The problem discussed and solved in this paper is the multi-objective routing problem for Deterministic Network. The technical requirements of resource allocation in the Deterministic Network implementation technology require us to reserve corresponding resources for deterministic flows to be transmitted in the network, which introduces a new constraint of bandwidth competition, making the existing multi-objective routing schemes unable to provide effective solutions. In order to solve this problem, we firstly establish a mathematical model and solve it with optimization methods. Then we propose a multi-objective routing scheme based on genetic algorithm. On the basis of satisfying delay and bandwidth constraints, good results are obtained. In order to test the scalability of the scheme, it was tested in network after adding packet loss constraint and the network of larger scales, which all achieved good results. By comparing the performance of our scheme with that of mathematical modeling optimization, it is found that our scheme has a significant and substantial improvement in efficiency at the cost of relaxing constraints. It is concluded that the multi-objective routing scheme based on genetic algorithm proposed in this paper is an effective scheme to solve the multi-objective problem for Deterministic Network.