Abstract. The location problem of interconnected facilities on the line with forbidden gaps is considered. The located facilities are connected among themselves and with gaps. Location in forbidden gaps is not allowed. It is need to minimize the total cost of connections between facilities and between facilities and gaps. It is known that the initial continuous problem is reduced to series discrete subproblems of smaller dimension. In this paper the definition of the local optimum of the problem is introduced. In order that to obtain the local optimum it is necessary to solve some subproblems. The variants of lower bounds of the goal function of the subproblems are proposed. The bounds can be used in the branch and bounds algorithm for solving the subproblems
