The Discrete Ordered Median Problem (DOMP) generalizes classical discrete location problems, such as the N -median, N -center and Uncapacitated Facility Location problems. It was introduced by Nickel [16], who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer l...

We consider the matroid median problem (MMP), which is defined as follows. As in the uncapacitated facility location problem, we are given a set of facilities F and a set of clients D. Each facility i has an opening cost of fi. Each client j ∈ D has demand dj and assigning client j to facility i incurs an assignment cost of djcij proportional to the distance between i and j. Further, we are giv...

We present an efficient metaheuristic based on Simulated Annealing for solving the p-Median problem. These ideas are tested on the well known OR-Lib set of problems with excellent results.

Given n customers and a set F of m potential facilities, the p-median problem consists in finding a subset of F with p facilities such that the cost of serving all customers is minimized. This is a well-known NP-complete problem with important applications in location science and classification (clustering). We present a multistart hybrid heuristic that combines elements of several traditional ...

Genome rearrangement analysis has attracted a lot of attentions in phylogenetic computation and comparative genomics. Solving the median problems based on various distance definitions has been a focus as it provides the building blocks for maximum parsimony analysis of phylogeny and ancestral genomes. The Median Problem (MP) has been proved to be NP-hard and although there are several exact or ...

In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − ∫ ΩJ J(x− y) uψ(y)− u(x) |uψ(y)− u(x)| dy = 0 for x ∈ Ω, with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J . We also show that solutions in the...