Multimodality and the linkage-learning difficulty of additively separable functions

Estimation of Distribution Algorithms (EDAs) have emerged from the synergy between machine-learning techniques and Genetic Algorithms (GAs). EDAs rely on probabilistic modeling for obtaining information about the underlying structure of optimization problems and implementing effective reproduction operators. The effectiveness of EDAs depends on the capacity of the model-building to extract reliable information about the problem. In this study we analyze additively separable functions and argue that the degree of multimodality of such functions defines their linkage-learning difficulty. Besides, by using entropy-based concepts and Jensen's inequality, we show how allelic pairwise independence may appear as a consequence of an increasing multimodality. The results characterize the linkage-learning difficulty of well-known functions, like the deceptive trap, bipolar and concatenated parity.