The aim of the alumina evaporation process is to improve the concentration of sodium aluminate solution by evaporating the excess water contained in the solution. The evaporation is achieved using heat from steam. Since steam consumption is the major operating costs, in this paper, we investigate an operation optimisation problem for the evaporation process to minimise steam consumption subject to a constraint on the particular quality of the final sodium aluminate solution. This paper proposes a new particle swarm optimisation (PSO) algorithm based on vortex motion to solve this optimisation problem. We demonstrate the effectiveness of the PSO algorithm on benchmark functions. We then apply it to a real industrial evaporation process, where the optimal results show that the steam consumption is considerably reduced. (c) 2012 Canadian Society for Chemical Engineering