caa a22 4500 605469423 CHVBK 20210128100322.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s00500-014-1279-8 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1279-8 Yong Wang School of Renewable Energy, North China Electric Power University, 102206, Beijing, China aut Hybrid Max-Min ant system with four vertices and three lines inequality for traveling salesman problem [Elektronische Daten] [Wang Yong] The objective of traveling salesman problem (TSP) is to find the optimal Hamiltonian circuit (OHC). It has been proven to be NP complete in most cases. The hybrid Max-Min ant system (MMA) integrated with a four vertices and three lines inequality is introduced to search the OHC. The four vertices and three lines inequality is taken as the constraints of the local optimal Hamiltonian paths (LOHP), including four vertices and three lines and all the LOHPs in the OHC conform to the inequality. At first, the MMA is used to search the approximate OHCs. Then, the local paths of adjacent four vertices in the approximate OHCs are converted into the LOHPs with the four vertices and three lines inequality to get the better approximation. The hybrid Max-Min ant system (HMMA) is tested with tens of TSP instances. The results show that the better approximations are computed with the HMMA than those with the MMA under the same preconditions. Springer-Verlag Berlin Heidelberg, 2014 Traveling salesman problem nationallicence Max-Min ant system nationallicence Four vertices and three lines inequality nationallicence Soft Computing Springer Berlin Heidelberg 19/3(2015-03-01), 585-596 1432-7643 19:3<585 2015 19 500 https://doi.org/10.1007/s00500-014-1279-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1279-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yong Wang School of Renewable Energy, North China Electric Power University, 102206, Beijing, China aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/3(2015-03-01), 585-596 1432-7643 19:3<585 2015 19 500