A partial disassembly line balancing problem under uncertainty is studied in this paper, which concerns the allocation of a sequence of tasks to workstations such that the overall profit is maximised. We consider the processing time uncertainty and develop robust solutions to accommodate it. The problem is formulated as a non-linear robust integer program, which is then converted into an equivalent linear program. Due to the intractability of such problems, the exact algorithms are only applicable to small-scale instances. We develop an improved migrating birds optimisation algorithm. Two enhancement techniques are proposed. The first one finds the optimal number of tasks to be performed for each sequence rather than random selection used in the literature; while the second one exploits the specific problem structure to construct effective neighbourhoods. The numerical results show the strong performance of our proposal compared to CPLEX and the improved gravitational search algorithm (IGSA), especially for large-scale problems. Moreover, the enhancement due to the proposed techniques is obvious across all instances considered.