In　recent　decades,　metasurfaces　have　shown　remarkable　advancements　in　the　development　of　integrated　and　miniaturized　optical　devices.　Among　these,　metalenses　have　emerged　as　a　prominent　and　significant　area　of　research.　In　this　paper,　a　broadband　achromatic　metalens　is　designed　to　operate　across　a　wide　wavelength　range,　specifically　from　9.6　mu　m　to　11.6　mu　m.　To　efficiently　achieve　the　optimization　of　initial　metalens　parameters,　we　employ　an　envelope-based　layering　strategy　that　divides　the　sample　space　into　multiple　adjacent　floors.　This　approach　effectively　reduces　the　loss　rate　and　computational　burden　in　a　comprehensive　manner.　An　enhanced　Archimedes　optimization　algorithm　is　utilized　to　obtain　the　optimal　solution.　It　incorporates　the　oppositionbased　learning　with　Sine　map　and　elite　retention　strategy　to　enhance　the　search　capability　and　avoid　getting　trapped　in　local　optima.　Following　the　optimization　process,　the　proposed　metalens　achieves　an　average　focusing　efficiency　of　53.64　%,　with　chromatic　aberration　correction　accomplished　at　a　coefficient　of　variation　of　only　2.27　%.　This　accomplishment　signifies　a　substantial　advancement　in　the　field　of　achromatic　metalenses.