Toward more efficient heuristic construction of Boolean functions

Abstract

Boolean functions have numerous applications in domains as diverse as coding theory, cryptography, and telecommunications. Heuristics play an important role in the construction of Boolean functions with the desired properties for a specific purpose. However, there are only sparse results trying to understand the problem's difficulty. With this work, we aim to address this issue. We conduct a fitness landscape analysis based on Local Optima Networks (LONs) and investigate the influence of different optimization criteria and variation operators. We observe that the naive fitness formulation results in the largest networks of local optima with disconnected components. Also, the combination of variation operators can both increase or decrease the network size. Most importantly, we observe correlations of local optima's fitness, their degrees of interconnection, and the sizes of the respective basins of attraction. This can be exploited to restart algorithms dynamically and influence the degree of perturbation of the current best solution when restarting.