Hybrid BRKGA with Reinforcement Learning applied to bike share station allocation

The optimization of bike-sharing station placements in urban areas is an essential issue in the context of smart cities. One way to model this problem is through the Knapsack Problem with Forfeit Sets (KPFS). In this model, each bike-sharing station is treated as an item with specific costs and associated profits. Placing multiple stations close can lead to underutilization and increased maintenance expenses, representing forfeit sets where penalties are incurred if predefined allowances are exceeded. To address this problem in smart cities optimization, we propose a hybrid metaheuristic that combines a Biased Random-Key Genetic Algorithm (BRKGA) with Q-learning and Local Branching, referred to as QVND-HBRKGA. This approach integrates a reinforcement learning-based variable neighborhood descent to explore neighborhood solutions. Computational experiments demonstrate that QVND-HBRKGA effectively balances resource allocation and minimizes penalties, outperforming existing methods in the literature.