Regret is defined as the deviation of objective value from the perfect information solution, and serves as an important evaluation metric for decision-making under uncertainty. This paper proposes a novel framework that effectively incorporates the minimax regret criterion into two-stage adaptive robust optimization (ARO). In addition to the conventional robustness criterion, this ARO framework also simultaneously optimizes the worst-case regret to push the performance of the resulting solution towards the utopia one under perfect information. By using a data-driven uncertainty set, we formulate a multiobjective ARO problem that generates a set of Pareto-optimal solutions to reveal the systematic trade-offs between the conventional robustness and minimax regret criteria. The resulting multi-level mixed-integer programming problem cannot be solved directly by any off-the-shelf optimization solvers, so we further propose tailored column-and-constraint generation algorithms to address the computational challenge. Two applications on process network planning and batch process scheduling are presented to demonstrate the applicability of the proposed framework and the efficiency of the proposed solution algorithms. (C) 2017 Elsevier Ltd. All rights reserved.