Modern Web applications offer a rich and unique user experience by taking advantages of the so called Web 2.0 technologies, among which Ajax. Ajax supports the intensive use of asynchronous communication between client-pages and the Web server and it allows on-the-fly manipulations of client-pages content and structure to realize a rich, dynamic and interactive user interface. Correspondingly, new types of faults that cannot be easily revealed by existing Web testing techniques are associated with modern Ajax-based applications. In our previous investigations, we used state-based testing for event sequence generation and it proved to be quite effective in exposing Ajax specific faults. However, the search space of the semantically interacting event sequences is huge, as it can grow exponentially with the event sequence length. In this paper, we apply search-based algorithms, namely hill climbing and simulated annealing, to the problem of generating maximally diverse event sequences of various lengths. In this way, we control the size of the generated test suites, while keeping the included test cases as diverse as possible. We evaluate the performance of the algorithms on two open source Ajax applications.