An iterative facility layout algorithm

In this paper we present a facility layout algorithm that iterates between a genetic algorithm with a slicing tree representation and a mixed-integer program with a subset of the binary variables set via the genetic algorithm. The genetic algorithm is very good at finding low-cost solutions while maintaining shape constraints on the departments. The slicing tree representation and the mixed-integer program are compatible in terms of layout representation, with the mixed-integer program representation more general. The mixed-integer program allows us to relax the last remaining constraints of the slicing tree representation of the genetic algorithm. We present our genetic algorithm and the iterative algorithm, while illustrating their performance on test problems from the literature. In 10 of the 12 problems, new lower best-cost solutions are found.