Three-fluid compact heat exchanger of plate-fin type with parallel-flow configuration is optimised for the entropy generation. Four different types of plate fins (plain rectangular, offset strip, corrugated louvered and wavy fin) are embodied within heat exchanger for both co-current and counter-current flow arrangements have been selected for the study. Genetic algorithm is selected as an optimisation tool having apt in handling various continuous variables and discrete variables and the problems with complexities in the objective function as well as in constraints. Validation of the optimization model is carried out by comparing the results with that from experimental results, Particle swarm optimization (without heat duty constraint) and from graphical method (with heat duty constraint). It is observed that for a specified heat duty and given operating conditions corrugated louvered fin with counter-current flow arrangement offers the minimum entropy generation amongst all.