It is crucial to reveal the energy conversion and heat and mass transfer characteristics in the electric arc furnaces (EAFs). In this paper, a transient mathematical model was built to adequately capture the distribution of multi-physical fields in EAF. The numerical modeling method was verified against brown corundum smelting experiment data. In addition, the influence on the brawn corundum smelting process of the typical operating parameters has been examined, and the major problems which limit the performance improvement of smelting were analyzed. Moreover, four indicators were proposed to comprehensively evaluate the EAF performance, consisting of liquid volume fraction β, energy efficiency η, temperature rise index ς, and temperature uniformity index ξ. Furthermore, the optimal combination of operating parameters was selected automatically based on the back propagation (BP) neural network predicting model and non-domestic sorting genetic algorithm II (NSGA-II). The results showed that the local overheating phenomenon is serious and that homogenizing the energy distribution in the furnace is the key to improving the melting performance. Increasing electrode immersion and voltage can significantly increase the rate of heat and mass transfer. In the case of ψ = 0.75, υ = 0.6, when χ is increased from 0.2 to 0.6, τmax is shortened by 13.3% and ηmax is increased by 12.0%. While with ψ = 0.75 and χ = 0.4, τmax is reduced by 36.0% when υ increases from 0.2 to 1.0, but ηmax is also decreased by 7.0%. It was found that decreasing the height diameter ratio will improve the overall EAF smelting performance, but it also increases the area of heat loss. In the case of χ = 0.4, υ = 0.6, ξave and ηmax improved by 3.1 and 14.5%, respectively, when ψ decreases from 1.0 to 0.5. The EAF performances are considerably enhanced in comparison to the operating basic parameters (ψ = 0.75, χ = 0.4 and υ = 0.6), subject to optimal operation parameters (ψ = 0.61, χ = 0.59 and υ = 0.59). In this case, τmax and ςmax reduced by 6.2 and 4.1%, respectively, while ηmax and ξave increased by 6.8 and 1.0%, respectively.