This paper reports our experiments to properly handle the multiobjective optimization nature of poetry generation - as defined in Manurung (2003) - as a stochastic search that seeks to produce a text that simultaneously satisfies the properties of grammaticality, meaningfulness, and poeticness. In particular, we employ the SPEA2 Algorithm (Zitzler, Laumanns, and Thiele 2001). Various results show that it consistently outperforms our previous system in its ability to generate a meaningful metrical text according to given semantic and metre specifications, and in some cases is able to generate the intended text, whereas our previous system fails to do so. However, it is still unable to reach the goal of generating an entire poem. We conclude with suggestions for further work to address this shortcoming.