In this paper we investigate logical topology design algorithms using local optimization technique. Since the problem of the optimal logical topology design for all traffic demands is NP-complete, we design a logical topology by sequentially constructing the shortest path for one source-destination pair at a time. The path is a locally optimized path in the sense that there are no other paths with less hop count that may be constructed from existing links and newly created links. For this we define an Estimated Logical Hop Count (ELH), which is the shortest logical hop count for a given source and destination when it is applied. Also, we propose two heuristic logical topology design algorithms making use of ELH: ELH with Maximum Traffic Demands (MTD) and with Resource Efficiency Factor (REF). Finally, we evaluate the performance of the proposed algorithms by GLASS/SSF simulator. The simulation results show that ELH with REF outperforms other well-known algorithms in terms of the weighted hop count and network throughput.