• Spirally coiled (Giauque-Hampson) type heat exchanger optimization. • Thermal analysis of optimum tube geometry predicted by Genetic Algorithm. • Design aimed at minimum exchanger weight under pressure drop constraints. • Design aimed at minimum exchanger height under pressure drop constraints. • Effect of different process parameters on the optimum heat exchanger design. A Genetic Algorithm based optimization of spirally wound two-fluid stream exchanger is presented. The proposed method elaborates a design methodology consistent with the user-defined specifications while simultaneously fulfilling a design objective linking optimization of either weight, height or thermo-hydraulic performances, etc., depending on the customer requirement. Optimization variables include tube material, tube size, normalized transverse and longitudinal pitches, number of tubes in the innermost layer, increment in the number of tubes with each successive layer, and the total number of tube layers. The effectiveness-NTU approach is adopted for design calculations, including fluid property variations with temperature. This paper explores the effect of optimization criteria like minimum weight or height and variation in pressure drop constraints on the optimized design. A compromise in exchanger effectiveness can substantially reduce its weight. Among the exchangers of the same effectiveness, the one handling 10 times larger flow could be 35 times heavier (subjected to other constraints). Exchanger designed with the minimum height criterion is nearly two times shorter than the one created on a minimum weight basis, while the shorter unit could be two times heavier. The optimum design is a trade-off between achievable minimum mass and maximum allowable pressure drop.