An Interior-point Genetic Algorithm with Restarts for Flexible Job Shop Scheduling Problems

David Hutter, Michael Hellwig, Thomas Steinberger

Abstract: The Flexible Job Shop Problem (FJSSP) represents an extension of the Job Shop Scheduling Problem (JSSP), in which the sequence of operations on assigned machines has to be optimized. In the FJSSP, operations can be processed by different machines, with different processing times on each machine type. The paper proposes a Genetic Algorithm (GA) variant that uses an encoding capable to be applied to as general FJSSP instances as possible and variation principles designed to maintain a population of feasible candidate solutions over the whole search process. Additionally, the GA parameter setting for each FJSSP instance is derived from problem-specific attributes, such as the production environments flexibility and the variety of duration values, and a restart scheme that accounts for the dissimilarity of the initial population is introduced to avoid premature convergence. The GA results are compared to best- known solutions in literature as well as to the solutions of the commercial solver GUROBI being applied to a Mixed-Integer Linear Programming (MILP) representation of the FJSSP. In addition to demonstrating the decent results of the developed GA on 402 recognized FJSSP benchmark instances, the paper investigates the influence of different aspects of problem complexity on the relative GA performance to assert the GAs viability for more complex FJSSP variants Including uncertainties. Regardless of the machine flexibility of a FJSSP instance, the experimental results suggest that both approaches tie on smaller and medium sized problem instances. With increasing complexity in problem characteristics like problem size, flexibility, and duration variety, the GA gains advantage over the MILP/GUROBI approach. The observation substantiates the expectation that the proposed GA is well suited for practical (more realistic) scheduling problems with additional requirements like worker flexibility or uncertainty effects.