Localization is crucial to wireless sensor networks. Among the recently proposed localization algorithms, the mobile anchor-assisted localization (MAL) algorithm seems promising. A MAL algorithm using a single mobile anchor has low energy consumption but a high localization error. Conversely, a MAL algorithm with three or more mobile anchors has minor localization errors but high energy consumption. By balancing energy consumption and localization accuracy, our study developed a localization algorithm assisted by two mobile anchors. A mobile anchor traverses the network along a double anchor SCAN (DASCAN) path, which divides the deployment region into grids and requires the two mobile anchors to traverse different horizontal lines in a zigzag pattern. Sensor nodes estimate their locations using a multiple-disturbance strategy grey wolf optimization (MDS-GWO) algorithm, which improves optimization by introducing a nonlinearly decreasing weight, a random perturbation of grey wolves and a mirror grey wolf. Using MATLAB, DASCAN was compared with GTURN, GSCAN, PP-MMAN, H-Curves, M-Curves, and SCAN paths by their energy consumption and localization rates. The localization error of MDS-GWO was compared with trilateration, PSO, WOA, and GWO. The impacts of radio irregularity, radio radius, and fading effect on MDS-GWO with different paths were also analyzed. The simulation results showed that the energy consumption of DASCAN was, on average, 30.1% less than GSCAN, GTURN, and PP-MMAN, but they had almost the same localization accuracy. The energy consumption of DASCAN was an average of 18.67% more than M-Curves, H-Curves, and SCAN, but the localization error of DASCAN was average of 32.3% less than SCAN, H-Curves, and M-Curves. The localization error of MDS-GWO was average of 25.5% less than trilateration, PSO, WOA, and GWO. Moreover, the performance of the proposed algorithm was less affected by different setups than the compared methods.