This paper studies the particle swarm optimization (PSO) with switched topology and its application to the multi-solution problems (MSPs). The switched topology can give variety in the swarm structure and can be effective to control information transmission speed. We introduce the switched distance as a basic measure to evaluate the switched topology. The proposed PSO does not include stochastic parameters and is suitable for theoretical analysis. Applying the proposed PSO to typical benchmarks of the MSPs, the algorithm efficiency is investigated.