Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

In modern industrial and logistics environments, the rapid expansion of fast delivery services has heightened the demand for storage systems that combine high efficiency with increased density. Multi-deep autonomous vehicle storage and retrieval systems (AVS/RS) present a viable solution for achieving greater storage density. However, these systems encounter significant challenges during retrieval operations due to lane blockages. A conventional approach to mitigate this issue involves storing items with homogeneous characteristics in a single lane, but this strategy restricts the flexibility and adaptability of multi-deep storage systems. In this study, we propose a deep reinforcement learning-based framework to address the retrieval problem in multi-deep storage systems with heterogeneous item configurations. Each item is associated with a specific due date, and the objective is to minimize total tardiness. To effectively capture the system's topology, we introduce a graph-based state representation that integrates both item attributes and the local topological structure of the multi-deep warehouse. To process this representation, we design a novel neural network architecture that combines a Graph Neural Network (GNN) with a Transformer model. The GNN encodes topological and item-specific information into embeddings for all directly accessible items, while the Transformer maps these embeddings into global priority assignments. The Transformer's strong generalization capability further allows our approach to be applied to storage systems with diverse layouts. Extensive numerical experiments, including comparisons with heuristic methods, demonstrate the superiority of the proposed neural network architecture and the effectiveness of the trained agent in optimizing retrieval tardiness.

First of all, there is a lack of systematic methods that improve the performance of algorithms on unseen instances by gathering the experience from the instances solved in the past. Therefore, all the information obtained during the past runs of an algorithm is neglected when a new instance is encountered. A good example is the branchand-bound-and-remember method [34, 40], where the algorithm remembers the information derived during an instance solving, but the information is forgotten as soon as the instance is solved. Second, the development of efficient heuristic rules requires a substantial amount of time devoted to its design and testing. This process is tedious and requires a skilled human professional to fine-tune the heuristic's parameters. A typical example of this feature is genetic algorithms having many parameters for selection, cross-over, mutation, and other operators. The apparent response to the above challenges is utilizing the existing data. However, the main obstacle to the successful application of machine learning to enhance algorithms for combinatorial problems remains. It can be formulated as the following fundamental question--is it possible to extract any useful information from the solved instances and use it efficiently to accelerate solving of an unseen instance?

Ensuring flexible and efficient manufacturing of customized products in an increasing dynamic and turbulent environment without sacrificing cost effectiveness, product quality and on-time delivery has become a key issue for most industrial enterprises. A promising approach to cope with this challenge is the integration of cognitive capabilities in systems and processes with the aim of expanding the knowledge base used to perform managerial and operational tasks. In this work, a novel approach to real-time rescheduling is proposed in order to achieve sustainable improvements in flexibility and adaptability of production systems through the integration of artificial cognitive capabilities, involving perception, reasoning/learning and planning skills. Moreover, an industrial example is discussed where the SOAR cognitive architecture capabilities are integrated in a software prototype, showing that the approach enables the rescheduling system to respond to events in an autonomic way, and to acquire experience through intensive simulation while performing repair tasks.