The Flexible Job Shop Scheduling Problem (FJSSP) is a well-known NP-hard optimization problem that plays a critical role in production systems. Evaluating dispatching rules typically relies on simulation models that emulate job shop settings and constraints. While accurate, these simulations are computationally expensive, especially when large numbers of rules must be evaluated, as in evolutionary algorithms and other population-based meta-heuristics. To address this challenge, this study proposes an adapted version of MathBERT—a mathematical extension of Bidirectional Encoder Representations from Transformers (BERT)—as a surrogate model for fitness prediction in FJSSP. The model’s default classification head is replaced with a custom regression head composed of multiple fully connected layers with ReLU activation functions, allowing for continuous fitness value prediction. MathBERT was trained on datasets of 10,000, 20,000, and 30,000 dispatching rules and evaluated across ten benchmark FJSSP instances. The results show that the model achieved a relative percentage error of approximately 9% across the training set and 11% across the testing set. Although the proposed model requires a significant initial training cost, this represents a one-time effort. Once trained, the model can be reused or fine-tuned for new scheduling environments with minimal overhead. Importantly, inference time remained extremely low across all instances, consistently under 0.12 s per test set. These findings highlight MathBERT’s potential as a scalable and computationally efficient alternative to simulation-based evaluation, supporting scheduling in real-world manufacturing systems.

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Transformer-Based Approach for Fitness Prediction in the Flexible Job Shop Scheduling Problem

  • Shady Salama,
  • Mate Kovacs,
  • Guhan Elangovan

摘要

The Flexible Job Shop Scheduling Problem (FJSSP) is a well-known NP-hard optimization problem that plays a critical role in production systems. Evaluating dispatching rules typically relies on simulation models that emulate job shop settings and constraints. While accurate, these simulations are computationally expensive, especially when large numbers of rules must be evaluated, as in evolutionary algorithms and other population-based meta-heuristics. To address this challenge, this study proposes an adapted version of MathBERT—a mathematical extension of Bidirectional Encoder Representations from Transformers (BERT)—as a surrogate model for fitness prediction in FJSSP. The model’s default classification head is replaced with a custom regression head composed of multiple fully connected layers with ReLU activation functions, allowing for continuous fitness value prediction. MathBERT was trained on datasets of 10,000, 20,000, and 30,000 dispatching rules and evaluated across ten benchmark FJSSP instances. The results show that the model achieved a relative percentage error of approximately 9% across the training set and 11% across the testing set. Although the proposed model requires a significant initial training cost, this represents a one-time effort. Once trained, the model can be reused or fine-tuned for new scheduling environments with minimal overhead. Importantly, inference time remained extremely low across all instances, consistently under 0.12 s per test set. These findings highlight MathBERT’s potential as a scalable and computationally efficient alternative to simulation-based evaluation, supporting scheduling in real-world manufacturing systems.