Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.
Unable to display preview. Download preview PDF.
- 2.Bringmann, K., Friedrich, T.: Convergence of hypervolume-based archiving algorithms I: Effectiveness. In: Krasnogor, N., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2011, pp. 745–752. ACM Press, New York (2011)Google Scholar
- 5.Kauffman, S.A.: The Origins of Order. Oxford University Press (1993)Google Scholar
- 6.Knowles, J.D.: Local-Search and Hybrid Evolutionary Algorithms for Pareto Optimization. Ph.D. thesis, University of Reading, UK (2002)Google Scholar
- 7.Knowles, J., Corne, D.: Bounded Pareto archiving: Theory and practice. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’kindt, V. (eds.) Metaheuristics for Multiobjective Optimisation. LNEMS, vol. 535, pp. 39–64. Springer, Heidelberg (2004)Google Scholar
- 11.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. LNEMS, vol. 535, pp. 177–200. Springer, Heidelberg (2004)CrossRefGoogle Scholar