Contrails and aircraft-induced cirrus clouds are reputed being the largest components of aviation-induced global warming, even greater than carbon dioxide (CO2) exhaust emissions by aircraft. This article presents a contrail model algorithm specifically developed to be integrated within a multi-objective flight trajectory optimization software framework. The purpose of the algorithm is to supply to the optimizer a measure of the estimated radiative forcing from the contrails generated by the aircraft while flying a specific trajectory. In order to determine the precise measure, a comprehensive model is employed exploiting the Schmidt-Appleman criterion and ice-supersaturation regions. Additional parameters such as the solar zenith angle, contrail lifetime and spread are also considered. The optimization of flight trajectories encompassing such contrail model allows for selective avoidance of the positive radiative forcing conditions, such as only avoiding persistent contrails, or contrails which lead to negative radiative forcing. The model assesses the radiative forcing associated with 4-Dimensional (4D) trajectories in a 4D weather field, encompassing both the local time-of-day and the contrail lifetime. Some preliminary algorithm validation activities are presented, including a simulation case study involving a medium-range domestic flight of a turbofan aircraft from Melbourne to Brisbane.