Many approximate heuristics for optimization are either based on neighborhood search or on the construction of solutions. Examples for the latter ones include ant colony optimization and greedy randomized adaptive search procedures. These techniques generally construct solutions probabilistically by sampling a probability distribution over the search space. Solution constructions are generally independent from each other. Recent algorithmic variants include two important features that are inspired by deterministic branch & bound derivatives such as beam search: the use of bounds for evaluating partial solutions, and the parallel and non-independent construction of solutions. In this paper we first give a theoretical reason of why these variants have the potential to improve over standard algorithms. Second, we confirm our theoretical findings by means of practical examples. Our results for the open shop scheduling problem clearly demonstrate the potential of using parallel and non-independent solution constructions.