In this paper, a multi-objective optimization method is proposed which is a combination of Genetic algorithm, Differential Evolution and Adaptive Simulated Annealing algorithms. This technique is intended to generalize and improve the robustness of the three population based algorithms. In optimization problems, it is essential to keep the balance between local and global search abilities of algorithms. In the current method, DE, GA and ASA algorithms are linked in the variation stage to enrich the searching behavior and enhance the diversity of the population. The performance of the proposed DE-GA-ASA is tested against benchmark problems for multi-objectives and compared with two widely recognized vector optimizers. Next, the proposed technique is successfully implemented to optimize the design of plate-fin heat exchanger. The effectiveness of the present method is illustrated by comparing with various case studies. Some of the earlier case studies violated the constraints and/or only focused on single objective optimization. Results show that DE-GA-ASA method can be used effectively for the optimal design of plate-fin heat exchanger. Moreover, the effect of variation of fin and heat exchanger parameters on the optimal design is also investigated. Hot, cold and no-flow length of the heat exchanger, fin offset length, fin height and fin length are introduced as the optimization variables to obtain maximum heat transfer rate and minimum total annual cost. The investment cost and operating costs are independently optimized to provide a detailed investigation on the effect of fin and heat exchanger geometry parameters on their variation. Furthermore, a multi-criteria decision making method, TOPSIS is introduced for the selection of final optimal solution from the set of non-dominated solutions. (C) 2017 Elsevier Ltd. All rights reserved.