Neural Multi-Objective Combinatorial Optimization for Flexible Job Shop Scheduling Problems

Neural combinatorial optimization (NCO) has made significant advances in applying deep learning techniques to efficiently and effectively solve single-objective flexible job shop scheduling problems (FJSPs). However, the more practical multi-objective FJSPs (MOFJSPs) remain underexplored, limiting the applicability of NCO in multi-criteria decision-making scenarios. In this paper, we propose a decomposition-based NCO method to solve MOFJSPs. We present the dual conditional attention network (DCAN), a neural network architecture that takes the objective preferences along with the problem instance, aiming to learn adaptable policies over the preferences. By decomposing an MOFJSP into a set of subproblems with different preferences, the learned DCAN policies generate a set of solutions that reflect the corresponding trade-offs. We customize the Proximal Policy Optimization algorithm based on decomposition to effectively train the policy network for multiple objectives and define the state and reward based on combinations of different objectives. Extensive results showcase that our approach outperforms traditional multi-objective optimization methods and generalizes well across diverse types of problem instances.