In recent times, non-orthogonal multiple access (NOMA) is a growing technique for the future 5G networks to address the incredible evolution of mobile data traffic and radio access issues based on concurrent communication between multiple users. However, the performance of the NOMA is affected due to an inappropriate power allocation to the users, which affects the system's sum rate. In this research, the multi-objective sum rate-based butterfly optimization algorithm (M-SRBOA) is proposed to address the power allocation challenges of the NOMA network. The M-SRBOA is optimized by considering distinct objective functions like sum rate and Rayleigh fading coefficients. Therefore, the developed M-SRBOA method allocates an appropriate power for all users of the NOMA, which increases higher sum rate. The performance of the M-SRBOA method is analyzed using achievable sum rate and outage probability. The existing researches such as equal power allocation (EPA), optimal power allocation (OPA) factors and difference of convex optimization (DCO) are used to justify the efficiency of the M-SRBOA method. The achievable sum rate of M-SRBOA for the SNR of 15 dB with noise variance of 2 is 13.09 bps/Hz, which is high compared to the EPA, OPA and DCO.