A method for separating a fuel on-board a vehicle, comprising: mixing, in an on-board fuel separation assembly of a vehicle, an input fuel stream and a fluid solvent; separating the mixture of the input fuel stream and the fluid solvent into a first liquid fuel stream and a second liquid fuel stream, the first liquid fuel stream comprising a first portion of the input fuel stream defined by a first auto-ignition characteristic value and the fluid solvent, the second liquid fuel stream comprising a second portion of the input fuel stream defined by a second auto-ignition characteristic value that is different than the first auto-ignition characteristic value, wherein the first auto-ignition characteristic value comprises a first octane number or a first cetane number, and the second auto-ignition characteristic value comprises a second octane number or a second cetane number; directing the first liquid fuel stream and the first portion of the input fuel stream through a first heat exchanger of the on-board fuel separation assembly; heating the first liquid fuel stream in the first heat exchanger with heat from the first portion of the input fuel stream; directing the heated first liquid fuel stream through a second heat exchanger of the on-board fuel separation assembly; heating the heated first liquid fuel stream in the second heat exchanger with heat from an engine exhaust stream; directing the heated first liquid fuel stream through a third heat exchanger of the on-board fuel separation assembly; and heating the heated first liquid fuel stream in the third heat exchanger with heat from a flow of the fluid solvent separated from the first portion of the input fuel stream; directing the heated first liquid fuel stream to be separated into the fluid solvent and the first portion of the input fuel stream; separating the first liquid fuel stream into the fluid solvent and the first portion of the input fuel stream; directing the first portion of the input fuel stream to a first fuel tank on the vehicle; and directing the second portion of the input fuel stream to a second fuel tank on the vehicle. mixing, in an on-board fuel separation assembly of a vehicle, an input fuel stream and a fluid solvent; separating the mixture of the input fuel stream and the fluid solvent into a first liquid fuel stream and a second liquid fuel stream, the first liquid fuel stream comprising a first portion of the input fuel stream defined by a first auto-ignition characteristic value and the fluid solvent, the second liquid fuel stream comprising a second portion of the input fuel stream defined by a second auto-ignition characteristic value that is different than the first auto-ignition characteristic value, wherein the first auto-ignition characteristic value comprises a first octane number or a first cetane number, and the second auto-ignition characteristic value comprises a second octane number or a second cetane number; directing the first liquid fuel stream and the first portion of the input fuel stream through a first heat exchanger of the on-board fuel separation assembly; heating the first liquid fuel stream in the first heat exchanger with heat from the first portion of the input fuel stream; directing the heated first liquid fuel stream through a second heat exchanger of the on-board fuel separation assembly; heating the heated first liquid fuel stream in the second heat exchanger with heat from an engine exhaust stream; directing the heated first liquid fuel stream through a third heat exchanger of the on-board fuel separation assembly; and heating the heated first liquid fuel stream in the third heat exchanger with heat from a flow of the fluid solvent separated from the first portion of the input fuel stream; directing the heated first liquid fuel stream to be separated into the fluid solvent and the first portion of the input fuel stream; separating the first liquid fuel stream into the fluid solvent and the first portion of the input fuel stream; directing the first portion of the input fuel stream to a first fuel tank on the vehicle; and directing the second portion of the input fuel stream to a second fuel tank on the vehicle.