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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 network (SON) attracts attention as an effective way to reduce OPEX. This paper proposes a self-optimization algorithm for handover (HO) parameters. In conventional studies, the HO optimization techniques are discussed in models with stationary mobility of user equipment (UE). On the other hand, the key feature of the proposed algorithm is the mobility robustness, which means that the HO performance is robust against the change in UE mobility. In order to realize the mobility robustness, the proposed algorithm adaptively adjusts the HO parameters considering cause of HO failures, which changes in UE mobility. We examine the performance of the proposed algorithm through the computer simulations and confirm the mobility robustness. The simulation study demonstrates the following; The HO parameters are initially set to the optimum values for UEs with 3 km/h based on the random walk. Then, when the mobility changes from 3 km/h random walk to 300 km/h linear motion, the HO failure rates increases to 19%. The proposed algorithm reduces such increasing HO failure rates less than 0.2%.