Definition
Bi Knapsack Optimisation Problem
Instance: Indexed items
with positive integer sizes and nonnegative integer capacities , encoded in binary. Feasible solutions: Index sets
with
Objective: Maximise
, the number of selected items.
Each selected item consumes capacity in both dimensions simultaneously. Unlike Two-Bag Knapsack, there is no choice of which bag receives an item. Equal size pairs at different indices remain distinct items.