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In this paper, a novel global routing algorithm is presented for congestion optimization based on efficient local search, named SSTT (search space traversing technology). This method manages to traverse the whole search space. A hybrid optimization strategy is adopted, consisting of three optimization sub-strategies: stochastic optimization, deterministic optimization and local enumeration optimization, to dynamically reconstruct the problem structure. Thus, "transition" can be made from a local minimum point to reach other parts of the search space, traverse the whole search space, and obtain the global (approximate) optimal routing solution. Since any arbitrary initial routing solution can be used as the start point of the search, the initialization in SSTT algorithm is greatly simplified. SSTT algorithm has been tested on both MCNC benchmark circuits and industrial circuits, and the experimental results were compared with those of typical existing algorithms. The experimental results show that SSTT algorithm can obtain the global (approximate) optimal routing solution easily and quickly. Moreover, it can meet the needs of practical applications. The SSTT global routing algorithm gives a general-purpose routing solution.