Randomized search heuristics (e.g., evolutionary algorithms, simulated annealing etc.) are very appealing to practitioners, they are easy to implement and usually provide good performance. The theoretical analysis of these algorithms usually focuses on convergence rates. This paper presents a mathematical study of randomized search heuristicswhich use comparison based selectionmechanism. The twomain results are: (i) comparison-based algorithms are the best algorithms for some robustness criteria, (ii) introducing randomness in the choice of offspring improves the anytime behavior of the algorithm. An original Estimation of Distribution Algorithm combining (i) and (ii) is proposed and successfully experimented.