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Based on the IEEE 802.16e standard, WiMAX has proposed a relay-based approach, i.e., IEEE 802.16j, to extend the service area of Base Stations (BSs) and to improve the received signal strength (RSS) quality. IEEE 802.16j has the capability to achieve two significant advantages: low-cost of building IEEE 802.16 WiMAX networks and compatible with existing WiMAX standards. According to diverse features on mobility and relay range, the Relay Station (RS) can be classified into three types: Fixed RS (FRS), Nomadic RS (NRS) and Mobile RS (MRS). The relay-based WiMAX network includes different types of RSs. To efficiently construct the relay-based WiMAX and determine an optimal routing path between a Mobile Station (MS) and the MR-BS become two important issues. This paper thus proposes an IEEE 802.16j-conformed relay-based adaptive competitive on-line routing approach, in which a multihop optimal path is selected in terms of link bandwidth, path length and channel condition. Numerical results indicate that the proposed routing approach significantly outperforms other approaches in Fractional Reward Loss (FRL), network utilization and average end-to-end path delay.