Connection setup on various computer networks is now achieved by GMPLS. This technology is based on the source-routing approach, which requires the source node to store metric information of the entire network prior to computing a route. Thus all metric information must be distributed to all network nodes and kept up-to-date. However, as metric information become more diverse and generalized, it is hard to update all information due to the huge update overhead. Emerging network services and applications require the network to support diverse metrics for achieving various communication qualities. Increasing the number of metrics supported by the network causes excessive processing of metric update messages. To reduce the number of metric update messages, another scheme is required. This paper proposes a connection setup scheme that uses flooding-based signaling rather than the distribution of metric information. The proposed scheme requires only flooding of signaling messages with requested metric information, no routing protocol is required. Evaluations confirm that the proposed scheme achieves connection establishment without excessive overhead. Our analysis shows that the proposed scheme greatly reduces the number of control messages compared to the conventional scheme, while their blocking probabilities are comparable.