A Genetic Algorithm for Finding Minimal Multi-homogeneous Bézout Number

Homotopy continuation is a most efficient numerical method for finding all isolated solutions of system of polynomial equations, and finding minimal multi-homogeneous Bezout number is a basic problem of homotopy continuation. This paper presents a problem-specific genetic algorithm for finding minimal multi-homogeneous Bezout number. The algorithm is easy to implement and easy to be parallelized for large scale problems. It can find the minimal multi-homogeneous Bezout number in probability 1. Numerical results indicate that the proposed algorithm is reliable and efficient. The algorithm offers a competitive alternative for minimal multi-homogeneous Bezout number problem. Meanwhile, it extends the application fields of genetic algorithms.