Genetic Programming with Lexicase Selection for Large-scale Dynamic Flexible Job Shop Scheduling

Dynamic flexible job shop scheduling is a prominent combinatorial optimisation problem with many real-world applications. Genetic programming has been widely used to automatically evolve effective scheduling heuristics for dynamic flexible job shop scheduling. A limitation of genetic programming is the premature convergence due to the loss of population diversity. To overcome this limitation, this work considers using lexicase selection to improve population diversity, which has achieved success on regression and program synthesis problems. However, it is not trivial to apply lexicase selection to genetic programming for dynamic flexible job shop scheduling, since a fitness case (training scheduling simulation) is often large-scale, making the fitness evaluation very time-consuming. To address this issue, we propose a new multi-case fitness scheme, which creates multiple cases from a single scheduling simulation. Based on the multi-case fitness, we develop a new genetic programming algorithm with lexicase selection, which uses a single simulation for fitness evaluation, thus achieving a better balance between the number of cases for lexicase selection and evaluation efficiency. The experiments on a wide range of dynamic scheduling scenarios show that the proposed algorithm can achieve better population diversity and final performance than the current genetic programming parent selection methods and a state-of-the-art deep reinforcement learning method.