Multi-objective Dynamic Flexible Job Shop Scheduling with Biased Objectives via Multitask Genetic Programming

Dynamic flexible job shop scheduling is an important combinatorial optimisation problem which has rich real-world applications such as product processing in manufacturing. Genetic programming has been successfully used to learn scheduling heuristics for dynamic flexible job shop scheduling. Intuitively, users prefer small and effective scheduling heuristics that can not only generate promising schedules but also are computationally efficient and easy to be understood. However, a scheduling heuristic with better effectiveness tends to have a larger size, and the effectiveness of rules and rule size are potentially conflicting objectives. With the traditional dominance relation based multi-objective algorithms, there is a search bias towards rule size, since rule size is much easier to be optimised than effectiveness and larger rules are easily abandoned, resulting in the loss of effectiveness. To address this issue, this paper develops a novel multi-objective genetic programming algorithm that takes size and effectiveness of scheduling heuristics for optimisation via multitask learning mechanism. Specifically, we construct two tasks for the multi-objective optimisation with biased objectives using different search mechanisms for each task. The focus of the proposed algorithm is to improve the effectiveness of learned small rules by knowledge sharing between constructed tasks which is implemented with the crossover operator. The results show that our proposed algorithm performs significantly better, i.e., with smaller and more effective scheduling heuristics, than the state-of-the-art algorithms in the examined scenarios. By analysing the population diversity, we find that the proposed algorithm has a good balance between exploration and exploitation during the evolutionary process.