What makes an instance difficult for black-box 0-1 evolutionary multiobjective optimizers?

Arnaud Liefooghe (1, 2) , Sébastien Verel (3) , Hernan Aguirre (4) , Kiyoshi Tanaka (4)

1 LIFL - Laboratoire d'Informatique Fondamentale de Lille
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
3 LISIC - Laboratoire d'Informatique Signal et Image de la Côte d'Opale
4 Faculty of Engineering [Nagano]

This paper investigates the correlation between the characteristics extracted from the problem instance and the performance of a simple evolutionary multiobjective optimization algorithm. First, a number of features are identified and measured on a large set of enumerable multiobjective NK-landscapes with objective correlation. A correlation analysis is conducted between those attributes, including low-level features extracted from the problem input data as well as high-level features extracted from the Pareto set, the Pareto graph and the fitness landscape. Second, we experimentally analyze the (estimated) running time of the global SEMO algorithm to identify a (1 + ε)-approximation of the Pareto set. By putting this performance measure in relation with problem instance features, we are able to explain the difficulties encountered by the algorithm with respect to the main instance characteristics.

Domaines: Recherche opérationnelle [math.OC]

Arnaud Liefooghe, Sébastien Verel, Hernan Aguirre, Kiyoshi Tanaka. What makes an instance difficult for black-box 0-1 evolutionary multiobjective optimizers?. 11th International Conference on Artificial Evolution (EA 2013), Oct 2013, Bordeaux, France. pp.3-15, ⟨10.1007/978-3-319-11683-9⟩. ⟨hal-00855252⟩