## 1 Introduction
The multiobjective optimization approach was proposed to obtain the optimal combination of milling parameters for achieving minimum cutting power, surface roughness and maximum material removal rate through using the adaptive neuro fuzzy interface system combining the vibration and communication particle swarm optimization algorithm [11]. Alternatively, the genetic algorithm was also applied for optimizing the cutting parameters to reduce the energy consumption as well as the processing time [12]. Their study demonstrated that 32.07% of the consumed energy can be decreased and 34.11% of the processing time can be reduced. [PERSON] et al. [13] conducted an experimental study for the optimization of the machining parameters in high-speed milling process of Inconel 718 based on chip variation. In order to maximize the material removal rate and to minimize the machining time as well as the surface roughness, the grey relational analysis was used for optimizing the output parameters on the turning of oil-hardened nonshrinking die steel [14]. By reviewing the previous literature of machining parameter optimization, the search of optimal cutting parameters was mainly achieved based on the assumed connection between the work-piece surface quality and the tooling parameters. However, the work-piece surface quality, such as the surface roughness, is partially influenced by the combinations of machining parameters and the tool machine vibration behaviors. Furthermore, due to the nature of cutting Inconel 718 work-piece, the factors, such as build-up-edge (BUE) phenomenon and rapid tool wearing, may also affect the surface quality during the cutting steps, and hence it makes the prediction of surface roughness more difficult in the manufacturing process. To advance the state-of-art of cutting parameter optimization based on surface roughness prediction in this research, the characteristics of BUE phenomenon in cutting Inconel 718 were assumed to reflect on the vibration behaviors. The vibration measurements of spindle and fixture are investigated during the milling process of Inconel 718. On the other hand, the factor of tool wearing was simplified by computing the accumulated volume removal as well as the accumulated operation time for each cutter. The correlation between the roughness average (Ra) values of Inconel 718 work-piece and the vibration signals was analyzed to extract the vibration features. Owing to the nature of sequential milling process in this research, the signal features may be various in different milling stages. It is also well known that the Elman neural network has the characteristics of general recurrent neural network that accommodates the time-varying features of data series and has the outperformance of prediction [15]. Therefore, the Elman neural network was utilized to build the surface roughness prediction model of Inconel 718 in the milling process. Based on the prediction model, the cutting parameters were optimized through the PSO algorithm. In general, the feed rate is one of the factors dominating the Ra value of work-piece surface. The Ra value normally increases as increasing the feed rate under the condition of fixing the other parameters. Meanwhile, the cutting time consumption is determined by the feed rate. Based on this concept, the optimization scenario was set to maximize the feed rate under the different constraints of Ra values. Therefore, the optimal combination of cutting parameters can achieve acceleration of the tooling process for different surface quality requirements of Inconel 718 work-piece. For the purpose of further usage and reference, all the measurements, the corresponding Ra values and the cutting parameters utilized in this research article are available at the website [16].