Related information of optimal cutting parameters for machining and spring force operations is required for process planning. Numerous nonlinear constrained machining models have been developed with the objective of determining optimal operating conditions. The purpose of this article includes studying two algorithms to test their efficiency in solving several benchmark machining models. Two promising metaheuristic algorithms for the numerical process improvement are particle swarm optimisation (PSO) and firefly (FFA) algorithms. A brief description of each algorithm is presented along with its pseudocode to facilitate the implementation and use of such algorithms by researchers and practitioners. Benchmark comparisons between the algorithms are presented in terms of processing time, convergence speed, and quality of the results. The experimental results show that FFA is clearly and consistently superior compared to the PSO both with respect to precision as well as robustness of the results including design points to achieve the final solution. Only for simple data sets, the PSO and FFA can obtain the same quality of performance measures. Apart from higher levels of performance measures, FFA is easy to implement and requires hardly any parameter tuning compared to substantial tuning for the PSO.