Metaheuristics and Their Hybridization to Solve the Bi-objective Ring Star Problem: a Comparative Study

This paper presents and experiments approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The first objective is the minimization of a ring cost that is related to the length of the cycle. The second one is the minimization of an assignment cost from non-visited nodes to visited ones. In spite of its obvious bi-objective formulation, this problem has always been investigated in a single-objective way. To tackle the bi-objective ring star problem, we first investigate different stand-alone search methods. Then, we propose two cooperative strategies that combines two multiple objective metaheuristics: an elitist evolutionary algorithm and a population-based local search. We apply this new hybrid approaches to well-known benchmark test instances and demonstrate their effectiveness in comparison to non-hybrid algorithms and to state-of-the-art methods.

[1]  El-Ghazali Talbi,et al.  ParadisEO-MOEO: A Framework for Evolutionary Multi-objective Optimization , 2007, EMO.

[2]  Gilbert Laporte,et al.  Efficient heuristics for Median Cycle Problems , 2004, J. Oper. Res. Soc..

[3]  J. Current,et al.  The median tour and maximal covering tour problems: Formulations and heuristics , 1994 .

[4]  Karl F. Doerner,et al.  Multicriteria tour planning for mobile healthcare facilities in a developing country , 2007, Eur. J. Oper. Res..

[5]  Carlos M. Fonseca,et al.  Exploring the Performance of Stochastic Multiobjective Optimisers with the Second-Order Attainment Function , 2005, EMO.

[6]  Marco Laumanns,et al.  PISA: A Platform and Programming Language Independent Interface for Search Algorithms , 2003, EMO.

[7]  Carlos A. Coello Coello,et al.  Pareto-adaptive -dominance , 2007, Evolutionary Computation.

[8]  D. Corne,et al.  On Metrics for Comparing Non Dominated Sets , 2001 .

[9]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[10]  John E. Beasley,et al.  A tabu search algorithm for the single vehicle routing allocation problem , 2007, J. Oper. Res. Soc..

[11]  Inmaculada Rodríguez Martín,et al.  Locating median cycles in networks , 2005, Eur. J. Oper. Res..

[12]  Juan José Salazar González,et al.  The Median Cycle Problem , 2001 .

[13]  Thomas Stützle,et al.  Pareto Local Optimum Sets in the Biobjective Traveling Salesman Problem: An Experimental Study , 2004, Metaheuristics for Multiobjective Optimisation.

[14]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[15]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  El-Ghazali Talbi,et al.  COSEARCH: A Parallel Cooperative Metaheuristic , 2006, J. Math. Model. Algorithms.

[18]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[19]  Edmund K. Burke,et al.  Indicator-based multi-objective local search , 2007, 2007 IEEE Congress on Evolutionary Computation.

[20]  Umit Akinc,et al.  Optimal routing and process scheduling for a mobile service facility , 1992, Networks.

[21]  Antonio Mauttone,et al.  A hybrid metaheuristic algorithm to solve the Capacitated m -Ring Star Problem , 2007 .

[22]  X. Gandibleux,et al.  Approximative solution methods for multiobjective combinatorial optimization , 2004 .

[23]  El-Ghazali Talbi,et al.  A multiobjective genetic algorithm for radio network optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[24]  Edmund K. Burke,et al.  Metaheuristics for the Bi-objective Ring Star Problem , 2008, EvoCOP.

[25]  Xavier Gandibleux,et al.  Hybrid Metaheuristics for Multi-objective Combinatorial Optimization , 2008, Hybrid Metaheuristics.

[26]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[27]  John E. Beasley,et al.  The Vehicle Routing-Allocation Problem: A unifying framework , 1996 .

[28]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

[29]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[30]  Marco Laumanns,et al.  On the Effects of Archiving, Elitism, and Density Based Selection in Evolutionary Multi-objective Optimization , 2001, EMO.

[31]  Lothar Thiele,et al.  The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration , 2007, EMO.

[32]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[33]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[34]  El-Ghazali Talbi,et al.  Design of multi-objective evolutionary algorithms: application to the flow-shop scheduling problem , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[35]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[36]  E. L. Ulungu,et al.  MOSA method: a tool for solving multiobjective combinatorial optimization problems , 1999 .

[37]  Xavier Gandibleux,et al.  A Tabu Search Procedure to Solve MultiObjective Combinatorial Optimization Problems , 1997 .

[38]  G. Laporte,et al.  Maximizing user convenience and postal service efficiency in post box location , 1986 .

[39]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[40]  Lucídio dos Anjos Formiga Cabral,et al.  An Efficient Heuristic for the Ring Star Problem , 2006, WEA.

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

[42]  이용호,et al.  A Branch and Cut Algorithm for the Steiner Ring Star Problem , 1998 .

[43]  Inmaculada Rodríguez Martín,et al.  Variable neighborhood tabu search and its application to the median cycle problem , 2003, Eur. J. Oper. Res..

[44]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[45]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[46]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[47]  Jiefeng Xu,et al.  Optimizing a Ring-Based Private Line Telecommunication Network Using Tabu Search , 1999 .

[48]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[49]  Mauro Dell'Amico,et al.  The Capacitated m-Ring-Star Problem , 2007, Oper. Res..

[50]  Nicolas Jozefowiez,et al.  Multi-objective vehicle routing problems , 2008, Eur. J. Oper. Res..

[51]  C. L. Valenzuela.  A simple evolutionary algorithm for multi-objective optimization (SEAMO) , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[52]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[53]  Inmaculada Rodríguez Martín,et al.  The Ring Star Problem: Polyhedral analysis and exact algorithm , 2004, Networks.

[54]  Gilbert Laporte,et al.  Path, Tree and Cycle Location , 1998 .

[55]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.