Diculty of linkage learning in estimation of distribution algorithms

This paper investigates the difficulty of linkage learning, an essential core, in EDAs. Specif-ically, it examines allelic-pairwise independent functions including the parity, parity-with-trap, and Walsh-code functions. While the parity function was believed to be difficult for EDAs in previous work, our experiments indicate that it can be solved by CGA within a polynomial number of function evaluations to the problem size. Consequently, the apparently difficult parity-with-trap function can be easily solved by ECGA, even though the linkage model is incorrect. A convergence model for CGA on the parity function is also derived to verify and support the empirical findings. Finally, this paper proposes a so-called Walsh-code function, which is more difficult than the parity function. Although the proposed function does deceive the linkage-learning mechanism in most EDAs, EDAs are still able to solve it to some extent