{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T06:21:33Z","timestamp":1788848493960,"version":"build-2803163510"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Land, Infrastructure, and Transport","award":["RS-2021-KA163182"],"award-info":[{"award-number":["RS-2021-KA163182"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>The vehicle routing problem (VRP) attempts to find optimal (minimum length) routes for a set of vehicles visiting a set of locations. Solving a VRP calls for a cost matrix between locations. The size of the matrix grows quadratically with an increasing number of locations, restricting large-sized VRPs from being solved in a reasonable amount of time. The time needed to obtain a cost matrix is expensive when routing engines are used, which solve shortest path problems in the back end. In fact, details on the shortest path are redundant; only distance or time values are necessary for VRPs. In this study, an artificial neural network (ANN) that receives two geo-coordinates as input and provides estimated cost (distance and time) as output is trained. The trained ANN model was able to estimate with a mean absolute percentage error of 7.68%, surpassing the quality of 13.2% with a simple regression model on Euclidean distance. The possibility of using a trained model in VRPs is examined with different implementation scenarios. The experimental results with VRPs confirm that using ANN estimation instead of Euclidean distance produces a better solution, which is verified to be statistically significant. The results also suggest that an ANN can be a better choice than routing engines when the trade-off between response time and solution quality is considered.<\/jats:p>","DOI":"10.3390\/ijgi12020057","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T02:32:07Z","timestamp":1675909927000},"page":"57","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Estimation of Travel Cost between Geographic Coordinates Using Artificial Neural Network: Potential Application in Vehicle Routing Problems"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9504-369X","authenticated-orcid":false,"given":"Keyju","family":"Lee","sequence":"first","affiliation":[{"name":"School of Air Transport, Transportation and Logistics, Korea Aerospace University, Goyang 10540, Gyeonggi-do, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2657-047X","authenticated-orcid":false,"given":"Junjae","family":"Chae","sequence":"additional","affiliation":[{"name":"School of Air Transport, Transportation and Logistics, Korea Aerospace University, Goyang 10540, Gyeonggi-do, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Toth, P., and Vigo, D. 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