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In this research work, the machinability of turning Hastelloy X with a PVD Ti-Al-N coated insert tool in dry, wet, and cryogenic machining environments is investigated. The machinability indices namely cutting force (CF), surface roughness (SR), and cutting temperature (CT) are studied for the different set of input process parameters such as cutting speed, feed rate, and machining environment, through the experiments conducted as per L₂₇ orthogonal array. Minitab 17 is used to create quadratic Multiple Linear Regression Models (MLRM) based on the association between turning parameters and machineability indices. The Moth-Flame Optimization (MFO) algorithm is proposed in this work to identify the optimal set of turning parameters through the MLRM models, in view of minimizing the machinability indices. Three case studies by considering individual machinability indices, a combination of dual indices, and a combination of all three indices, are performed. The suggested MFO algorithm’s effectiveness is evaluated in comparison to the findings of Genetic, Grass-Hooper, Grey-Wolf, and Particle Swarm Optimization algorithms. From the results, it is identified that the MFO algorithm outperformed the others. In addition, a confirmation experiment is conducted to verify the results of the MFO algorithm’s optimal combination of turning parameters.