Exact solutions of some OR-library test instances for the p-next center problem

Abstract

OR-Library is a platform that provides standardized examples for testing problem-solving algorithms in many fields of the operational research and combinatorial optimization. One of the problems emerged in the previous decade is the p-next center problem. The solution to the p-next center problem implies locating p centers in order to minimize the maximum user distance to the closest center plus the distance between that center and the center closest to it. There are several heuristic algorithms for solving this NP-hard problem that give optimal or near-optimal solutions. We propose an algorithm for solving the p-next center problem based on the variable neighborhood search method, capable of recognizing whether some of the found solutions from the OR-Library test set are exact. As a result of the algorithm execution, more than 50% of the solutions are identified as globally optimal. The paper presents a table with the found exact solution values for the p-next center problem from the OR-Library test set.