To maintain the pressure of cargo tank and to minimize natural gas loss, two nitrogen expansion cycles for boil-off gas (BOG) re-liquefaction systems, specifically designed for small LNG ships are proposed and optimized: 1) Case 1, re-liquefaction process with the parallel nitrogen expansion, 2) Case 2, re-liquefaction process with the serial nitrogen expansion. The simulation and analysis of the two processes are carried out by using Aspen HYSYS and the genetic algorithms are selected as the optimization method. It can be found that the specific energy consumption (SEC) of 0.7333 kWh/kg(LNG), the coefficient of performance (COP) of 0.2538 and the figure of merit (FOM) of 0.2827 are achieved in Case 1 and the SEC of 0.7539 kWh/kg(LNG), the COP of 0.2464 and the FOM of 0.2757 are achieved in Case 2 by comparing the two optimized cases. Moreover, the total exergy losses for Case 1 and Case 2 are 153.34 kW and 160.69 kW, respectively. (C) 2019 Elsevier Ltd. All rights reserved.