Variable Neighborhood Search for the Minimum Interference Frequency Assignment Problem

The frequency assignment is an important task in the design of radio network. Let us concider a GSM network N composed of a set of nc cells: C= {C1, C2 . . . Ci, . . . Cnc}. Each cell required a number of frequencies which is defined by the number of transceivers TRX or traffic demand Di= {1, 2 . . . , x}An interval of operational frequencies: [Fmax − Fmin]. Further, consider a matrix: MCo[nc][nc]: which contains the Co-channel rate generated if the j TRX of cell j uses the same channel (f) of the j TRX of cell i. The matrix MAdj[nc][nc] : which contains the Adjacent-channel rate generated if one TRX of cell j use an Adjacent channel (f+1) or (f−1) to the channel (f) , used by a TRX from cell i. So we are facing the following Frequency Assignment Problem(FAP): Given a list of TRX, an interval of operational frequencies, a matrix of Co-channel and Adjacent channel interference, the goal is then to assign a frequency to each TRX, with minimum Co-channel and Adjacent-channel interferences generated by the reuse frequency principle. The Minimum Interfrence-FAP is the problem of finding an assignment for each TRX that minimizes the cost function given in formula (1) and taken from[1].