In DS-CDMA communications, pseudonoise sequence sets must fulfil crosscorrelation and autocorrelation minimization properties in order to minimize multiuser interference and improve the probability of acquisition. When a multiresolutive acquisition scheme is to be used  the pseudonoise sequences (PN) have to satisfy more strict constraints for achieving proper acquisition performance. In this paper we present a multiobjective evolutionary algorithm to design a set of pseudonoise sequences meeting all the constraints that the receiver of DS-CDMA communication system demands. The new pseudonoise sequence set accomplishes not only the basic pseudorandom waveform properties but also the new crosscorrelation and autocorrelation features required by the multiresolutive structure, obtaining better results in terms of crosscorrelation and stability. This way a better trade off between mean acquisition time and computational requirements can be achieved regarding traditional adquisition schemes.