It is well known that the performances of evolutionary algorithms are influenced by the quality of their initial populations. Over the years, many different techniques for generating an initial population by uniformly covering as much of the search space as possible have been proposed. However, none of these approaches considers any input from the function that must be evolved using that population. In this paper, a new initialization technique, which can be considered a heuristic space-filling approach, based on both function to be optimized and search space, is proposed. It was tested on two well-known unconstrained sets of benchmark problems using several computational intelligence algorithms. The results obtained reflected its benefits as the performances of all these algorithms were significantly improved compared with those of the same algorithms with currently available initialization techniques. The new technique also proved its capability to provide useful information about the function's behavior and, for some test problems, the initial population produced high-quality solutions. This method was also tested on a few multiobjective problems, with the results demonstrating its benefits.