An ant colony optimization inspired algorithm for the Set Packing Problem with application to railway infrastructure

The paper concerns an Ant Colony Optimisation (ACO) procedure as approximation method for the railway infrastructure capacity (RIC) problem. Railway infrastructure managers now have to deal with operators’ requests for increased capacity. Planning the construction or reconstruction of infrastructures must be done very carefully due to the huge required investments and the long term implications. Usually, assessing the capacity of one component of a rail system is done by measuring the maximum number of trains that can be operated on this component within a certain time period. In our work, we deal with two real situations. The first is Pierrefitte-Gonnesse crossing point located at the north of Paris. The second is the Lille-Flandres station which is the largest station in North of France. Measuring the capacity of junctions is a matter of solving an optimisation problem called the saturation problem [1], and which can be formulated as a Set Packing Problem (SPP). Given a finite set I = {1, . . . , n} of items and {Tj}, j ∈ J = {1, . . . ,m}, a collection of m subsets of I, a packing is a subset P ⊆ I such that |Tj ∩ P | ≤ 1,∀j ∈ J . The set J can be also seen as a set of exclusive constraints between some items of I. Each item i ∈ I has a positive weight denoted by ci and the aim of the SPP is to calculate the packing which maximises the total weight. This problem