Poor surface finish on die and mould transfers the bad quality to processed parts. High surface roughness is an example of bad surface finish that is normally reduced by manual polishing after conventional milling machining process. Therefore, in order to avoid disadvantages by manual polishing and disadvantage by the machining, a sequence of two machining operations is proposed. The main operation is run by the machining and followed by Rotary Ultrasonic Machining Assisted Milling (RUMAM). However, this sequence operation requires optimum input parameters to generate the lowest surface roughness. Hence, this paper aims to optimize the input parameters for both machining operations by three soft-computing approaches – Genetic Algorithm, Tabu Search, and Particle Swarm Optimization. The method adopted in this paper begins with a fitness function development, optimization approach usage and ends up with result evaluation and validation. The soft-computing approaches result outperforms the experiment result in having minimum surface roughness. Based on the findings, the conclusion suggests that the lower surface roughness can be obtained by applying the input parameters at maximum for the cutting speed and vibration frequency, and at minimum for machining feed rate. This finding assists manufacturers to apply proper input values to obtain parts with minimum surface roughness.