{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T05:01:22Z","timestamp":1764997282273,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,5]],"date-time":"2020-02-05T00:00:00Z","timestamp":1580860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Gansu Province Higher Education Research Project","award":["2019B-086"],"award-info":[{"award-number":["2019B-086"]}]},{"name":"National Nature Science Foundation of China","award":["61741201"],"award-info":[{"award-number":["61741201"]}]},{"name":"2019 General Planning Project of the 13th Five-Year Plan for Education Science in Gansu Province","award":["GS[2019]GHB2152"],"award-info":[{"award-number":["GS[2019]GHB2152"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This paper proposes an improved Harmony Search algorithm, and gives the definition of the Global Sharing Factor of the Harmony Search (HS) algorithm. In the definition, the number of creations of the HS algorithm is applied to the sharing factor and calculated. In this algorithm, the natural harmony encoding method is used to encode the initial harmony, and the total path length of all vehicles is taken as the optimization objective function. A new harmony generation strategy is proposed as follows: each tone component in an evolution is calculated separately using the new learning strategy and update strategy. In the calculation process, the tone component is judged by whether it needs to be adjusted according to the adjustment strategy. In this way, the problems of singularity and randomness of the new harmony generation strategy of basic HS are solved to improve the diversity of algorithm solutions. Then, a new Harmony Search method with Global Sharing Factor based on natural number coding and decoding for the Vehicle Routing Problem (GSF-HS-VRP) is proposed. The improved Global Sharing Factor-Harmony Search-Vehicle Routing Problem (GSF-HS-VRP) algorithm is applied to capacity-limited vehicle path optimization problems compared with the HS, Improved Harmony Search (IHS), Global-best Harmony Search (GHS), and Self-adaptive Global Best Harmony Search (SGHS) algorithms. The small-scale data and Solomon examples were adopted as the experimental data. Compared with the other four algorithms, the GSF-HS-VRP algorithm has the shortest running time, more rapid convergence speed, and higher efficiency. In the multi-vehicle test, with the increase of the number of vehicles, the optimized path of the vehicle is more satisfied in relation to the actual needs of customers. The results showed that this method could effectively improve the optimization performance of the capacity-limited vehicle routing problem.<\/jats:p>","DOI":"10.3390\/info11020086","type":"journal-article","created":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T02:59:18Z","timestamp":1580957958000},"page":"86","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Harmony Search Method with Global Sharing Factor Based on Natural Number Coding for Vehicle Routing Problem"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8103-2308","authenticated-orcid":false,"given":"Liqun","family":"Liu","sequence":"first","affiliation":[{"name":"College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiuyuan","family":"Huo","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongqiang","family":"Dai","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,5]]},"reference":[{"key":"ref_1","unstructured":"Yan, T. 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