{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T15:50:28Z","timestamp":1766159428313,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T00:00:00Z","timestamp":1717545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61502239","BK20150924"],"award-info":[{"award-number":["61502239","BK20150924"]}]},{"name":"Natural Science Foundation of Jiangsu","award":["61502239","BK20150924"],"award-info":[{"award-number":["61502239","BK20150924"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price and testing capacity of various agencies and introduces a cross-depot collaborative transport method. Both the cost and the testing time are minimized by determining the optimal sampling routes and testing agencies, subjecting to the constraints of vehicle capacity, number of vehicles, and delivery time. To solve the model, a knowledge-guided multi-objective shuffled frog leaping algorithm (KMOSFLA) is proposed. KMOSFLA adopts a convertible encoding mechanism to realize the diversified search in different search spaces. Three novel strategies are designed: the population initialization with historical information reuse, the leaping rule based on the greedy crossover and genetic recombination, and the objective-driven enhanced search. Systematic experimental studies are implemented. First, feasibility analyses of the model are carried out, where effectiveness of the cross-depot collaborative transport is validated and sensitivity analyses on two parameters (vehicle capacity and proportion of the third-party testing agencies) are performed. Then, the proposed algorithm KMOSFLA is compared with five state-of-the-art algorithms. Experimental results indicate that KMOSFLA can provide a set of non-dominated schedules with lower cost and shorter testing time in each scheduling period, which provides a reference for the dispatcher to make a final decision.<\/jats:p>","DOI":"10.3390\/sym16060697","type":"journal-article","created":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T05:59:42Z","timestamp":1717567182000},"page":"697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Knowledge-Guided Multi-Objective Shuffled Frog Leaping Algorithm for Dynamic Multi-Depot Multi-Trip Vehicle Routing Problem"],"prefix":"10.3390","volume":"16","author":[{"given":"Yun","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoning","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"},{"name":"Jiangsu Key Laboratory of Big Data Analysis Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China"},{"name":"Jiangsu Engineering Research Center on Meteorological Energy Using and Control (C-MEIC), Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongpei","family":"Ge","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102542","DOI":"10.1016\/j.tre.2021.102542","article-title":"A multi-echelon dynamic cold chain for managing vaccine distribution","volume":"156","author":"Manupati","year":"2021","journal-title":"Transp. 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