ORIGINAL ARTICLE A standard deviation based firefly algorithm for multi-objective optimization of WEDM process during machining of Indian RAFM steel Arindam Majumder 1 • Argha Das 1 • Pankaj Kr. Das 1 Received: 12 October 2015 / Accepted: 6 July 2016 Ó The Natural Computing Applications Forum 2016 Abstract Non-conventional machining processes always suffer due to their low productivity and high cost. How- ever, a suitable machining process should improve its productivity without compromising product quality. This implies the necessity to use efficient multi-objective opti- mization algorithm in non-conventional machining pro- cesses. In this present paper, an effective standard deviation based multi-objective fire-fly algorithm is pro- posed to predict various process parameters for maximum productivity (without affecting product quality) during WEDM of Indian RAFM steel. The process parameters of WEDM considered for this study are: pulse current (I), pulse-on time (T on ), pulse-off time (T off ) and wire tension (WT).While, cutting speed (CS) and surface roughness (SR) were considered as machining performance parame- ters. Mathematical models relating the process and response parameters had been developed by linear regres- sion analysis and standard deviation method was used to convert this multi objective into single objective by uni- fying the responses. The model was then implemented in firefly algorithm in order to optimize the process parame- ters. The computational results depict that the proposed method is well capable of giving optimal results in WEDM process and is fairly superior to the two most popular evolutionary algorithms (particle swarm optimization algorithm and differential evolution algorithm) available in the literature. Keywords Multi-objective optimization  Standard deviation method  Firefly algorithm  Wire cut EDM  Reduced activation ferritic martensitic steel List of symbols I Pulse current T on Pulse-on time T off Pulse-off time WT Wire tension CS Cutting speed min CS The minimum value of cutting speed max CS The maximum value of cutting speed SR Surface roughness min SR The minimum value of surface roughness max SR The maximum value of surface roughness FA Firefly algorithm PSO Particle swarm optimization algorithm DE Differential evolution algorithm RAFM Reduced activation ferritic martensitic steel WEDM Wire electrical discharge machining r Distance between two fire-fly I(r) Light intensity at distance (r) I 0 Original light intensity at zero distance c Light absorption coefficient b Attractiveness measure at distance (r) b 0 Original attractiveness at zero distance x i *(k) Normalized value of output parameter ‘i’ at kth experiment x i (o) (k) Experimental value of output parameter ‘i’ at kth experiment minx i (o) (k) The minimum value of output parameter ‘i’ maxx i (o) (k) The maximum value of output parameter ‘i’ m i Variances of normalized output parameter ‘i’ l i Mean of all normalized experimental values (n) for output parameter ‘i’ & Arindam Majumder arindam2012@gmail.com 1 Mechanical Engineering Department, National Institute of Technology-Agartala, Agartala, Tripura 799046, India 123 Neural Comput & Applic DOI 10.1007/s00521-016-2471-9