Multicarrier transmission strategy provides great benefits in wireless communication technology. For this reason, all of the waveform contenders proposed for the fifth generation and beyond technologies are built on this strategy. Universal filtered multicarrier (UFMC) is one of the foremost representatives of the related waveform contenders. However, utilizing the multicarrier transmission strategy causes the UFMC to generate transmission signals with high peak-to-average power ratio (PAPR), which leads to serious deteriorations in the communication quality. In order to solve this issue, it is crucial to reduce the PAPR of transmission signal before giving it to the wireless channel. With the aim of developing an efficient PAPR reduction scheme for the UFMC waveform, we first developed a new discrete version of the invasive weed optimization (DIWO) algorithm and integrated it to one of the classical PAPR reduction techniques called partial transmit sequence (PTS) as a phase optimizer. By doing so, we obtained an advanced scheme called DIWO-PTS. The function of DIWO algorithm in this new scheme is to optimize the phase sequences in discrete space. The usage of DIWO as a phase optimizer enables PTS to reach better phase combinations in less number of searches. Thus, it becomes possible to boost the PAPR reduction performance of the PTS scheme to a quite high level. Simulation results support the advantage of DIWO-based phase optimization. In the simulations, neither of the algorithms used for comparison in our paper could reach the performance level achieved by DIWO algorithm due to its efficient optimization capability.