A molecular design method (MDM) that explores chemical space accounting for geometric stability is demonstrated for general functionalities. We improved the optimization algorithm of MDM introduced in our previous work, which enables computationally efficient design targeting general properties. MDM simultaneously predicts the molecular species, desired property, and equilibrium geometry of functional molecules without experimental records. MDM is based on quantum alchemy and is effective for large chemical space. APDFT was adopted as a quantum alchemy method. The electric dipole strength (EDS) and atomization energy are set to target properties for molecular design as examples. Few studies have applied APDFT to the electric dipole moment. Therefore, we investigated the accuracy with (N2, CO)CS and (BN-doped benzene derivatives)CS prior to molecular design. The accurate APDFT EDS of CO was obtained with reference N2. In (BN-doped benzene derivatives)CS, we showed that APDFT up to the third-order perturbation expansion cannot correctly reproduce the EDS trend of derivatives at the reference PBE0 level of theory, regardless of the reference electronic structure theory, perturbation order, and basis set. Higher-order APDFT calculations based on analytical and numerical differentiation or integral transformation are expected to enable more accurate molecular design by MDM. We applied MDM to search for molecules with high EDS and atomization energy in the chemical spaces (BF, CO)CS, (N2, CO)CS, and (BN-doped benzene derivatives)CS. In (BF, CO)CS, BF with high atomization energy was obtained. This result was compared with Ref. 10. It was found that the update of the molecular species by the optimality criteria method leads to rapid convergence of the optimization with small computational cost. In (N2, CO)CS, CO with high EDS was designed.