Surrogate upper bound sets for bi-objective bi-dimensional binary knapsack problems.

•We define an upper bound set for the bi-objective bi-dimensional knapsack problem.•It is based on the surrogate relaxation and generalizes the dual surrogate problem.•We propose two exact algorithms: an enumerative algorithm and its improved version.•We analyze the surrogate multipliers and the dominance relations between bound sets.•Based on the improved exact algorithm, an approximated version is derived.