{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T16:55:48Z","timestamp":1783184148763,"version":"3.54.6"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T00:00:00Z","timestamp":1670976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The gravitational search algorithm is a global optimization algorithm that has the advantages of a swarm intelligence algorithm. Compared with traditional algorithms, the performance in terms of global search and convergence is relatively good, but the solution is not always accurate, and the algorithm has difficulty jumping out of locally optimal solutions. In view of these shortcomings, an improved gravitational search algorithm based on an adaptive strategy is proposed. The algorithm uses the adaptive strategy to improve the updating methods for the distance between particles, gravitational constant, and position in the gravitational search model. This strengthens the information interaction between particles in the group and improves the exploration and exploitation capacity of the algorithm. In this paper, 13 classical single-peak and multi-peak test functions were selected for simulation performance tests, and the CEC2017 benchmark function was used for a comparison test. The test results show that the improved gravitational search algorithm can address the tendency of the original algorithm to fall into local extrema and significantly improve both the solution accuracy and the ability to find the globally optimal solution.<\/jats:p>","DOI":"10.3390\/e24121826","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T01:52:30Z","timestamp":1671069150000},"page":"1826","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Improved Gravitational Search Algorithm Based on Adaptive Strategies"],"prefix":"10.3390","volume":"24","author":[{"given":"Zhonghua","family":"Yang","sequence":"first","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"},{"name":"Faculty of Electronics & Information, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7364-3101","authenticated-orcid":false,"given":"Yuanli","family":"Cai","sequence":"additional","affiliation":[{"name":"Faculty of Electronics & Information, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ge","family":"Li","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1007\/s11633-016-1019-x","article-title":"An intelligent multi-robot path planning in a dynamic environment using improved gravitational search algorithm","volume":"18","author":"Das","year":"2021","journal-title":"Int. J. Autom. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"57033","DOI":"10.1109\/ACCESS.2021.3072796","article-title":"Path planning for unmanned aerial vehicle using a Mix-strategy-based gravitational search algorithm","volume":"9","author":"Xu","year":"2021","journal-title":"IEEE Access."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"10590","DOI":"10.1007\/s11227-021-03706-7","article-title":"An adaptive gravitational search algorithm for multilevel image thresholding","volume":"77","author":"Wang","year":"2021","journal-title":"J. Supercomput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4983","DOI":"10.1007\/s12652-020-01777-7","article-title":"A fuzzy adaptive gravitational search algorithm for two-dimensional multilevel thresholding image segmentation","volume":"11","author":"Tan","year":"2020","journal-title":"J. Ambient Intell. Hum. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1080\/02564602.2020.1825125","article-title":"An automatic facial expression recognition system employing convolutional neural network with multi-strategy gravitational search algorithm","volume":"39","author":"Alenazy","year":"2022","journal-title":"IETE Tech. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.1007\/s00521-020-05131-y","article-title":"Memetic algorithms for training feedforward neural networks: An approach based on gravitational search algorithm","volume":"33","author":"Linares","year":"2021","journal-title":"Neural. Comput. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2636515","DOI":"10.1155\/2022\/2636515","article-title":"Training a feedforward neural network using hybrid gravitational search algorithm with dynamic multiswarm particle swarm optimization","volume":"2022","author":"Nagra","year":"2022","journal-title":"BioMed Res. Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1734","DOI":"10.1002\/oca.2757","article-title":"A nonlinear model predictive controller based on the gravitational search A nonlinear model predictive controller based on the gravitational search algorithm","volume":"42","author":"Nobahari","year":"2021","journal-title":"Optim. Control Appl. Meth."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6959","DOI":"10.2166\/ws.2022.263","article-title":"A seasonal Arima model based on the gravitational search algorithm (GSA) for runoff prediction","volume":"22","author":"Zhang","year":"2022","journal-title":"Water Supply"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"e6901","DOI":"10.1002\/cpe.6901","article-title":"Gravitational search algorithm-driven missing links prediction in social networks","volume":"34","author":"Singh","year":"2022","journal-title":"Concurr. Computat. Pract. Experience"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1016\/j.asej.2020.10.021","article-title":"A memory-based gravitational search algorithm for solving economic dispatch problem in micro-grid","volume":"12","author":"Younes","year":"2021","journal-title":"Ain. Shams Eng. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5592","DOI":"10.1080\/00207543.2020.1788732","article-title":"An improved gravitational search algorithm to the hybrid flowshop with unrelated parallel machines scheduling problem","volume":"59","author":"Cao","year":"2021","journal-title":"Int. J. Prod. Res."},{"key":"ref_13","first-page":"475","article-title":"An Intelligent Traffic Light Scheduling Algorithm by using fuzzy logic and gravitational search algorithm and considering emergency vehicles","volume":"11","author":"Habibi","year":"2021","journal-title":"Int. J. Nonlinear Anal. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1007\/s11227-020-03292-0","article-title":"Binary quantum-inspired gravitational search algorithm-based multi-criteria scheduling for multi-processor computing systems","volume":"77","author":"Thakur","year":"2021","journal-title":"J. Supercomput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"He, J.F., Wang, T., Li, Y.J., Deng, Y.L., and Wang, S.B. (2022). Dynamic chaotic gravitational search algorithm-based kinetic parameter estimation of hepatocellular carcinoma on F-18-FDG PET\/CT. BMC Med. Imaging, 22.","DOI":"10.1186\/s12880-022-00742-4"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s11144-021-01927-8","article-title":"Gravitational search algorithm for determining the optimal kinetic parameters of propane pre-reforming reaction","volume":"132","author":"Enikeeva","year":"2021","journal-title":"React. Kinet. Mech. Cat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.biosystems.2017.09.013","article-title":"An improved hybrid of particle swarm optimization and the gravitational search algorithm to produce a kinetic parameter estimation of aspartate biochemical pathways","volume":"162","author":"Ismail","year":"2017","journal-title":"Biosystems"},{"key":"ref_18","unstructured":"Zhenkai, X. (2014). Modification and Application of Gravitational Search Algorithm. [Master\u2019s Thesis, University of Shanghai for Science & Technology]."},{"key":"ref_19","unstructured":"Yuhao, X. (2018). The Improvement and Application of Gravitational Search Algorithm. [Master\u2019s Thesis, Henan University]."},{"key":"ref_20","first-page":"1528","article-title":"Research and simulation of the gravitational search algorithms with immunity","volume":"33","author":"Jing","year":"2012","journal-title":"Acta Armamentarii"},{"key":"ref_21","first-page":"193","article-title":"Application of improved gravitational search algorithm in function optimization","volume":"43","author":"Xiaogang","year":"2021","journal-title":"J. Shenyang Univ. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1109\/JSEE.2013.00080","article-title":"Improved gravitational search algorithm based on free search differential evolution","volume":"24","author":"Liu","year":"2013","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"11739","DOI":"10.1007\/s00521-021-05880-4","article-title":"A hybrid sperm swarm optimization and gravitational search algorithm (HSSOGSA) for global optimization","volume":"33","author":"Shehadeh","year":"2021","journal-title":"Neural. Comput. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huang, Y., Wang, J.R., and Guo, F. (2015, January 28\u201330). Economic load dispatch using improved gravitational search algorithm. Proceedings of the 2016 2nd ISPRS International Conference on Computer Vision in Remote Sensing (CVRS), Xiamen, China.","DOI":"10.1117\/12.2234725"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, R.P., Su, F., Hao, T.G., and Li, J.L. (2018, January 22\u201323). RGSA: A new improved gravitational search algorithm. Proceedings of the 2016 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM), Shanghai, China.","DOI":"10.2991\/msam-18.2018.43"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1515\/comp-2020-0223","article-title":"L\u00e9vy flight and chaos theory-based gravitational search algorithm for mechanical and structural engineering design optimization","volume":"11","author":"Rather","year":"2021","journal-title":"Open Comput. Sci."},{"key":"ref_27","first-page":"60","article-title":"Improvement of universal gravitation search algorithm based on reverse evaluation mechanism","volume":"35","author":"Chen","year":"2016","journal-title":"J. Wuhan Polytech. Univ."},{"key":"ref_28","unstructured":"Teng, F. (2016). Research on Improved Artificial Fish Swarm Algorithm and Its Application in Logistics Location Optimization. [Ph.D. Thesis, Tianjin University]."},{"key":"ref_29","first-page":"188","article-title":"Enhanced version of gravitational search algorithm: Weighted GSA","volume":"47","author":"Xu","year":"2011","journal-title":"Comput. Eng. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1826\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:41:20Z","timestamp":1760146880000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1826"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,14]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121826"],"URL":"https:\/\/doi.org\/10.3390\/e24121826","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,14]]}}}