Authors: Ristic, Dalibor
Urošević, Dragan 
Mladenović, Nenad 
Todosijević, Raca 
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Solving the P-Second Center Problem with Variable Neighborhood Search
Journal: Computer Science and Information Systems
Volume: 20
Issue: 1
First page: 95
Last page: 115
Issue Date: 1-Jan-2023
Rank: ~M23
ISSN: 1820-0214
DOI: 10.2298/CSIS210804049R
Abstract: 
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: combinatorial optimization | heuristic algorithms | p-second center problem | variable neighborhood method
Publisher: ComSIS Consortium

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