The Genomic Median Problem is an optimization problem inspired by a biological issue: it aims at finding the genome organization of the common ancestor to multiple living species. It is formulated as the search for a genome that minimizes some distance measure among given genomes. Several attempts have been made at solving the problem. These range from simple heuristic methods to a stochastic l...

Let the graph G = (V,E) be a cycle with n + 1 vertices, nonnegative vertex weights and positive edge lengths. The inverse 1-median problem on a cycle consists in changing the vertex weights at minimum cost such that a prespecified vertex becomes the 1-median. The cost is proportional to the increase or decrease of the corresponding weight. We show that this problem can be formulated as a linear...

The p-median problem, like most location problems, is classified as NP -hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview ...

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 NPcomplete problem with important applications in location science and classification (clustering). We present here a GRASP (Greedy Randomized Adaptive Search Procedure) with path-relinkin...

In this paper, we have proposed a new genetic algorithm for p-median location problem. In this regard, prior genetic algorithms were designed for p-median location problem by proposing several methods that are used in generation of initial population, crossover and mutation operators, and new operator socalled re-allocation has been incorporated into the algorithm that causes to find the optima...

Heuristic concentration (HC) is a two-stage metaheuristic that can be applied to a wide variety of combinatorial problems. It is particularly suited to location problems in which the number of facilities is given in advance. In such settings, the ®rst stage of HC repeatedly applies some random-start interchange (or other) heuristic to produce a number of alternative facility con®gurations. A su...

Metaheuristics represent an important class of techniques to solve, approximately, hard combinatorial optimization problems for which the use of exact methods is impractical. In this work, we propose a hybrid version of the GRASP metaheuristic, which incorporates a data mining process, to solve the p-median problem. We believe that patterns obtained by a data mining technique, from a set of sub...

Scatter search is a population-based method that has been shown to yield high-quality outcomes for combinatorial optimization problems. It uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation for an NP-hard variant of the classic p-hub median problem. Specifically, we tackle the unca...

In this paper we present a neural network model and new formulation for the p-median problem. The effectiveness and efficiency of our algorithm under varying problem sizes are analyzed in comparison to conventional heuristic methods. The results for small-scale problems (less than 100 points) indicate that our implementation of algorithm is effective. Furthermore, we also have applied our algor...

We present an efficient algorithm for the approximate median selection problem. The algorithm works in-place; it is fast and easy to implement. For a large array it returns, with high probability, a very close estimate of the true median. The running time is linear in the length n of the input. The algorithm performs fewer than 4 3 n comparisons and 1 3 n exchanges on the average. We present an...