This paper presents a robust, efficient and parameter-setting-free evolutionary approach for the optimal design of compact heat exchangers. A learning automata based particle swarm optimization (LAPSO) is developed for optimization task. Seven design parameters, including discreet and continuous ones, are considered as optimization variables. To make the constraint handling straightforward, a self-adaptive penalty function method is employed. The efficiency and the accuracy of the proposed method are demonstrated through two illustrative examples that include three objectives, namely minimum total annual cost, minimum weight and minimum number of entropy generation units. Numerical results indicate that the presented approach generates the optimum configuration with higher accuracy and a higher success rate when compared with genetic algorithms (GAs) and particle swarm optimization (PSO).