A routing optimization problem is solved by a non- deterministic algorithm in this paper. The DNA computing is applied for a case of cable trench problem. The cable trench problem is a combination of the shortest path problem and the minimum spanning tree problem, which makes it difficult to be solved by a conventional computing method. DNA computing is applied to overcome the limitation of a silicon-based computer. The numerical values are represented by the fixed-length DNA strands, and the weights are varied by the melting temperatures. Biochemical techniques with DNA thermodynamic properties are used for effective local search of the optimal solution.