An alternate option for improving the performance of the thermoelectric heat pump (TEHP) is the variation in thermoelectric leg configuration. In this paper, the thermodynamic model based on first and second law of thermodynamics for an exoreversible TEHP including influence of Thomson effect as well as leg geometry on the coefficient of performance and heating load of the device has been developed and optimized. Modified expressions have been derived analytically for dimensionless heating load, irreversibilities, figure of merit, energy, and exergy efficiency. The effects of operating and geometry parameters such as shape parameter (A(c)/A(h)), temperature ratio (T-c/T-h), Thomson effect, thermal and electrical contact resistances on the coefficient of performance, and heating load of the TEHP have been analysed. The results indicate that the Thomson effect has adverse effect on heating load of the system. The optimal parameters obtained through GA optimization process have been compared with the optimal parameters obtained through analytical method which proved the validity of GA optimization method for optimization of TEHP. After the testing, the GA optimization has been performed to determine the optimum parameters corresponding to maximum energy efficiency and maximum heating load. It was found that the GA population converges quickly after 20 runs only which proved the GA as time and cost-effective optimization tool. This study will be useful for designing of practical TEHP systems of different leg geometries.