Mamba Meets Scheduling: Learning to Solve Flexible Job Shop Scheduling with Efficient Sequence Modeling

TL;DR

This paper introduces an innovative architecture that harnesses Mamba, a state-space model with linear computational complexity, to facilitate comprehensive sequence modeling tailored for FJSP, and demonstrates that this model is more efficient than state-of-the-art learning-based methods for FJSP.

Abstract

The Flexible Job Shop Problem (FJSP) is a well-studied combinatorial optimization problem with extensive applications for manufacturing and production scheduling. It involves assigning jobs to various machines to optimize criteria, such as minimizing total completion time. Current learning-based methods in this domain often rely on localized feature extraction models, limiting their capacity to capture overarching dependencies spanning operations and machines. This paper introduces an innovative architecture that harnesses Mamba, a state-space model with linear computational complexity, to facilitate comprehensive sequence modeling tailored for FJSP. In contrast to prevalent graph-attention-based frameworks that are computationally intensive for FJSP, we show our model is more efficient. Specifically, the proposed model possesses an encoder and a decoder. The encoder incorporates a dual Mamba block to extract operation and machine features separately. Additionally, we introduce an efficient cross-attention decoder to learn interactive embeddings of operations and machines. Our experimental results demonstrate that our method achieves faster solving speed and surpasses the performance of state-of-the-art learning-based methods for FJSP across various benchmarks.

Figures (8)

• Figure 1: Disjunctive graph representations of JSP and FJSP with 3 jobs and 3 machines. The arrows on black lines indicate precedence within jobs, while dotted lines represent disjunctive arcs, whose directions must be determined to establish a valid schedule. Disjunctive arcs of the same color indicate the linked operations should be executed by the same machine(s).
• Figure 2: The overall architecture of our proposed Mamba-CrossAttention framework. It comprises two fundamental components: the feature extraction network and the decision-making network. At each step in the scheduling process, the feature extraction network extracts raw features of operations and machines from the environment. The decision network concatenates the output of the feature extraction network with the machine-operation pair features to form candidates, and selects the optimal O-M pair according to the probability to complete the end-to-end solution generation.
• Figure 3: Average gaps on Benchmarks with greedy strategy.
• Figure 4: Training curves for all problem sizes.
• Figure 5: Brandimarte Mk10.