  The multiple knapsack problem with grouped items aims to maximize rewards by
assigning groups of items among multiple knapsacks, considering knapsack
capacities. Either all items in a group are assigned or none at all. We propose
algorithms which guarantee that rewards are not less than the optimal solution,
with a bound on exceeded knapsack capacities. To obtain capacity-feasible
solutions, we propose a binary-search heuristic combined with these algorithms.
We test the performance of the algorithms and heuristics in an extensive set of
experiments on randomly generated instances and show they are efficient and
effective, i.e., they run reasonably fast and generate good quality solutions.
