A hybrid optimization methodology is proposed for the working fluid selection of an organic Rankine cycle (ORC). First, a stochastic global solver is used to select the chemical species of the working fluid; then, a deterministic global solver is used to optimize the composition. The first step is a mixed integer nonlinear programing (MINLP) and the second a nonlinear program (NLP). The methodology is applied to the recovery of cryogenic energy during the evaporation of liquefied natural gas (LNG), which is a promising way to produce electricity with relatively high efficiency from the large amount of otherwise wasted heat. Seawater or low-grade heat sources can be used as heat source. Multicomponent working fluids have advantages compared to pure fluids because of the nonisothermal evaporation of LNG. Herein, a ternary mixture is considered. A mixture of CF4, CHF3, n-pentane is identified as an optimum ternary working fluid. It produces about 1.1 MJ/kmol LNG with a simple organic Rankine cycle using seawater as heat source. The optimization results are quantitatively compared with the literature in terms of power generation and are shown to have substantially higher electricity generation.