Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Survey and unification of local search techniques in metaheuristics for multi-objective combinatorial optimisation

  • 351 Accesses

  • 1 Citations

Abstract

Metaheuristics are algorithms that have proven their efficiency on multi-objective combinatorial optimisation problems. They often use local search techniques, either at their core or as intensification mechanisms, to obtain a well-converged and diversified final result. This paper surveys the use of local search techniques in multi-objective metaheuristics and proposes a general structure to describe and unify their underlying components. This structure can instantiate most of the multi-objective local search techniques and algorithms in literature.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2

References

  1. Abbasi, M., Paquete, L., Pereira, F.B.: Local search for multiobjective multiple sequence alignment. In: Guzman, F.M.O., Rojas, I. (eds.) Bioinformatics and Biomedical Engineering—Third International Conference, IWBBIO 2015. Proceedings, Part II, Springer, Lecture Notes in Computer Science, vol. 9044, pp. 175–182 (2015)

  2. Aguirre, H., Tanaka, K.: Random bit climbers on multiobjective MNK-landscapes: effects of memory and population climbing. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 88(1), 334–345 (2005)

  3. Angel, E., Bampis, E., Gourvés, L.: Approximating the pareto curve with local search for the bicriteria TSP (1, 2) problem. Theor. Comput. Sci. 310(1–3), 135–146 (2004)

  4. Arroyo, J.E.C., dos Santos, Ottoni R., de Paiva, Oliveira A.: Multi-objective variable neighborhood search algorithms for a single machine scheduling problem with distinct due windows. Electron. Notes Theor. Comput. Sci. 281, 5–19 (2011)

  5. Bandyopadhyay, S., Saha, S., Maulik, U., Deb, K.: A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans. Evol. Comput. 12(3), 269–283 (2008)

  6. Basseur, M., Burke, E.K.: Indicator-based multi-objective local search. In: IEEE Congress on Evolutionary Computation, IEEE, pp. 3100–3107 (2007)

  7. Basseur, M., Zeng, R.Q., Hao, J.K.: Hypervolume-based multi-objective local search. Neural Comput. Appl. 21(8), 1917–1929 (2012)

  8. Baykasoglu, A., Owen, S., Gindy, N.: A taboo search based approach to find the pareto optimal set in multiple objective optimization. Eng. Optim. 31(6), 731–748 (1999)

  9. Beausoleil, R.P.: Multiple criteria scatter search. In: 4th Metaheuristics International Conference, pp. 534–539 (2001)

  10. Blot, A., Aguirre, H., Dhaenens, C., Jourdan, L., Marmion, M.É., Tanaka, K.: Neutral but a winner! how neutrality helps multiobjective local search algorithms. In: Evolutionary Multi-criterion Optimization. Proceedings, Part I, pp. 34–47 (2015)

  11. Blot, A., Hoos, H.H., Jourdan, L., Marmion, M.É., Trautmann, H.: MO-ParamILS: a multi-objective automatic algorithm configuration framework. In: LION 10 (2016)

  12. Blot, A., Jourdan, L., Kessaci-Marmion, M.É.: Automatic design of multi-objective local search algorithms: case study on a bi-objective permutation flowshop scheduling problem. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 227–234 (2017a)

  13. Blot, A., Pernet, A., Jourdan, L., Kessaci-Marmion, M.É., Hoos, H.H.: Automatically configuring multi-objective local search using multi-objective optimisation. In: Evolutionary Multi-criterion Optimization, Proceedings, pp. 61–76 (2017b)

  14. Czyzak, P., Jaszkiewicz, A.: A multiobjective metaheuristic approach to the location of petrol stations by the capital budgeting model. Control Cybern. 25, 177–187 (1996)

  15. Czyzak, P., Jaszkiewicz, A.: Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization. J. Multi-Criteria Decis. Anal. 7(1), 34–47 (1998)

  16. Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms, vol. 1. Wiley, New York (2001)

  17. Drugan, M.M., Thierens, D.: Path-guided mutation for stochastic Pareto local search algorithms. In: 11th International on Conference on Parallel Problem Solving from Nature—PPSN XI, pp. 485–495. Springer (2010)

  18. Drugan, M.M., Thierens, D.: Stochastic Pareto local search: Pareto neighbourhood exploration and perturbation strategies. J. Heuristics 18(5), 727–766 (2012)

  19. Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: A hybrid TP\(+\)PLS algorithm for bi-objective flow-shop scheduling problems. Comput. Oper. Res. 38(8), 1219–1236 (2011)

  20. Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: Pareto local search algorithms for anytime bi-objective optimization. In: European Conference on Evolutionary Computation in Combinatorial Optimization, pp. 206–217. Springer (2012)

  21. Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: Anytime Pareto local search. Eur. J. Oper. Res. 243(2), 369–385 (2015)

  22. Engrand, P.: A multi-objective optimization approach based on simulated annealing and its application to nuclear fuel management. Technical Report, Electricite de France (1998)

  23. Feo, T.A., Resende, M.G.C., Smith, S.H.: A greedy randomized adaptive search procedure for maximum independent set. Oper. Res. 42(5), 860–878 (1994)

  24. Fortemps, P., Teghem, J., Ulungu, B.: Heuristics for multiobjective combinatorial optimization by simulated annealing. In: XIth International Conference on MCDM, pp. 1–6 (1994)

  25. Geiger, M.J.: Randomised variable neighbourhood search for multi objective optimisation. In: Proceedings of the 4th EU/ME Workshop: Design and Evaluation of Advanced Hybrid Meta-Heuristics, November 4–5, Nottingham, UK, pp. 34–42 (2008). arXiv:0809.0271

  26. Gendreau, M., Potvin, J.Y.: Handbook of Metaheuristics, vol. 2. Springer, Berlin (2010)

  27. Glover, F., Laguna, M., Taillard, E., de Werra, D.: Tabu Search. Baltzer, Basel (1993)

  28. Hansen, M.P.: Tabu search for multiobjective optimization: MOTS. In: Proceedings of the 13th International Conference on Multiple Criteria Decision Making, pp. 574–586 (1997)

  29. Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations & Applications. Elsevier/Morgan Kaufmann, Amsterdam (2004)

  30. Inja, M., Kooijman, C., de Waard, M., Roijers, D.M., Whiteson, S.: Queued Pareto local search for multi-objective optimization. In: 13th International on Conference on Parallel Problem Solving from Nature—PPSN XIII, pp. 589–599 (2014)

  31. Ishibuchi, H., Murata, T.: Multi-objective genetic local search algorithm. In: Proceedings of IEEE International Conference on Evolutionary Computation, 1996, pp. 119–124. IEEE (1996)

  32. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: a short review. In: IEEE Congress on Evolutionary Computation, IEEE, pp 2419–2426 (2008)

  33. Jaeggi, D., Asselin-Miller, C., Parks, G., Kipouros, T., Bell, T., Clarkson, J.: Multi-objective parallel tabu search. In: 8th International on Conference on Parallel Problem Solving from Nature—PPSN VIII, pp. 732–741. Springer (2004)

  34. Jaeggi, D., Parks, G.T., Kipouros, T., Clarkson, P.J.: The development of a multi-objective Tabu search algorithm for continuous optimisation problems. Eur. J. Oper. Res. 185(3), 1192–1212 (2008)

  35. Jaszkiewicz, A.: Genetic local search for multi-objective combinatorial optimization. Eur. J. Oper. Res. 137(1), 50–71 (2002)

  36. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P., et al.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

  37. Knowles, J., Corne, D.: The Pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation. In: 1999. CEC 99. Proceedings of the 1999 Congress on Evolutionary Computation, vol. 1, pp. 98–105. IEEE (1999)

  38. Knowles, J., Corne, D.: Approximating the nondominated front using the Pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000a)

  39. Knowles, J., Corne, D.: M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, 2000, vol. 1, pp. 325–332. IEEE (2000b)

  40. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comput. 10(3), 263–282 (2002)

  41. Liefooghe, A., Humeau, J., Mesmoudi, S., Jourdan, L., Talbi, E.: On dominance-based multiobjective local search: design, implementation and experimental analysis on scheduling and traveling salesman problems. J. Heuristics 18(2), 317–352 (2012)

  42. Lourenço, H., Martin, O., Stützle, T.: Iterated local search. In: Glover, F.W., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 320–353. Springer (2003)

  43. Lourenço, H., Martin, O., Stützle, T.: Iterated local search: framework and applications. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics, vol. 2, pp. 363–397. Springer (2010)

  44. Lust, T., Teghem, J.: Two-phase Pareto local search for the biobjective traveling salesman problem. J. Heuristics 16(3), 475–510 (2010)

  45. Martí, R., Campos, V., Resende, M.G.C., Duarte, A.: Multiobjective GRASP with path relinking. Eur. J. Oper. Res. 240(1), 54–71 (2015)

  46. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

  47. Moalic, L., Caminada, A., Lamrous, S.: A fast local search approach for multiobjective problems. In: International Conference on Learning and Intelligent Optimization, pp. 294–298. Springer (2013)

  48. Molina, J., Laguna, M., Martí, R., Caballero, R.: SSPMO: a scatter Tabu search procedure for non-linear multiobjective optimization. INFORMS J. Comput. 19(1), 91–100 (2007)

  49. Moslehi, G., Mahnam, M.: A pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search. Int. J. Prod. Econ. 129(1), 14–22 (2011)

  50. Murata, T., Ishibuchi, H., Gen, M.: Cellular genetic local search for multi-objective optimization. In: Proceedings of the 2nd Annual Conference on Genetic and Evolutionary Computation, pp. 307–314. Morgan Kaufmann Publishers Inc. (2000)

  51. Paquete, L., Stützle, T.: A two-phase local search for the biobjective traveling salesman problem. In: Evolutionary Multi-criterion Optimization, pp. 69–69. Springer (2003)

  52. Paquete, L., Chiarandini, M., Stützle, T.: Pareto local optimum sets in the biobjective traveling salesman problem: an experimental study. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’Kindt, V. (eds.) Metaheuristics for Multiobjective Optimisation, pp. 177–199. Springer, Berlin (2004)

  53. Serafini, P.: Simulated annealing for multi objective optimization problems. In: Tzeng, G.H., Wang, H.F., Wen, U.P., Yu, P.L. (eds.) Multiple Criteria Decision Making, pp. 283–292. Springer, Berlin (1994)

  54. Suman, B.: Simulated annealing-based multiobjective algorithms and their application for system reliability. Eng. Optim. 35(4), 391–416 (2003)

  55. Suman, B., Kumar, P.: A survey of simulated annealing as a tool for single and multiobjective optimization. J. Oper. Res. Soc. 57(10), 1143–1160 (2006)

  56. Suppapitnarm, A., Parks, G.: Simulated annealing: an alternative approach to true multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), pp. 406–407. Morgan Kaufmann Publishers (1999)

  57. Suresh, R., Mohanasundaram, K.: Pareto archived simulated annealing for permutation flow shop scheduling with multiple objectives. In: 2004 IEEE Conference on Cybernetics and Intelligent Systems, vol.2, pp. 712–717. IEEE (2004)

  58. Talbi, E.G., Rahoual, M., Mabed, M.H., Dhaenens, C.: A hybrid evolutionary approach for multicriteria optimization problems: application to the flow shop. In: International Conference on Evolutionary Multi-criterion Optimization, pp 416–428. Springer (2001)

  59. Tricoire, F.: Multi-directional local search. Comput. OR 39(12), 3089–3101 (2012)

  60. Ulungu, B., Teghem, J., Fortemps, P.: Heuristic for multi-objective combinatorial optimization problems by simulated annealing. In: Gu, J., Chen, G., Wei, Q., Wang, S. (eds.) MCDM: Theory and Applications, pp. 229–238. Sci-Tech (1995)

  61. Ulungu, B., Teghem, J., Fortemps, P., Tuyttens, D.: MOSA method: a tool for solving multiobjective combinatorial optimization problems. J. Multi-criteria Decis. Anal. 8(4), 221 (1999)

  62. Vianna, D.S., Arroyo, J.E.C.: A grasp algorithm for the multi-objective knapsack problem. In: Computer Science Society, 2004. SCCC 2004. 24th International Conference of the Chilean, pp. 69–75. IEEE (2004)

  63. Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: International Conference on Parallel Problem Solving from Nature, pp. 832–842. Springer (2004)

  64. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE TEVC 3(4), 257–271 (1999)

Download references

Author information

Correspondence to Aymeric Blot.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Blot, A., Kessaci, M. & Jourdan, L. Survey and unification of local search techniques in metaheuristics for multi-objective combinatorial optimisation. J Heuristics 24, 853–877 (2018). https://doi.org/10.1007/s10732-018-9381-1

Download citation

Keywords

  • Multi-objective optimisation
  • Combinatorial optimisation
  • Metaheuristics
  • Unification
  • Local search algorithms