Solving two location models with few facilities by using a hybrid heuristic: a real health resources case

We propose a metaheuristic procedure based on the scatter search approach for solving two location problems with few facilities (p ≤ 10).The first problem is the well-known p-center problem. The second one is the maximum set covering problem (MSCP). This scatter search algorithm incorporates procedures based on different strategies, such as local search, GRASP, and path relinking. We first designed the algorithm for the p-center problem, and then modified it for the MSCP.The aim is to solve problems with real data provided by the Health Authorities of Burgos (northern Spain). Because the authorities have a limited budget, less than 10 facilities can considered in both problems. A series of computational experiments were also performed. The proposed algorithm gave similar results to the recently reported methods for the p-center problem but much faster. The quality of the solutions is also very good for the MSCP (less than 1% deviation from the lower bound). We show its application to the location of health resources with real data in the province of Burgos.

[1]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[2]  Pierre Hansen,et al.  First vs. best improvement: An empirical study , 1999, Discret. Appl. Math..

[3]  S. L. HAKIMIt.  AN ALGORITHMIC APPROACH TO NETWORK LOCATION PROBLEMS. , 1979 .

[4]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[5]  R. A. Whitaker,et al.  A Fast Algorithm For The Greedy Interchange For Large-Scale Clustering And Median Location Problems , 1983 .

[6]  Ángel Corberán,et al.  Heuristic solutions to the problem of routing school buses with multiple objectives , 2002, J. Oper. Res. Soc..

[7]  F. Glover,et al.  Fundamentals of Scatter Search and Path Relinking , 2000 .

[8]  Pierre Hansen,et al.  Variable Neighbourhood Search , 2003 .

[9]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[10]  J. M. Moreno-Vega,et al.  THE CHAIN-INTERCHANGE HEURISTIC METHOD1 , 1996 .

[11]  M. Resende,et al.  A GRASP WITH PATH-RELINKING FOR PERMANENT VIRTUAL CIRCUIT ROUTING , 2001 .

[12]  Reiner Horst,et al.  A new simplicial cover technique in constrained global optimization , 1992, J. Glob. Optim..

[13]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[14]  J. Mulvey,et al.  Solving capacitated clustering problems , 1984 .

[15]  Panos M. Pardalos,et al.  Handbook of applied optimization , 2002 .

[16]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[17]  Celso C. Ribeiro,et al.  A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs , 2002, INFORMS J. Comput..

[18]  Rafael Martí,et al.  Scatter Search: Diseño Básico y Estrategias avanzadas , 2002, Inteligencia Artif..

[19]  Pierre Hansen,et al.  First improvement may be better than best improvment: an empirical study , 2005 .

[20]  George O. Wesolowsky,et al.  FACILITIES LOCATION: MODELS AND METHODS , 1988 .

[21]  Pierre Hansen,et al.  Variable Neighborhood Search: A Chapter of Handbook of Applied Optimization , 2000 .

[22]  Fred W. Glover,et al.  An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem , 2001, J. Glob. Optim..

[23]  Rafael Martí,et al.  GRASP and Path Relinking for 2-Layer Straight Line Crossing Minimization , 1999, INFORMS J. Comput..

[24]  José Andrés Moreno Pérez,et al.  A Chain-interchange Tabu Search Method (Tabu search in solving p -facility location-allocation problems) , 1995 .

[25]  Celso C. Ribeiro,et al.  A GRASP with path‐relinking for private virtual circuit routing , 2003, Networks.

[26]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[27]  Mauricio G. C. Resende,et al.  Computing Approximate Solutions of the Maximum Covering Problem with GRASP , 1998, J. Heuristics.

[28]  P. Hansen,et al.  Variable neighborhood search for the p-median , 1997 .

[29]  Joaquín A. Pacheco,et al.  A scatter search approach for the minimum sum-of-squares clustering problem , 2005, Comput. Oper. Res..

[30]  Joaquín A. Pacheco,et al.  Minimizing Labor Requirements in a Periodic Vehicle Loading Problem , 2005, Comput. Optim. Appl..

[31]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

[32]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.

[33]  Fred W. Glover,et al.  A Template for Scatter Search and Path Relinking , 1997, Artificial Evolution.

[34]  Pierre Hansen,et al.  Solving the p‐Center problem with Tabu Search and Variable Neighborhood Search , 2000, Networks.