In the present work the multi-objective genetic algorithm is employed to optimize the design variables in a double-layer microchannel heat sink. The design matrix is formulated with Latin hypercube sampling and the model approximation is implemented with response surface approximation to reduce the computing time. The design variables for optimization are the relative axial ridge length (X-i) from 0.4 to 1.4, the relative transverse ridge length (Y-i) from 0.4 to 0.9, the relative channel length ratio (L-i) from 0.2 to 1, and the relative flow rate ratio (sigma) from 0.25 to 0.75, respectively. The objective functions are lambda(R) (ratio of the thermal resistance of the modified case over base case) and lambda(P) (ratio of the total pumping power of the modified case over base case), respectively. The Pareto optimal solutions are extracted and depicted tradeoff between the two objective functions, thus providing a principal understanding into the design variables and allowing autonomy of selection among the optimal solutions. Total 135 Pareto optimal solutions are extracted by using the K-means clustering. Six Pareto optimal combinations (POCs) named as POC - A, POC - B, POC - C, POC - D, POC - E, and POC - F are selected for the comparison of designs. The best design for the heat transfer performance is POC - A (X-i = 0.4003, Y-i = 0.4481, L-i = 0.6378, sigma = 0.2504) with 37.34% lower lambda(R) than that for the POC-F, while the best design for the pumping power is POC - F (X-i = 0.4149, Y-i = 0.4081, L-i = 0.6544, sigma = 0.2515) with 96.51% lower lambda(p) than that for the POC-A. (C) 2019 Elsevier Ltd. All rights reserved.