The p-median problem: A survey of metaheuristic approaches

Abstract

Abstract. The p-median problem, like most location problems, is classified as N P -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 on advances in solving it using recent procedures based on metaheuristic rules.

A Computational Comparison of Different Algorithms for Very Large $$p$$-median Problems

“…A survey of metaheuristics has been published by Mladenovic [20]. The earliest solution techniques mentioned are enumerationbased or heuristics such as vertex-substitution [3,18].…”

“…The earliest solution techniques mentioned are enumerationbased or heuristics such as vertex-substitution [3,18]. Simulated Annealing (SA) based approaches have also been applied to the p-median problem [20,9,1]. Genetic algorithms (GA) have been used in [2,11].…”

A new local search for continuous location problems

“…However, the aim of our study is to present an adaptive approach that augments the set of potential sites in discrete space by adding newly found points in continuous space in a systematic and simple way and not to promote efficient implementations which could without any doubt be useful at producing better solutions. This latter objective could be achieved by the combined BLS/RLS approach noted above, or by using powerful global optimisation techniques such as metaheuristics to produce such initial discrete high quality solutions (see Mladenović et al [34]). …”

“…For an overview of the continuous location-allocation problem, the in-terested reader is referred to the survey paper by Brimberg et al [9] and the references therein, while for the discrete p-median model and solution approaches the review by Mladenović et al [34] can be useful. The relation between discrete and continuous formulations may be extended to many other location models.…”

Metodologías para la ubicación de plantas de biomasa mediante modelos de localización basados en programación lineal y evaluación multicriterio en el entorno de los Sistemas de Información Geográfica

“…En la misma línea, nos encontramos con otro algoritmo denominado" sustitución del vértice ajustado" (adjusted vertex substitution) (Ashayeri 2005) que mejora considerablemente los tiempos de cálculo y resolución de un problema de p-mediano, pudiendo aplicar a un gran número de escenarios. Mladenovic´ et al (2007) hace una revisión de la heurística clásica (dividida en constructiva, búsqueda local y programación matemática) utilizada para resolver los problemas p-medianos, así como presentar los últimos avances utilizando para ello procedimientos metahurísticos (en nomenclatura anglosajona: Tabu search, Variable neighborhoodsearch, Genetic search, Scattersearch, Simulated annealing, Heuristic concentration, Ant colony optimization, Neural Networks, Decomposition heuristics, Hybrid heuristics), de donde se concluye que estos mejoran considerablemente la calidad de la solución a grandes escalas en un tiempo razonablemente corto. Recientemente, Richard Church (Church 2008) publica un nuevo modelo mediante programación lineal entera del p-mediano, como extensión del ya formulado por ReVelle y Swain (1974) pero eliminado muchas de las condiciones y variables, consiguiendo una mayor eficiencia en el planteamiento y resolución de grandes modelos.…”