Abstract
In the last few years, a significant number of multi-objective metaheuristics have been proposed in the literature in order to address real-world problems. Local search methods play a major role in many of these metaheuristic procedures. In this paper, we adapt a recent and popular indicator-based selection method proposed by Zitzler and Künzli in 2004, in order to define a population-based multi-objective local search. The proposed algorithm is designed in order to be easily adaptable, parameter independent and to have a high convergence rate. In order to evaluate the capacity of our algorithm to reach these goals, a large part of the paper is dedicated to experiments. Three combinatorial optimisation problems are tested: a flow shop problem, a ring star problem and a nurse scheduling problem. The experiments show that our algorithm can be applied with success to different types of multi-objective optimisation problems and that it outperforms some classical metaheuristics. Furthermore, the parameter sensitivity analysis enables us to provide some useful guidelines about how to set the parameters.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Aarts, E., Korst, J., Michiels, W.: Simulated annealing. In: Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques. Springer, Berlin (2005), Chap. 7
Auger, A., Hansen, N.: A restart CMA evolution strategy with increasing population size. In: IEEE Congress on Evolutionary Computation (CEC 2005), vol. 2, pp. 1769–1776 (2005)
Basseur, M.: Design of cooperative algorithms for multi-objective optimization: application to the flow-shop scheduling problem. PhD thesis, University of Sciences and Technology of Lille, France (2005)
Basseur, M., Burke, E.K.: Indicator-based multiobjective local search. In: IEEE Congress on Evolutionary Computation (CEC 2007), Singapore, September 2007, pp. 3100–3107 (2007)
Basseur, M., Seynhaeve, F., Talbi, E.-G.: Design of multi-objective evolutionary algorithms: application to the flow-shop scheduling problem. In: IEEE Congress on Evolutionary Computation (CEC), 2002, Honolulu, USA, vol. 2, pp. 1151–1156 (2002)
Basseur, M., Zitzler, E.: Handling uncertainty in indicator-based multiobjective optimization. Int. J. Comput. Intell. Res. 2(3), 255–272 (2006)
Bentley, P.J., Wakefield, J.P.: Finding acceptable solutions in the Pareto-optimal range using multiobjective genetic algorithms. Soft Comput. Eng. Des. Manuf. 5, 231–340 (1997)
Bringmann, K., Friedrich, T.: Approximating the least hypervolume contributor: NP-hard in general, but fast in practice. In: 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 6–20. Springer, Berlin (2009)
Burke, E., De Causmaecker, P., Vanden Berghe, G., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7(6), 441–499 (2004)
Cahon, S., Melab, N., Talbi, E.-G.: ParadisEO: a framework for the reusable design of parallel and distributed metaheuristics. J. Heuristics 10(3), 357–380 (2004)
Cheang, B., Li, H., Lim, A., Rodrigues, B.: Nurse rostering problems—a bibliographic survey. Eur. J. Oper. Res. 151, 447–460 (2003)
Deb, K.: Multi-objective optimization. In: Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Chap. 10, pp. 273–316. Springer, Berlin (2006)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 181–197 (2002)
Du, J., Leung, J.Y.-T.: Minimizing total tardiness on one machine is NP-hard. Math. Oper. Res. 15, 483–495 (1990)
Ehrgott, M., Gandibleux, X.: Approximative solution methods for multiobjective combinatorial optimization. Trab. Investig. Oper. 12(1), 1–63 (2004)
Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: 3rd International Conference on Evolutionary Multi-criterion Optimization (EMO 2005). Lecture Note in Computer Science, vol. 3410, pp. 62–76. Springer, Berlin (2005)
Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: formulation discussion and generalization. In: Fifth International Conference on Genetic Algorithms (ICGA’93), San Mateo, USA, pp. 416–423 (1993)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Boston (1989)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)
Grunert da Fonseca, V., Fonseca, C.M., Hall, A.O.: Inferential performance assessment of stochastic optimisers and the attainment function. In: 1st International Conference on Evolutionary Multi-criterion Optimization (EMO 2001). Lecture Note in Computer Science, vol. 1993, pp. 213–225. Springer, Berlin (2001)
Ishibuchi, T.H.: A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. Syst. Man Cybern., Part C, Appl. Rev. 28(3), 1998 (1998)
Hansen, M.P.: Tabu search for multiobjective optimization: MOTS. In: MCDM’97 Conference, Cap town, South Africa (1997)
Kim, Y.-D.: Minimizing total tardiness in permutation flowshops. Eur. J. Oper. Res. 33, 541–551 (1995)
Knowles, J.D.: Local-search and hybrid evolutionary algorithms for Pareto optimization. PhD thesis, University of Reading (2002)
Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)
Knowles, J.D., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastive multiobjective optimizers. Technical report TIK-Report No. 214, Computer Engineering and Networks Laboratory, ETH Zurich, July 2005
Labbé, M., Laporte, G., Rodríguez Martín, I., Salazar González, J.J.: The ring star problem: polyhedral analysis and exact algorithm. Networks 43, 177–189 (2004)
Landa-Silva, D., Burke, E.K., Petrovic, S.: An introduction to multiobjective metaheuristics for scheduling and timetabling. In: Metaheuristics for Multiobjective Optimisation, pp. 91–129, Chap. 4. Springer, Berlin (2004)
Landa-Silva, D., Le, K.N.: A simple evolutionary algorithm with self-adaptation for multi-objective nurse scheduling. In: Adaptive and Multilevel Metaheuristics, vol. 136, pp. 133–155, Chap. 7. Springer, Berlin (2008)
Lenstra, J.K., Kan, A.H.G.R., Brucker, P.: Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362 (1977)
Liefooghe, A., Jourdan, L., Jozefowiez, N., Talbi, E.-G.: On the integration of a TSP heuristic into an EA for the bi-objective ring star problem. In: International Workshop on Hybrid Metaheuristics (HM 2008), Malaga, Spain. Lecture Notes in Computer Science, vol. 5296, pp. 117–130. Springer, Berlin (2008)
Liefooghe, A., Mesmoudi, S., Humeau, J., Jourdan, L., Talbi, E.-G.: A study on dominance-based local search approaches for multiobjective combinatorial optimization. In: Second International Workshop on Engineering Stochastic Local Search Algorithms (SLS 2009), Brussels, Belgium. Lecture Notes in Computer Science, vol. 5752, pp. 120–124 (2009)
Murata, T., Nozawa, H., Ishibuchi, H., Gen, M.: Modification of local search directions for non-dominated solutions in cellular multiobjective genetic algorithms for pattern classification problems. In: 2nd International Conference on Evolutionary Multi-criterion Optimization (EMO 2003). Lecture Notes in Computer Science, vol. 2632, pp. 593–607. Springer, Berlin (2003)
Nagar, A., Haddock, J., Heragu, S.: Multiple and bicriteria scheduling: a literature survey. Eur. J. Oper. Res. 81, 88–104 (1995)
Oliver, I.M., Smith, D.J., Holland, J.R.C.: A study of permutation crossover operators on the traveling salesman problem. In: Proceedings of the Second International Conference on Genetic algorithms and their application, Mahwah, NJ, USA, pp. 224–230. Erlbaum, Hillsdate (1987)
Paquete, L., Stützle, T.: A study of local search algorithms for the biobjective QAP with correlated flow matrices. Eur. J. Oper. Res. 169(3), 943–959 (2006)
Ross, P.: Hyper-heuristics. In: Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 527—556, Chap. 17. Springer, Berlin (2006)
Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)
Taillard, E.: Benchmarks for basic scheduling problems. Cent. Eur. J. Oper. Res. 64, 278–285 (1993)
Talbi, E.G., Rahoual, M., Mabed, M.H., Dhaenens, C.: A hybrid evolutionary approach for multicriteria optimization problems: application to the flow shop. In: 1st International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001). Lecture Notes in Computer Science, vol. 1993, pp. 416–428 (2001)
Tan, K.C., Lee, T.H., Khor, E.F.: Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. Evol. Comput. 5(6), 565–588 (2001)
Viana, A., Pinho de Sousa, J., Matos, M.A.: Multiobjective constraint oriented neighbourhoods. In: 6th Metaheuristics International Conference (MIC 2005), Vienna, Austria, pp. 896–903 (2005)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII), Birmingham, UK, pp. 832–842 (2004)
Zitzler, E., Laumanns, M., Bleuler, S.: A tutorial on evolutionary multiobjective optimization. In: Gandibleux, X., et al. (eds.) Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, pp. 3–37. Springer, Berlin (2004)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K. et al. (eds.) Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), pp. 95–100. International Center for Numerical Methods in Engineering (CIMNE), Barcelona (2002)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. Evol. Comput. 3, 257–271 (1999)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Basseur, M., Liefooghe, A., Le, K. et al. The efficiency of indicator-based local search for multi-objective combinatorial optimisation problems. J Heuristics 18, 263–296 (2012). https://doi.org/10.1007/s10732-011-9178-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-011-9178-y