Nature-inspired optimization algorithms named meta-heuristics are found to be versatile in engineering design fields. Their adaptability is also used in various areas of the Internet of things, structural design, and thermal system design. With the very rapid progress in industrial modernization, waste heat recovery from the power generating and thermal engineering organization is an imperative key point to reduce the emission and support the government norms. However, the heat exchanger is the component applied in various heat recovery processes. Out of the available designs, shell and tube heat exchangers (SHTHEs) are the most commonly adopted for the heat recovery process. Hence, cost minimization is the major aspect while designing the heat exchanger confirming various constraints and optimized design variables. In this study, cost minimization of the SHTHE is performed by applying a novel metaheuristic algorithm which is the African vultures optimization algorithm (AVOA). Adopting the AVOA for the best-optimized value (least cost of heat exchanger) and the design parameters are realized, confirming all the constraints. It was found that the AVOA is able to pursue the best results among the rest of them and can be used for the cost optimization of the plate-fin and tube-fin heat exchanger case studies.