Multi-Size Facility Allocation Under Competition: A Model with Competitive Decay and Reinforcement Learning-Enhanced Genetic Algorithm

In modern urban planning, the problem of bank location requires not only considering geographical factors but also integrating competitive elements to optimize resource allocation and enhance market competitiveness. This study addresses the multi-size bank location problem by incorporating competitive factors into the optimization process through a novel reinforcement learning-enhanced genetic algorithm (RL-GA) framework. Building upon an attraction-based model with competitive decay functions, we propose an innovative hybrid optimization approach that combines evolutionary computation with intelligent decision-making capabilities. The RL-GA framework employs Q-learning principles to adaptively select optimal genetic operators based on real-time population states and search progress, enabling meta-learning where the algorithm learns how to optimize rather than simply optimizing. Unlike traditional genetic algorithms with fixed operator probabilities, our approach dynamically adjusts its search strategy through an $\epsilon$-greedy exploration mechanism and multi-objective reward functions. Experimental results demonstrate that the RL-GA achieves improvements in early-stage convergence speed while maintaining solution quality comparable to traditional methods. The algorithm exhibits enhanced convergence characteristics in the initial optimization phases and demonstrates consistent performance across multiple optimization trials. These findings provide evidence for the potential of intelligence-guided evolutionary computation in facility location optimization, offering moderate computational efficiency gains and adaptive strategic guidance for banking facility deployment in competitive environments.