Bi-Criteria Multiple Knapsack Problem with Grouped Items

TL;DR

This paper introduces algorithms for a complex variant of the multiple knapsack problem with grouped items, providing guarantees on solution quality and capacity constraints, validated through extensive experiments.

Contribution

It presents new algorithms and heuristics for the bi-criteria grouped items multiple knapsack problem, ensuring near-optimal rewards with controlled capacity violations.

Findings

Algorithms guarantee rewards close to the optimal solution.

Heuristics effectively produce capacity-feasible solutions.

Methods are efficient and generate high-quality solutions in experiments.

Abstract

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.