Adaptation of Discrepancy-based Methods for Solving Hybrid Flow Shop Problems

This paper investigates how to adapt some discrepancy-based search methods to solve Hybrid Flow Shop (HFS) problems in which each stage consists of several identical machines operating in parallel. The objective is to determine a schedule that minimizes the makespan. We present here an adaptation of the Depth-bounded Discrepancy Search (DDS) method to obtain solutions with makespan of high quality. This adaptation for the HFS contains no redundancy for the search tree expansion. To improve the solutions of our HFS problem, we propose a local search method, called CDDS, which is a hybridization of two existing discrepancy-based methods (DDS and Climbing Discrepancy Search). CDDS introduces an intensification process around promising solutions. These methods are tested on benchmark problems. Results show that discrepancy methods give promising results.