1. A carrier selection method for a logistics network, the logistics network comprising a plurality of nodes and a plurality of minimal paths, wherein the nodes include a start and a terminal, and the minimal paths extend from the start to the terminal of respective said nodes, each of the minimal paths being formed by a plurality of routes without a loop, and each of the routes extending between two of the nodes, said method comprising the steps of: utilizing a computer to execute carrier selection software having a virtual network that simulates a logistics network, the computer including an input unit, an operating unit and an output unit; providing a plurality of carriers in the logistics network; choosing one of the carriers for each routes in the logistics network to form one carrier set, so as to generate a plurality of carrier sets; the input unit receiving a demand for transport from the start to the terminal in the logistics network by a user input to the carrier selection software; defining the demand distributed among and transmitted through the minimal paths; defining each of the carriers as having a plurality of cargo capacities and a maximal capacity; defining a flow vector having a flow of each of minimal paths so that each of the routes has a traveled flow, wherein the sum of the flows of the minimal paths is equal to the demand; the operating unit selecting the flow vector for satisfying a first constraint, wherein the first constraint is defined that the flow of each of minimal paths is smaller than or equal to the maximal capacity; the operating unit transforming each of the flow vectors satisfying the first constraint into a corresponding capacity vector, wherein the corresponding capacity vector has a needed capacity of each of the routes; the operating unit selecting the capacity vector for satisfying a second constraint, wherein the second constraint is defined that the needed capacity is equal to a minimal cargo capacity among the cargo capacities of the carriers, wherein the cargo capacities of the carriers are more than or equal to the traveled flow for each of the routes, so that the capacity vector satisfying the second constraint is defined as a lower vector; the operating unit calculating a probability that each of the capacity vectors is larger than or equal to the lower vector, and defining the probability as the network reliability; the operating unit executing a genetic algorithm with the carrier sets as chromosomes in the genetic algorithm to search for an optimal carrier set among the carrier sets, wherein the optimal carrier set has a maximal network reliability; and displaying the optimal carrier set on the output unit.