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A large number of cells will be deployed to provide high speed services in any places using the Long-Term Evolution (LTE) system. The management of such a large number of cells increases the operating expenditure (OPEX). Self-organizing networks (SON) attracted interest as an effective way to reduce OPEX. One of the main targets in SON is the self-optimization of handover (HO) that realizes mobility robustness. HO optimization algorithms adjust HO parameters between the serving and the reconnected cells based on the HO failure logs and cell selection, which is the procedure used to select a suitable reconnected cell, is very important for HO optimization algorithms. In this paper, we propose a cell selection scheme to enhance the performance of HO optimization. In the proposed scheme, both the uplink and downlink channel quality is considered when selecting a suitable reconnected cell. Through the computer simulation, we can see that the proposed scheme reduces the HO failure rate and the number of HO failures by 3 percentage points and 38%, respectively, compared to the conventional scheme based solely on downlink channel quality.