{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T03:57:31Z","timestamp":1779163051478,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T00:00:00Z","timestamp":1633996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Ant Colony Optimization (ACO) is a probabilistic technique inspired by the behavior of ants for solving computational problems that may be reduced to finding the best path through a graph. Some species of ants deposit pheromone on the ground to mark some favorable paths that should be used by other members of the colony. Ant colony optimization implements a similar mechanism for solving optimization problems. In this paper a warm-up procedure for the ACO is proposed. During the warm-up, the pheromone matrix is initialized to provide an efficient new starting point for the algorithm, so that it can obtain the same (or better) results with fewer iterations. The warm-up is based exclusively on the graph, which, in most applications, is given and does not need to be recalculated every time before executing the algorithm. In this way, it can be made only once, and it speeds up the algorithm every time it is used from then on. The proposed solution is validated on a set of traveling salesman problem instances, and in the simulation of a real industrial application for the routing of pickers in a manual warehouse. During the validation, it is compared with other ACO adopting a pheromone initialization technique, and the results show that, in most cases, the adoption of the proposed warm-up allows the ACO to obtain the same or better results with fewer iterations.<\/jats:p>","DOI":"10.3390\/a14100295","type":"journal-article","created":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T08:09:32Z","timestamp":1634026172000},"page":"295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Ant Colony Optimization with Warm-Up"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4507-4789","authenticated-orcid":false,"given":"Mattia","family":"Neroni","sequence":"first","affiliation":[{"name":"Department of Engineering and Architecture, University of Parma, 43124 Parma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/3477.484436","article-title":"Ant system: Optimization by a colony of cooperating agents","volume":"26","author":"Dorigo","year":"1996","journal-title":"IEEE Trans. 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