{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:23Z","timestamp":1760243243995,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2014,5,13]],"date-time":"2014-05-13T00:00:00Z","timestamp":1399939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The imperialist competitive algorithm (ICA) is a new heuristic algorithm proposed for continuous optimization problems. The research about its application on solving the traveling salesman problem (TSP) is still very limited. Aiming to explore its ability on solving TSP, we present a discrete imperialist competitive algorithm in this paper. The proposed algorithm modifies the original rules of the assimilation and introduces the 2-opt algorithm into the revolution process. To examine its performance, we tested the proposed algorithm on 10 small-scale and 2 large-scale standard benchmark instances from the TSPLIB and compared the experimental results with that obtained by two other ICA-based algorithms and six other existing algorithms. The proposed algorithm shows excellent performance in the experiments and comparisons.<\/jats:p>","DOI":"10.3390\/a7020229","type":"journal-article","created":{"date-parts":[[2014,5,13]],"date-time":"2014-05-13T11:44:55Z","timestamp":1399981495000},"page":"229-242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Application of Imperialist Competitive Algorithm on Solving the Traveling Salesman Problem"],"prefix":"10.3390","volume":"7","author":[{"given":"Shuhui","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Shandong University), Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Shandong University), Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiqin","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Shandong University), Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,5,13]]},"reference":[{"key":"ref_1","unstructured":"Hoffman, K.L., Padberg, M., and Rinaldi, G. 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