An improvement matheulist for the backpack problem with penalty sets

This work presents a mathemeuristic approach to the backpack problem with penalty sets, which is a recently introduced variant of the classical backpack problem. The objective of this work is to evaluate the efficacy of a well-known matheulistic, the large neighborhood search, applied to this variant. Matheuristics combines the partial destruction of an initial solution with its optimized repair using integer linear programming. The results are compared with those obtained by an exact algorithm and by the state-of-the-art, in order to measure the quality of the solutions generated. The study demonstrates that methods such as large neighborhood search can be competitive in solving more complex variants of the backpack problem.