The Flexible Job Shop scheduling Problem (FJSP) is a generalization of the classical Job Shop Problem in which each operation must be processed on a given machine chosen among a finite subset of candidate machines. The aim is to find an allocation for each operation and to define the sequence of operations on each machine so that the resulting schedule has a minimal completion time. We propose a variant of the Climbing Discrepancy Search approach for solving this problem. We also present various neighborhood structures related to assignment and sequencing problems. We report the results of extensive computational experiments carried out on well-known benchmarks for flexible job shop scheduling. The results demonstrate that the proposed approach outperforms the best-known algorithms for the FJSP on some types of benchmarks and remains comparable with them on other ones.

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 minimises the makespan. We present here an adaptation of the Depth-bounded Discrepancy Search (DDS) method to obtain near-optimal 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 Climbing Depth-bounded Discrepancy Search (CDDS), which is a hybridisation of two existing discrepancy-based methods: DDS and Climbing Discrepancy Search (CDS). CDDS introduces an intensification process around promising solutions. These methods are tested on benchmark problems. Results show that discrepancy methods give promising results and CDDS method gives the best solutions.