This chapter provides a brief introduction to the basic particle swarm optimisation (PSO) algorithm and some of its notable variants available in the literature. Then a process of developing multi-objective PSO (MOPSO) algorithms is described, and the approach is utilised to develop two alternative MOPSO algorithms. A case study exercise is presented where the two MOPSO algorithms are used in the design of command shapers for vibration reduction of a single-link flexible manipulator. The implementation results achieved are assessed and discussed.