AbstractIn this paper, a new location analysis method is presented. Given a connected graphG= (V, E)with nonnegative edge costcefor each edgee∊E,dijis the cost of the shortest path between verticesiandjin the graph. TheConnected p-facility Location Problem(CpLP) is to choosepvertices fromVso as to minimize the total cost of shortest path of pair-wise of thesepvertices. This problem is proved to be NP-hard and non-linear integer programming is formulated. Then, two algorithms are designed for solving the CpLP. One is a heuristic algorithm based on classical maximum clique approach, while the second one is genetic algorithm. Finally, computational results show the comparison between these two algorithms.