Geodesic
Solving the P-Second Center Problem with Variable Neighborhood Search
Computer Science and Information Systems, Tome 20 (2023) no. 1.

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The p-center problem is a well-known and highly studied problem pertaining to the identification of p of the potential n center locations in such a way as to minimize the maximum distance between the users and the closest center. As opposed to the p-center, the p-second center problem minimizes the maximum sum of the distances from the users to the closest and the second closest centers. In this paper, we propose a new Variable Neighborhood Search based algorithm for solving the p-second center problem. Its performance is assessed on the benchmark instances from the literature. Moreover, to further evaluate the algorithm’s performance, we generated larger instances with 1000, 1500, 2000, and 2500 nodes and instances defined over graphs up to 1000 nodes with different densities. The obtained results clearly demonstrate the effectiveness and efficiency of the proposed algorithm.
Keywords: variable neighborhood method, heuristic algorithms, p-second center problem, combinatorial optimization 
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     author = {Dalibor Ristic and Dragan Urosevic and Nenad Mladenovic and Raca Todosijevic},
     title = {Solving the {P-Second} {Center} {Problem} with {Variable} {Neighborhood} {Search}},
     journal = {Computer Science and Information Systems},
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     year = {2023},
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Dalibor Ristic; Dragan Urosevic; Nenad Mladenovic; Raca Todosijevic. Solving the P-Second Center Problem with Variable Neighborhood Search. Computer Science and Information Systems, Tome 20 (2023) no. 1. http://geodesic.mathdoc.fr/item/CSIS_2023_20_1_a8/