Over　recent　decades,　metasurfaces　have　achieved　significant　advancements　in　the　development　of　integrated　and　miniaturized　optical　devices.　A　notable　area　of　research　within　this　field　is　the　development　of　metalenses.　In　this　study,　we　propose　a　broadband　achromatic　metalens　that　operates　across　a　wide　wavelength　range　from　9.6　mu　m　to　11.6　mu　m.　For　the　initial　metalens,　based　on　the　geometric　phase　principle,　micro　adjustments　are　made　to　the　dimensions　of　individual　nanopillars　to　compensate　for　phase　deviations.　To　efficiently　optimize　this　metalens,　we　employ　a　hierarchical　iteration　strategy　that　divides　the　optimization　space　into　overlapping　groups,　significantly　reducing　the　loss　rate　and　computational　effort.　Within　each　group,　an　improved　reptile　search　algorithm　(IRSA)　is　proposed　to　find　the　optimal　solution.　This　algorithm　incorporates　a　quantum　mutation　strategy　to　address　the　issues　of　premature　convergence　and　imbalance　during　its　search　process.　The　results　indicate　that　the　proposed　metalens　attains　an　average　focusing　efficiency　of　39.7%　and　the　correction　of　chromatic　aberration　is　achieved　with　a　coefficient　of　variation　of　only　2.7%.　This　achievement　represents　a　significant　advancement　in　the　field　of　achromatic　metalenses.