Guiding Large Language Models with Genetic Programming-Evolved Heuristic Knowledge for Dynamic Multi-Mode Project Scheduling
Authors: Yuan Tian, Yi Mei, Mengjie Zhang
Organizations: Centre for Data Science and Artificial Intelligence & School of Engineering and Computer Science, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand
Abstract
In dynamic multi-mode project scheduling, activities have alternative execution modes and uncertain durations, while precedence relations and limited resources constrain their execution. Heuristic priority rules support fast online decisions, but their design requires substantial domain expertise. Genetic programming (GP) hyper-heuristics can automatically evolve such rules. Large language models (LLMs), meanwhile, provide a flexible interface for interpreting scheduling information and explaining decisions. However, zero-shot LLM decisions may lack domain knowledge, consume many tokens, and vary across repeated queries. GP-evolved rules therefore provide a potential source of scheduling knowledge for guiding LLM decisions. Unlike existing LLM--GP hybrids that use LLMs to support heuristic evolution, we transfer knowledge in the reverse direction, using knowledge extracted from high-quality GP rules to guide an online LLM decision maker. We extract knowledge from high-quality GP rules and inject it through Feature Selection, Feature Hint, Rule Reference, and Rule Follow. These mechanisms are evaluated in terms of scheduling performance, token consumption, decision stability, and the feature focus expressed in generated rationales. GP-derived guidance generally improves the unguided LLM, but its representation matters. Simplifying the decision context or supplying explicit decision logic is more effective than highlighting important features. Feature Selection offers the best token efficiency, whereas Rule Follow achieves strong performance at greater token cost. Guidance also improves decision stability and changes the features expressed in generated rationales.
This paper introduces SCHEDBench, a natural-language benchmark for evaluating combinatorial scheduling constraint faithfulness under surface-form variation. Grounded in canonical scheduling instances and solver-derived feasibility and optimality, SCHEDBench assesses whether large language models (LLMs) generate schedules with the same constraint-feasible behavior across varied natural-language (NL) surface forms. SCHEDBench spans 1,132 instances across job-shop scheduling problems (JSP), single and multi-mode resource-constrained project scheduling problems (RCPSP), nurse rostering/scheduling, and curriculum timetabling problems of varying difficulty. Instances are templated into natural language problems using domain-specific templates, themed entities, lexical-syntactic template rephrasing, and constraint-level surface-form variation, with reference solutions verified for feasibility and objective optimality. Across thirteen frontier and open-weight LLMs, we find that models are not reliably invariant to semantically equivalent renderings of the same scheduling problem. Surface-form variation reduces feasibility and induces above-noise shifts in per-instance hard-constraint violations on matched instances. Among the tested isolated axes, constraint reordering yields the clearest above-noise sensitivity.
Progress in neural combinatorial optimization for Dynamic Flexible Job Shop Scheduling Problem (DFJSP) is currently hindered by a methodological tension: static benchmarks encourage benchmark overfitting, while uncalibrated generators obscure algorithmic capability with stochastic noise. To resolve this, we introduce \textbf{DynaSchedBench}, a diagnostic framework for DFJSP that rigorously controls the instance-generation process. Instead of relying on parameter sampling, our approach utilizes Sequential Event-Space Calibrator (SESC) that computes a novel Schedule Stress Index (SSI) to stratify instances by difficulty. We demonstrate that SESC is substantially more computationally efficient than evolutionary baselines while converging reliably to the target metrics. The framework integrates modular components for instance generation, snapshot-based simulation, agents, evaluation, and visualization, thereby enabling rigorous testing of reactive and lookahead-based policies. Leveraging this calibrated environment, we identify key limitations of LLM-based scheduling agents. Specifically, in step-wise online decision-making for dynamic scheduling, we identify an ``Observability Paradox'': providing agents with oracle access to full structural information can degrade policy performance, underperforming concise information. Furthermore, despite substantial token overhead, tool-augmented and refinement strategies fail to reliably improve performance, and most LLM agents fail to consistently surpass strong dispatching baselines-behaving more like robust heuristic approximators than superior optimizers.
We study offline scheduling for large language model (LLM) serving under a fixed KV-cache memory budget, where requests have heterogeneous prompt (prefill) and response (decode) lengths. Prompt tokens determine initial KV-cache usage, while each generated token further increases memory consumption, creating dynamic memory constraints during autoregressive decoding. Given a backlog of n requests arriving together, the goal is to form mixed prefill and decode batches over time to minimize total end-to-end latency. We show that heterogeneous prompt lengths fundamentally change the scheduling problem: the problem is NP-hard, and standard policies such as first-come-first-served, shortest-output-first, and total-size-based prioritization can have unbounded approximation ratios. We propose Sorted-F, a scheduling algorithm that repeatedly forms feasible batches using an F-metric that balances batch size against downstream decode cost. We prove that Sorted-F achieves a constant-factor approximation guarantee in the offline/backlogged model. We also develop practical implementations, including an exact dynamic program for small instances and scalable local-search and greedy heuristics for larger instances, as well as LP-guided and receding-horizon variants. Experiments on public workloads that combine short conversations and long-document summarization show that F-metric-based scheduling consistently reduces latency relative to standard baselines and remains close to the LP relaxation lower bound for tractable instances.