Solving the bi-objective capacitated p-median problem with multilevel capacities using compromise programming and VNS

A bi-objective optimisation using a compromise programming approach is proposed for the capacitated p-median problem in the presence of the fixed cost of opening facility and several possible capacities that can be used by potential facilities. As the sum of distances between customers and their facilities and the total fixed cost for opening facilities are important aspects, the model is proposed to deal with those conflicting objectives. We develop a mathematical model using integer linear programming (ILP) to determine the optimal location of open facilities with their optimal capacity. Two approaches are designed to deal with the bi-objective capacitated p-median problem, namely compromise programming with an exact method and with a variable neighbourhood search based matheuristic. New sets of generated instances are used to evaluate the performance of the proposed approaches. The computational experiments show that the proposed approaches produce interesting results.

[1]  Luiz Antonio Nogueira Lorena,et al.  Clustering Search Heuristic for the Capacitated p -Median Problem , 2008, Innovations in Hybrid Intelligent Systems.

[2]  El-Ghazali Talbi,et al.  Hybridizing exact methods and metaheuristics: A taxonomy , 2009, Eur. J. Oper. Res..

[3]  Branislava Ratkovic,et al.  Generalized mixed integer and VNS heuristic approach to solving the multisize containers drayage problem , 2017, Int. Trans. Oper. Res..

[4]  S. Salhi,et al.  AGGREGATION AND NON AGGREGATION TECHNIQUES FOR LARGE FACILITY LOCATION PROBLEMS - A SURVEY , 2015 .

[5]  Nicos Christofides,et al.  Capacitated clustering problems by hybrid simulated annealing and tabu search , 1994 .

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

[7]  Mohammed El Amrani,et al.  Generalization of capacitated p-median location problem: Modeling and resolution , 2016, 2016 3rd International Conference on Logistics Operations Management (GOL).

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

[9]  Isabel Correia,et al.  A Lagrangean Heuristic for a Modular Capacitated Location Problem , 2003, Ann. Oper. Res..

[10]  Masoud Yaghini,et al.  A hybrid metaheuristic approach for the capacitated p-median problem , 2013, Appl. Soft Comput..

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Krzysztof Fleszar,et al.  An effective VNS for the capacitated p-median problem , 2008, Eur. J. Oper. Res..

[13]  Samad Ahmadi,et al.  Greedy random adaptive memory programming search for the capacitated clustering problem , 2005, Eur. J. Oper. Res..

[14]  Thomas Stützle,et al.  Combinations of Local Search and Exact Algorithms , 2003, EvoWorkshops.

[15]  Carlos Romero,et al.  Multiple Criteria Analysis for Agricultural Decisions , 1989 .

[16]  Juan A. Díaz,et al.  Hybrid scatter search and path relinking for the capacitated p , 2006, Eur. J. Oper. Res..

[17]  Saïd Salhi,et al.  Location-routing: Issues, models and methods , 2007, Eur. J. Oper. Res..

[18]  Francisco Saldanha-da-Gama,et al.  Discretized formulations for capacitated location problems with modular distribution costs , 2010, Eur. J. Oper. Res..

[19]  Claudio Sterle,et al.  A Cut and Branch Approach for the Capacitated p-Median Problem Based on Fenchel Cutting Planes , 2008, J. Math. Model. Algorithms.

[20]  Masoud Yaghini,et al.  An efficient heuristic algorithm for the capacitated $$p-\!$$ median problem , 2013, 4OR.

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

[22]  Bassem Jarboui,et al.  An integration of mixed VND and VNS: the case of the multivehicle covering tour problem , 2017, Int. Trans. Oper. Res..

[23]  Javier Del Ser,et al.  A comparative study of two hybrid grouping evolutionary techniques for the capacitated P-median problem , 2012, Comput. Oper. Res..

[24]  Chandra Ade Irawan,et al.  An adaptive multiphase approach for large unconditional and conditional p-median problems , 2014, Eur. J. Oper. Res..

[25]  Zvi Drezner,et al.  Hybrid meta-heuristics with VNS and exact methods: application to large unconditional and conditional vertex p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\ , 2015, Journal of Heuristics.

[26]  Roberto Baldacci,et al.  A Bionomic Approach to the Capacitated p-Median Problem , 1998, J. Heuristics.

[27]  Tore Grünert,et al.  A Hybrid Tabu Search/Branch-and-Bound Algorithm for the Direct Flight Network Design Problem , 2000, Transp. Sci..

[28]  Éric D. Taillard,et al.  Popmusic — Partial Optimization Metaheuristic under Special Intensification Conditions , 2002 .

[29]  Rubén Ruiz,et al.  Size-reduction heuristics for the unrelated parallel machines scheduling problem , 2011, Comput. Oper. Res..

[30]  Helena Ramalhinho Dias Lourenço,et al.  Optimised Search Heuristics: A Mapping of Procedures and Combinatorial Optimisation Problems , 2006 .

[31]  Günther R. Raidl,et al.  Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification , 2005, IWINAC.

[32]  El-Ghazali Talbi,et al.  A Taxonomy of Hybrid Metaheuristics , 2002, J. Heuristics.

[33]  P. Yu.  A Class of Solutions for Group Decision Problems , 1973 .

[34]  Nenad Mladenović,et al.  A Variable Neighbourhood Algorithm for Solving the Continuous Location-Allocation Problem , 1995 .

[35]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. I: The p-Centers , 1979 .

[36]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[37]  Rolf Wendolsky,et al.  A scatter search heuristic for the capacitated clustering problem , 2006, Eur. J. Oper. Res..

[38]  Hasan Pirkul,et al.  Efficient algorithms for the capacitated concentrator location problem , 1987, Comput. Oper. Res..

[39]  Sara Beheshtifar,et al.  A multiobjective optimization approach for location-allocation of clinics , 2015, Int. Trans. Oper. Res..

[40]  Abraham Duarte,et al.  Parallel variable neighborhood search for the min-max order batching problem , 2017, Int. Trans. Oper. Res..

[41]  Michel Gendreau,et al.  Bi-objective stochastic programming models for determining depot locations in disaster relief operations , 2016, Int. Trans. Oper. Res..

[42]  Sad Salhi,et al.  Heuristic Search: The Emerging Science of Problem Solving , 2017 .

[43]  Pierre Hansen,et al.  Variable neighbourhood search: methods and applications , 2010, Ann. Oper. Res..

[44]  Olinto César Bassi de Araújo,et al.  Matheuristics for the capacitated p-median problem , 2015, Int. Trans. Oper. Res..

[45]  Milan Zelany,et al.  A concept of compromise solutions and the method of the displaced ideal , 1974, Comput. Oper. Res..

[46]  Charles ReVelle,et al.  Central Facilities Location , 2010 .

[47]  Kenneth Sörensen,et al.  A variable neighborhood search algorithm to generate piano fingerings for polyphonic sheet music , 2017, Int. Trans. Oper. Res..

[48]  Roberto Baldacci,et al.  A new method for solving capacitated location problems based on a set partitioning approach , 2002, Comput. Oper. Res..

[49]  Mehrdad Tamiz,et al.  Goal programming, compromise programming and reference point method formulations: linkages and utility interpretations , 1998, J. Oper. Res. Soc..

[50]  Vittorio Maniezzo,et al.  Matheuristics: Hybridizing Metaheuristics and Mathematical Programming , 2009 .

[51]  Luiz Antonio Nogueira Lorena,et al.  A column generation approach to capacitated p-median problems , 2004, Comput. Oper. Res..

[52]  Chandra Ade Irawan,et al.  Solving large $$p$$p-median problems by a multistage hybrid approach using demand points aggregation and variable neighbourhood search , 2015, J. Glob. Optim..