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Syst."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Multi-echelon location-routing problems (ME-LRPs) deal with determining the location of facilities and the routes of vehicles on multi-echelon routing tasks. Since the assignment relationship in multi-echelon routing tasks is uncertain and varying, ME-LRPs are very challenging to solve, especially when the number of the echelons increases. In this study, the ME-LRP is formulated as a hierarchical fuzzy graph, in which high-order fuzzy sets are constructed to represent the uncertain assignment relationship as different routing tasks and cross-task operators are used for routing task selection. Then, an evolutionary multi-tasking optimization algorithm is designed to simultaneously solve the multiple routing tasks. To alleviate negative transfer between the different routing tasks, multi-echelon assignment information is considered together with associated routing task selection in multi-tasking evolution optimization. The experimental results on multi-echelon routing benchmark problems demonstrate the competitiveness of the proposed method.<\/jats:p>","DOI":"10.1007\/s40747-023-01109-0","type":"journal-article","created":{"date-parts":[[2023,6,5]],"date-time":"2023-06-05T17:02:01Z","timestamp":1685984521000},"page":"6845-6862","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multi-task evolutionary optimization of multi-echelon location routing problems via a hierarchical fuzzy graph"],"prefix":"10.1007","volume":"9","author":[{"given":"Xueming","family":"Yan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1100-0631","authenticated-orcid":false,"given":"Yaochu","family":"Jin","sequence":"additional","affiliation":[]},{"given":"Xiaohua","family":"Ke","sequence":"additional","affiliation":[]},{"given":"Zhifeng","family":"Hao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,5]]},"reference":[{"issue":"1","key":"1109_CR1","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.ejor.2012.06.018","volume":"223","author":"J Ahn","year":"2012","unstructured":"Ahn J, De Weck O, Geng Y, Klabjan D (2012) Column generation based heuristics for a generalized location routing problem with profits arising in space exploration. 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