mohammad Saadatseresht, and Alireza A. Ardalan. "On constrained integrated total Kalman filter for integrated direct geo-referencing." Survey Review 51, no. 364 (2019): 26-34. [25] Mahboub, Vahid, and Somayeh Ebrahimzadeh. "Non-linear block least-squares adjustment for a large number of observations." Survey Review 54, no. 387 (2022): 479-489. [26] Hwang, Cheinway, Cheng-Gi Wang, and Li-Hua Lee. "Adjustment of relative gravity measurements using weighted and datum-free constraints." Computers & Geosciences 28, no. 9 (2002): 1005-1015. | ||
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