Multi-threshold CMOS (MTCMOS) is currently the most popular methodology in industry for implementing a power gating design, which can effectively reduce the leakage power by turning off inactive circuit domains. However, large peak current may be consumed in a power-gated domain during its sleep-to-active mode transition. As a result, major IC foundries recommend turning on power switches one by one to reduce the peak current during the mode transition, which requires a Hamiltonian-cycle routing to serially connect all the power switches. In this paper, we propose an efficient power-switch routing framework, which can effectively and efficiently find a feasible Hamiltonian-cycle routing among power switches without violating the Manhattan distance constraint between any two power switches while handling the irregular placement of the power switches resulting from the hard macros. The proposed framework is compliant to commercial APR tools and has been used in a major design-service company for taping out complex MTCMOS designs.