A thermoelectric generator used to recover energy from the exhaust gases of a heavy-duty freight vehicle is numerically simulated and optimized using two different algorithms: a gradient-based search method, and a global and local direct search method. The model uses a one-dimensional finite volume method to calculate the temperature and the convective heat transfer of the hot and cold fluids along the streamwise direction, as well as the pressure drop, and employs a thermal resistance network and a global energy balance to account for the heat transfer and the thermoelectric effect. Three different heat exchanger configurations are studied with plain, offset strip or triangular fins. The objective function is the net output power, and the geometrical dimensions of the heat exchanger and thermoelectric units are taken as design variables. The results show that the height of the fins, the spacing between them, the height and side length of the cross section of the thermoelectric units, and the distance between the legs are critical parameters in the optimization process. The thickness of the fins, wall ducts, electrical conductor and ceramic strips should be as small as possible, as well as the height of the cooling wall duct. The two optimization methods yield similar optimal solutions.