Network throughput has become an important issue for big-data analysis on Warehouse-Scale Computing (WSC) systems. It has been reported that randomly-connected inter-switch networks can enlarge the network throughput. For irregular networks, a multi-path routing method called k-shortest path routing is conventionally utilized. However, it cannot efficiently exploit longer-than-shortest paths that would be detour paths to avoid bottlenecks. In this work, a novel routing method called k-optimized path routing to achieve high throughput is proposed for irregular networks. We introduce a heuristic to select detour paths that can avoid bottlenecks in the network to improve the network throughput. Experimental results show that the proposed k-optimized path routing can improve the throughput by up to 133 % compared to the conventional k-shortest path routing. Moreover, it can improve the network bandwidth while maintaining the low network latency.