{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T08:24:34Z","timestamp":1774945474109,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,25]],"date-time":"2018-12-25T00:00:00Z","timestamp":1545696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51507084,61363037"],"award-info":[{"award-number":["51507084,61363037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Grid Company Research Project","award":["5455HJ160005"],"award-info":[{"award-number":["5455HJ160005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>The traveling-salesman problem can be regarded as an NP-hard problem. To better solve the best solution, many heuristic algorithms, such as simulated annealing, ant-colony optimization, tabu search, and genetic algorithm, were used. However, these algorithms either are easy to fall into local optimization or have low or poor convergence performance. This paper proposes a new algorithm based on simulated annealing and gene-expression programming to better solve the problem. In the algorithm, we use simulated annealing to increase the diversity of the Gene Expression Programming (GEP) population and improve the ability of global search. The comparative experiments results, using six benchmark instances, show that the proposed algorithm outperforms other well-known heuristic algorithms in terms of the best solution, the worst solution, the running time of the algorithm, the rate of difference between the best solution and the known optimal solution, and the convergent speed of algorithms.<\/jats:p>","DOI":"10.3390\/info10010007","type":"journal-article","created":{"date-parts":[[2018,12,26]],"date-time":"2018-12-26T04:29:54Z","timestamp":1545798594000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":56,"title":["Traveling-Salesman-Problem Algorithm Based on Simulated Annealing and Gene-Expression Programming"],"prefix":"10.3390","volume":"10","author":[{"given":"Ai-Hua","family":"Zhou","sequence":"first","affiliation":[{"name":"Global Energy Interconnection Research Institute Co., Ltd., Beijing 102200, China"},{"name":"Power Systems Artificial Intelligence Joint Laboratory of SGCC, Beijing 102200, China"}]},{"given":"Li-Peng","family":"Zhu","sequence":"additional","affiliation":[{"name":"Global Energy Interconnection Research Institute Co., Ltd., Beijing 102200, China"},{"name":"Power Systems Artificial Intelligence Joint Laboratory of SGCC, Beijing 102200, China"}]},{"given":"Bin","family":"Hu","sequence":"additional","affiliation":[{"name":"Global Energy Interconnection Research Institute Co., Ltd., Beijing 102200, China"},{"name":"Power Systems Artificial Intelligence Joint Laboratory of SGCC, Beijing 102200, China"}]},{"given":"Song","family":"Deng","sequence":"additional","affiliation":[{"name":"Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 230001, China"}]},{"given":"Yan","family":"Song","sequence":"additional","affiliation":[{"name":"Electric Power Research Institute of State Grid Shanghai Municipal Electric Power Company, Shanghai 200437, China"}]},{"given":"Hongbin","family":"Qiu","sequence":"additional","affiliation":[{"name":"Global Energy Interconnection Research Institute Co., Ltd., Beijing 102200, China"},{"name":"Power Systems Artificial Intelligence Joint Laboratory of SGCC, Beijing 102200, China"}]},{"given":"Sen","family":"Pan","sequence":"additional","affiliation":[{"name":"Global Energy Interconnection Research Institute Co., Ltd., Beijing 102200, China"},{"name":"Power Systems Artificial Intelligence Joint Laboratory of SGCC, Beijing 102200, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,25]]},"reference":[{"key":"ref_1","first-page":"135","article-title":"Application of Ant Colony Algorithm to Power Cable Patrol Route Planning","volume":"5","author":"Xu","year":"2015","journal-title":"Comput. Syst. Appl."},{"key":"ref_2","first-page":"78","article-title":"Intelligent patrolling robot addressing program based on graph method","volume":"9","author":"Wang","year":"2007","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.socnet.2006.08.002","article-title":"An introduction to exponential random graph (p*) models for social networks","volume":"29","author":"Robins","year":"2007","journal-title":"Soc. Netw."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Soussi, R., Aufaure, M.-A., and Baazaoui, H. (2010, January 2\u20136). Towards social network extraction using a graph database. Proceedings of the 2010 Second International Conference on Advances in Databases Knowledge and Data Applications (DBKDA), Menuires, France.","DOI":"10.1109\/DBKDA.2010.19"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Cattuto, C., Quaggiotto, M., Panisson, A., and Averbuch, A. (2013, January 22\u201327). Time-varying social networks in a graph database: A Neo4j use case. Proceedings of the First International Workshop on Graph Data Management Experiences and Systems, New York, NY, USA.","DOI":"10.1145\/2484425.2484442"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1145\/290179.290180","article-title":"Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems","volume":"45","author":"Arora","year":"1998","journal-title":"J. ACM"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cook, W., Espinoza, D., and Goycoolea, M. (2007). Computing with Domino-Parity Inequalities for the TSP, Georgia Institute of Technology, Industrial and Systems Engineering.","DOI":"10.1287\/ijoc.1060.0204"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1155\/2016\/1712630","article-title":"List-based simulated annealing algorithm for traveling salesman problem","volume":"2016","author":"Zhan","year":"2016","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.asoc.2016.08.036","article-title":"Developing a dynamic neighborhood structure for an adaptive hybrid simulated annealing\u2013tabu search algorithm to solve the symmetrical traveling salesman problem","volume":"49","author":"Lin","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.eswa.2017.01.053","article-title":"Simulated annealing based symbiotic organisms search optimization algorithm for traveling salesman problem","volume":"77","author":"Ezugwu","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.ifacol.2015.08.109","article-title":"A modified simulated annealing algorithm for SUAVs path planning","volume":"48","author":"Behnck","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1166\/jctn.2015.3868","article-title":"Simulated annealing with a hybrid local search for solving the traveling salesman problem","volume":"12","author":"Zhao","year":"2015","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_13","first-page":"523","article-title":"An investigation of hybrid tabu search for the traveling salesman problem","volume":"562","author":"Xu","year":"2015","journal-title":"Bio-Inspired Comput. Theor. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.dam.2012.06.002","article-title":"An ILP-refined tabu search for the directed profitable rural postman problem","volume":"163","author":"Archetti","year":"2014","journal-title":"Discret. Appl. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1007\/s00500-013-1203-7","article-title":"A quantum-inspired Tabu search algorithm for solving combinatorial optimization problems","volume":"18","author":"Chiang","year":"2014","journal-title":"Soft Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Min, H., Dazhi, P., and Song, Y. (2014, January 20\u201321). An improved hybrid ant colony algorithm and its application in solving TSP. Proceedings of the 2014 IEEE 7th Joint International Information Technology and Artificial Intelligence Conference (ITAIC), Chongqing, China.","DOI":"10.1109\/ITAIC.2014.7065084"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2016\/8932896","article-title":"Annealing ant colony optimization with mutation operator for solving tsp","volume":"2016","author":"Mohsen","year":"2016","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1534","DOI":"10.1080\/13658816.2015.1013960","article-title":"An improved ant colony optimization (I-ACO) method for the quasi travelling salesman problem (Quasi-TSP)","volume":"29","author":"Yang","year":"2015","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1515\/jaiscr-2015-0032","article-title":"Optimization of traveling salesman problem using affinity propagation clustering and genetic algorithm","volume":"5","author":"Ashour","year":"2015","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"key":"ref_20","first-page":"27","article-title":"Solving travelling salesman problem using genetic algorithm based on heuristic crossover and mutation operator","volume":"3","author":"Rani","year":"2014","journal-title":"Int. J. Res. Eng. Technol."},{"key":"ref_21","first-page":"1","article-title":"An improved genetic algorithm with initial population strategy for symmetric TSP","volume":"2015","author":"Deng","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.cie.2014.01.015","article-title":"The hybrid genetic algorithm with two local optimization strategies for traveling salesman problem","volume":"70","author":"Wang","year":"2014","journal-title":"Comput. Ind. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.asoc.2016.02.021","article-title":"Multi-offspring genetic algorithm and its application to the traveling salesman problem","volume":"43","author":"Wang","year":"2016","journal-title":"App. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.swevo.2013.11.001","article-title":"An efficient genetic algorithm for multi-objective solid travelling salesman problem under fuzziness","volume":"15","author":"Changdar","year":"2014","journal-title":"Swarm Evol. Comput."},{"key":"ref_25","first-page":"28","article-title":"A Performance Comparison of GA and ACO Applied to TSP","volume":"117","author":"Haroun","year":"2015","journal-title":"Int. J. Comput. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ferreira, C. (2002). Gene Expression Programming in problem Solving, Springer.","DOI":"10.1007\/978-1-4471-0123-9_54"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ferreira, C. (2006). Automatically Defined Functions in Gene Expression Programming, Springer.","DOI":"10.1007\/3-540-32498-4_2"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1142\/S0219525902000626","article-title":"Genetic representation and genetic neutrality in gene expression programming","volume":"5","author":"Ferreira","year":"2002","journal-title":"Adv. Complex Syst."},{"key":"ref_29","unstructured":"Ferreira, C. (2006). Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence, Springer."},{"key":"ref_30","first-page":"396","article-title":"Gene Expression Programming Based on Diversified Development Strategy","volume":"28","author":"Wu","year":"2010","journal-title":"J. Jilin Univ. Inf. Sci. Ed."},{"key":"ref_31","first-page":"7","article-title":"Knowledge discovery based on Gene Expression Programming-History, achievements and future directions","volume":"10","author":"Tang","year":"2004","journal-title":"Comput. Appl."},{"key":"ref_32","unstructured":"Ferreira, C. (2002). Combinatorial Optimization by Gene Expression Programming: Inversion Revisited, Springer."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1109\/TCYB.2014.2323936","article-title":"A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems","volume":"45","author":"Sabar","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Van Laarhoven, P.J.M., and Aarts, E.H.L. (1987). Simulated Annealing, Springer.","DOI":"10.1007\/978-94-015-7744-1_2"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1287\/ijoc.3.4.376","article-title":"TSPLIB-A traveling salesman problem library","volume":"3","author":"Reinelt","year":"1991","journal-title":"ORSA J. Comput."},{"key":"ref_37","unstructured":"(2018, November 21). Discrete and Combinatorial Optimization\u2014IWR, Heidelberg. Available online: http:\/\/comopt.ifi.uni-heidelberg.de\/software\/TSPLIB95\/tsp\/."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:36:05Z","timestamp":1760196965000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,25]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["info10010007"],"URL":"https:\/\/doi.org\/10.3390\/info10010007","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,25]]}}}