Robust optimization tries to find flexible solutions when solving problems with uncertain scenarios and vague information. In this paper we present a multiobjective evolutionary algorithm to solve robust multiobjective optimization problems. This algorithm is a novel adaptive method able to evolve separate populations of robust and non-robust solutions during the search. It is based on the infeasibility driven evolutionary algorithm (IDEA) and uses an additional objective to evaluate the robustness of the solutions. The original and adaptive IDEAs are applied to solve the r-TSALBP-m/A, an assembly line balancing model that considers a set of demand production plans and includes robustness functions for measuring the temporal overloads of the stations of the assembly line with respect to the plans. Our results show that the proposed adaptive IDEA gets more robust non-dominated solutions for the problem. Also, we show that, for the case of the r-TSALBP-m/A, we can obtain Pareto fronts with a higher convergence by using the adaptive version of the algorithm.