Population initialization is one of the important tasks in evolutionary and genetic algorithms (GAs). It can affect considerably the speed of convergence and the quality of the obtained results. In this paper, some heuristic strategies (procedures) for construction of the initial populations in genetic algorithms are investigated. The purpose is to try to see how the different population initialization strategies (procedures) can influence the quality of the final solutions of GAs. Several simple procedures were algorithmically implemented and tested on one of the hard combinatorial optimization problems, the quadratic assignment problem (QAP). The results of the computational experiments demonstrate the usefulness of the proposed strategies. In addition, these strategies are of quite general character and may be easily transferred to other population-based metaheuristics (like particle swarm or bee colony optimization methods).