Conflict-Free Genetic Algorithm with Nash Equilibrium Seeking for Game-Based Battery Swapping Station Recommendation

The rapid growth of electric vehicles (EVs) has led to significant challenges in providing efficient and sustainable charging solutions. This paper addresses the battery swapping station (BSS) recommendation problem by proposing a novel conflict-free genetic algorithm (CFGA) integrated with a Nash equilibrium seeking (NES) approach to identify optimal Nash equilibrium (ONE) solutions to such a non-cooperative optimization problem. The CFGA employs specialized crossover and mutation operators to generate offspring that satisfy the constraints of the problem, ensuring that each EV decides a unique battery swap strategy without conflict. Firstly, an order crossover operator is proposed to preserve the order of genes in the chromosomes. Secondly, a replacement and exchange mutation operator is proposed to enhance mutation diversity. The resulting optimal solution is then used as the initial strategy for the NES, which iteratively converges to the ONE. The proposed CFGA with NES algorithm is evaluated under both small-scale and large-scale cases, demonstrating its effectiveness in achieving a balance between costs for EVs and utilization for BSSs. The study's findings have practical implications for the smart grid and EV integration, offering a robust method for optimizing EV infrastructure and operations.