Drug resistance and tumor relapse in melanoma patients is attributed to a combination of genetic and non-genetic mechanisms. Non-genetic mechanisms of drug resistance commonly involve reversible changes in the cell-state or phenotype, i.e., alterations in molecular profiles that can help cells escape being killed by targeted therapeutics. In melanoma, one of the most common mechanisms of non-genetic resistance is de-differentiation, which is characterized by loss of melanocytic markers. While various molecular attributes of de-differentiation have been identified, the transition dynamics remains poorly understood. Here, we construct cell-state transition landscapes, to quantify the stochastic dynamics driving phenotypic switch in melanoma based on its underlying regulatory network. These landscapes reveal the existence of multiple alternative paths to resistance - de-differentiation and transition to a hyper-pigmented phenotype. Finally, by visualizing the changes in the landscape during in silico molecular perturbations, we identify combinatorial strategies that can lead to the most optimal outcome - a landscape with the minimal occupancy of the two drug-resistant states. Therefore, we present these landscapes as platforms to screen possible therapeutic interventions in terms of their ability to lead to most favourable patient outcomes.