A Q-Learning Hybrid BRKGA Applied to the Knapsack Problem with Forfeits

This paper presents a hybrid BRKGA (Q-HBRKGA) that combines BRKGA with Q-learning and a Local Branching technique to solve the Knapsack Problem with Forfeits(KPF). The aim is to tackle this problem, a vari-ant of the 0–1 Knapsack Problem, where a penalty cost is imposed when both items of a forfeit pair are included in the solution. Notably, Q-HBRKGA achieves superior results compared to existing approaches, establishing a valid strategy for KPF problem-solving. Computational experiments, utilizing benchmark instances, demonstrate the efficacy of Q-HBRKGA by outperforming state-of-the-art methods documented in the literature.