The optimization and assessment study of a thermal energy adsorption storage system is presented. The system integrates an adsorption heat storage module in a conventional hot water storage tank of a solar thermal system, operating with the silica-gel/water adsorption pair. The system was modeled using TRNSYS circle and MATLAB(circle), and was previously assessed and improved through a set of parametric tests for each main component. In this work, the GenOpt(circle) optimization software was used to obtain the optimal performance of the whole system. It is found that a slender and lengthy adsorber with a large number of thin fins, a thick and lengthy condenser, and an evaporator with a large number of lengthy tubes improve the system's performance, by increasing the heat transfer areas and the adsorbent mass. The performance also improves by controlling the adsorber-condenser valve only through the system's pressure and opening the evaporator-adsorber valve at the hot water setpoint temperature. The optimized system presents a 16% saving in annual backup energy consumption compared with a similar conventional storage system, thus validating the results of the previous segregated parametric study. This optimized system operates at the highest performance with the same configuration in different locations/ climates, as only the inclination of the solar collector affects the results: larger inclinations improve the system's performance, by favoring its operation in Winter. Results present this system as a promising solution to increase the energy storage capacity of solar thermal systems, and potentially of systems using other primary energy sources.