In this paper, we consider multi-objective knapsack problems where the decision maker's preferences are represented by a non-linear aggregation function whose parameters are initially not known. More precisely, we focus on rank-dependent aggregators such as ordered weighted averages (OWA) and Choquet integrals which are non-linear scalarizing functions that assign weights to ranks rather than to objectives in the aggregation process, so as to control the importance attached to the bottom performance or to any other order statistics; for instance, an OWA operator with decreasing weights helps promoting balanced solutions while ensuring overall efficiency. In this setting, we propose new interactive heuristic methods consisting in combining regret-based preference elicitation and heuristic search so as to quickly focus the search on the most promising solutions. For OWA operators and Choquet integrals, the proposed methods run in polynomial time and are guaranteed to generate no more than a polynomial number of queries. We perform numerical tests comparing our methods to different interactive solving methods in order to show the practical efficiency of our approach in terms of number of queries, computation time and gap to optimality.