In order to improve the economy and battery service life during the operation of household heat pump DC microgrid, a multi-scenario joint optimization model of household heat pump DC microgrid was established, which taked into account the factors of power generation cost, discharge cost, power purchase cost, power sales revenue, power balance constraints, and charging/discharging time constraints. Taking the lowest cost and the optimal battery charging state as the objective function, the improved swarm adaptive particle swarm optimization algorithm was used to balance the local optimization and global optimization problems of multi-objective optimization. By comparing and analyzing the simulation results, it is found that the improved particle swarm algorithm outperforms the other algorithms in different scenarios. Especially in sunny days with sufficient PV power generation, the operation cost of this algorithm is 8.8% lower than the traditional particle swarm algorithm, 24% lower than the genetic algorithm, and 13.9% lower than the linear programming algorithm. The results validate the effectiveness of the improved particle swarm algorithm in reducing the daily operating cost in the grid-connected mode of household heat pump microgrid.