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There is no meta-heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta-heuristic algorithms. Out of all meta-heuristic algorithms, swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves, considered as apex predators, motivated us to simulate Grey Wolves in the optimization of geophysical data sets. The grey wolf optimizer is a swarm-based meta-heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behaviour of Grey Wolves. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolves. The three main phases of hunting, that is searching, encircling and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the grey wolf optimizer, we performed inversion on the total gradient of magnetic, gravity and self-potential anomalies. The results have been compared with the particle swarm optimization technique. Global minimum for all the examples from grey wolf optimizer was obtained with seven wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise-free and noise-corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that, compared with particle swarm optimization, the grey wolf optimizer is less sensitive to search space variations. Inversion of noise-corrupted data shows that grey wolf optimizer has a better capability in handling noisy data as compared to particle swarm optimization. Practical applicability of the grey wolf optimizer has been demonstrated by adopting four profiles (i.e. surface magnetic, airborne magnetic, gravity and self-potential) from the published literature. The grey wolf optimizer results show better data fit than the particle swarm optimizer results and match well with borehole data.