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An efficient estimation of transmission map for desmogging model is an ill-posed problem. The quality of restored image depends upon the accurate estimation of transmission map. However, transmission map obtained using various dehazing models is not accurate in case of images with large haze gradient, and fail while image desmogging. As a result, the restored images suffer from numerous issues such as halo and gradient reversal artefacts, edge and texture distortion, color distortion, etc. Therefore, this paper designs a novel transmission map estimation by using weighted integrated transmission maps obtained from foreground and sky regions. Additionally, transmission map is further refined using an integrated variational regularized model with hybrid constraints. However, the proposed technique suffers from hyper-parameters tuning issue, therefore, in this paper, a non-dominated sorting genetic algorithm is also used to tune the hyper-parameters of the proposed technique. The comparison of designed desmogging model is also done with other dehazing models by considering benchmark and real-time hazy images. The comparative analyses reveal that the designed model outperforms existing models subjectively and quantitatively.