A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion

Abstract

This paper deals with a classic flow-shop scheduling problem with makespan criterion. Some new properties of the problem associated with the blocks have been presented and discussed. These properties allow us to propose a new very fast local search procedure based on a tabu search approach. Computational experiments (up to 500 jobs and 20 machines) are given and compared with the results yielded by the best algorithms discussed in the literature. These results show that the algorithm proposed solves the flow-shop instances with high accuracy in a very short time. The presented properties and ideas can be applied in any local search procedures. Scope and purpose The permutation flow shop scheduling problem with makespan criterion is relatively simply formulated, but it is unfortunately a hard combinatorial problem. For this reason many various algorithms have been proposed and tested to solve the problem in a short time. This paper deals with the new properties and techniques, which allow one to construct a very efficiency algorithm based on a tabu search approach. In the algorithm, we propose to use the lower bounds on the makespans instead of computing the makespans explicitly, for selecting the best solution. Besides a dynamic tabu list is used that assists additionally to avoid trapped at a local optimum. Finally, the appropriate perturbations are introduced that guide the search to the more promising areas of solution space, where ”good solutions” can be found. All these components make that proposed algorithm solves the large-size flow shop instances with high accuracy in very short time.