The purpose of this study was to determine the optimal surface roughness for an end milled Al 7075-T6 alloy by using the Taguchi method and multiobjective quantum behaved particle swarm optimisation (MOQPSO). First, the Taguchi orthogonal array (L27)(3(5)) and analysis of variance (ANOVA) were used to determine the factors crucial to surface roughness: the feedrate, spindle speed and cutting depth. Response surface methodology (RSM) was then used to construct prediction models for the surface roughness characteristics R-a,R- R-max and R-z. Finally, an MOQPSO algorithm was used to solve the multiobjective optimisation problem. The results show that the surface roughness quality generated using this algorithm is superior to that produced in non-optimal conditions, Taguchi method and traditional multiobjective particle swarm optimisation. Therefore, the methods proposed in this study enhance machining quality and can be widely applied to other metal materials to improve machining efficiency.