With the progress and growth of society, the field of computer science and technology has also continued to improve rapidly. Human beings have conducted in-depth research on algebraic learning, solving multi-objective homotopy algorithm nonlinear equations and applying them to integrated technology systems of distributed systems. More and more people's attention. In order to solve the shortcomings of the existing research on the integration technology of the distributed system of the multi-objective homotopy algorithm, this paper uses the function equation and the integration of the distributed system in the distributed system integration technology based on the function of the multi-objective homotopy algorithm. On the basis of discussing the characteristics of the technology, the development tools and development environment of the distributed system integration technology based on the multi-objective homotopy algorithm are briefly introduced. And it discusses the workflow design of the model of the integration technology of the distributed system based on the multi-objective homotopy algorithm, and finally compares the data classification accuracy and operation of the application of the multi-objective homotopy algorithm in the integration technology of the distributed system with CGX, The SVN algorithm is compared and experimentally analyzed. The experimental data shows that the multi-objective homotopy algorithm is better than the CGX and SVN algorithms in data classification accuracy, and the classification accuracy is as high as 99.87%. In the running situation, the multi-objective homotopy algorithm and CGX are not much different.but the multi-objective homotopy algorithm is still better than CGX.