The transformation to a truly sustainable energy system will require taking better advantage of the waste heat. Integrating heat exchangers with the triply periodic minimal surface (TPMS) is a promising and efficient way to build waste heat recovery systems that harness heat emissions from the low pitch thermal systems. This is mainly due to the low hydrodynamic resistance and pressure drop in the TPMS while securing good heat transfer at low-temperature gradient. This study establishes a computational design and analysis of heat and mass transfer inside a heat exchanger based on the TPMS structure and determine thermal effectiveness, heat transfer coefficient, and pressure drop inside the channel. The non-linearity dependence of results to several design variables makes obtaining the optimal design configuration solely using conventional CFD or experimental study nearly impossible. Hence, a multi-objective optimization workflow based on a Genetic Algorithm for laminar flow is employed to reveal the underlying relationships between design variables for the optimal configurations. The results illustrate the local sensitivity of important parameters such as the heat transfer coefficient, Nusselt number, and thermal performance of the heat exchanger against various design variables. It is shown that the pressure drop is directly affected by gas inlet velocity, viscosity, and density, from high to low, respectively. The Pareto frontiers for the optimal thermal performance are extracted, and the correlation between design objectives is determined. This methodology provides a promising framework for heat exchangers' design analysis, including multi-objective goals and design constraints.