Vertex Weighting-Based Tabu Search for p-Center Problem

Abstract

<jats:p>The p-center problem consists of choosing p centers from a set of candidates to minimize the maximum cost between any client and its assigned facility. In this paper, we transform the p-center problem into a series of set covering subproblems, and propose a vertex weighting-based tabu search (VWTS) algorithm to solve them. The proposed VWTS algorithm integrates distinguishing features such as a vertex weighting technique and a tabu search strategy to help the search to jump out of the local optima. Computational experiments on 138 most commonly used benchmark instances show that VWTS is highly competitive comparing to the state-of-the-art methods in spite of its simplicity. As a well-known NP-hard problem which has already been studied for over half a century, it is a challenging task to break the records on these classic datasets. Yet VWTS improves the best known results for 14 out of 54 large instances, and matches the optimal results for all remaining 84 ones. In addition, the computational time taken by VWTS is much shorter than other algorithms in the literature.</jats:p>

Weighting-based Variable Neighborhood Search for Optimal Camera Placement

“…It is a common technique to convert an optimization problem into a series of decision sub-problems and conquer them in sequence or even concurrently (Lü and Hao 2010;Gao et al 2015;Zhang et al 2020). Regarding OCP, it can be transformed into a series of k-set covering problems, denoted by OCP k , which determines whether all elements can be covered by exact k sets.…”

“…Instead of naively evaluating each neighboring solution by Equation ( 2), WVNS adopts an incremental evaluation technique inspired by Zhang et al (2020). In other words, we maintain the improvement ∆(p) of picking a set p ∈ S \ X so that we can evaluate the neighboring solution by f (X ⊕ p) = f (X) + ∆(p).…”

“…The unicost set covering problem is one of the most classical NP-hard problems (Gao et al 2015). It can be used to formulate many real-world optimization problems, such as logical function minimization (Seda 2007;Steinbach and Posthoff 2012), sensor placement (Rui et al 2017), software test suite reduction (Chi et al 2017), team formation (Demirović et al 2018), and facility location (Zhang et al 2020). In addition, several well-known NP-hard problems can be reduced to USCP, including dominating set (Cai et al 2020) and vertex cover (Cai, Su, and Sattar 2011).…”