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This paper proposes human-like stable bipedal walking with a large stride by the height variation of the center of mass (COM) using an evolutionary optimized central pattern generator (CPG). A modifiable walking pattern generator (MWPG) is utilized to generate a walking pattern for the bipedal robot. For the height variation of the COM, its height trajectory is generated by the CPG. A sensory feedback is utilized to compensate the disturbance caused by the height variation. Besides, the CPG is optimized by the quantum-inspired evolutionary algorithm (QEA) to obtain the desired output signals from the CPG. The proposed method is applied to a simulation model of the small-sized bipedal robot, HanSaRam-IX (HSR-IX), developed at the Robot Intelligence Technology laboratory, KAIST and the effectiveness is demonstrated through the simulations.