Abstract: The muon collider has the potential to be a powerful tool for exploring frontiers in particle physics. Achieving high luminosity requires reducing the 6D emittance of the muon beam generated from the decay of the pions from the target by several orders of magnitude. The cooling process for a muon collider involves two stages: initial six-dimensional cooling and final transverse cooling. This paper focuses on the latter, presenting a conceptual design for the final cooling system that includes high-field solenoids. Using the well-known differential evolution algorithm, we design a cooling channel that reduces the normalized transverse emittance to approximately 22.4 μm, meeting the luminosity requirements for collisions.