Search-based software testing (SBST) often uses objective-based approaches to solve testing problems. There are, however, situations where the validity and completeness of objectives cannot be ascertained, or where there is insufficient information to define objectives at all. Incomplete or incorrect objectives may steer the search away from interesting behavior of the software under test (SUT) and from potentially useful test cases. This papers investigates the degree to which exploration-based algorithms can be used to complement an objective-based tool we have previously developed and evaluated in industry. In particular, we would like to assess how exploration-based algorithms perform in situations where little information on the behavior space is available a priori. We have conducted an experiment comparing the performance of an exploration-based algorithm with an objective-based one on a problem with a high-dimensional behavior space. In addition, we evaluate to what extent that performance degrades in situations where computational resources are limited. Our experiment shows that exploration-based algorithms are useful in covering a larger area of the behavior space and result in a more diverse solution population. Typically, of the candidate solutions that exploration-based algorithms propose, more than 80% were not covered by their objective-based counterpart. This increased diversity is present in the resulting population even when computational resources are limited. We conclude that exploration-focused algorithms are a useful means of investigating high-dimensional spaces, even in situations where limited information and limited resources are available.