Minimizing multi-homogeneous Bezout numbers by a local search method

Consider the multi-homogeneous homotopy continuation method for solving a s ystem of polynomial equations. For any partition of variables, the multi-ho mogeneous Bezout number bounds the number of isolated solution curves one h as to follow in the method. This paper presents a local search method for f inding a partition of variables with minimal multi-homogeneous Bezout numbe r. As with any other local search method, it may give a local minimum rathe r than the minimum over all possible homogenizations. Numerical examples sh ow the efficiency of this local search method.