Lin Xie

Federico Berto, Chuanbo Hua, Laurin Luttmann et al.

Combinatorial optimization problems involving multiple agents are notoriously challenging due to their NP-hard nature and the necessity for effective agent coordination. Despite advancements in learning-based methods, existing approaches often face critical limitations, including suboptimal agent coordination, poor generalization, and high computational latency. To address these issues, we propose PARCO (Parallel AutoRegressive Combinatorial Optimization), a general reinforcement learning framework designed to construct high-quality solutions for multi-agent combinatorial tasks efficiently. To this end, PARCO integrates three key novel components: (1) transformer-based communication layers to enable effective agent collaboration during parallel solution construction, (2) a multiple pointer mechanism for low-latency, parallel agent decision-making, and (3) priority-based conflict handlers to resolve decision conflicts via learned priorities. We evaluate PARCO in multi-agent vehicle routing and scheduling problems, where our approach outperforms state-of-the-art learning methods, demonstrating strong generalization ability and remarkable computational efficiency. We make our source code publicly available to foster future research: https://github.com/ai4co/parco.

Laurin Luttmann, Lin Xie

The Mixed-Shelves Picker Routing Problem (MSPRP) is a fundamental challenge in warehouse logistics, where pickers must navigate a mixed-shelves environment to retrieve SKUs efficiently. Traditional heuristics and optimization-based approaches struggle with scalability, while recent machine learning methods often rely on sequential decision-making, leading to high solution latency and suboptimal agent coordination. In this work, we propose a novel hierarchical and parallel decoding approach for solving the min-max variant of the MSPRP via multi-agent reinforcement learning. While our approach generates a joint distribution over agent actions, allowing for fast decoding and effective picker coordination, our method introduces a sequential action selection to avoid conflicts in the multi-dimensional action space. Experiments show state-of-the-art performance in both solution quality and inference speed, particularly for large-scale and out-of-distribution instances. Our code is publicly available at http://github.com/LTluttmann/marl4msprp.

Lin Xie, Nils Thieme, Ruslan Krenzler et al.

Robotic mobile fulfillment systems (RMFSs) are a new type of warehousing system, which has received more attention recently, due to increasing growth in the e-commerce sector. Instead of sending pickers to the inventory area to search for and pick the ordered items, robots carry shelves (called "pods") including ordered items from the inventory area to picking stations. In the picking stations, human pickers put ordered items into totes; then these items are transported by a conveyor to the packing stations. This type of warehousing system relieves the human pickers and improves the picking process. In this paper, we concentrate on decisions about the assignment of pods to stations and orders to stations to fulfill picking for each incoming customer's order. In previous research for an RMFS with multiple picking stations, these decisions are made sequentially. Instead, we present a new integrated model. To improve the system performance even more, we extend our model by splitting orders. This means parts of an order are allowed to be picked at different stations. To the best of the authors' knowledge, this is the first publication on split orders in an RMFS. We analyze different performance metrics, such as pile-on, pod-station visits, robot moving distance and order turn-over time. We compare the results of our models in different instances with the sequential method in our open-source simulation framework RAWSim-O.

Lin Xie, Hanyi Li, Nils Thieme

In a new type of automated parts-to-picker warehouse system - a Robotic Mobile Fulfillment System (RMFS) - robots are sent to transport pods (movable shelves) to human operators at stations to pick/put items from/to pods. There are many operational decision problems in such a system, and some of them are interdependent and influence each other. In order to analyze the decision problems and the relationships between them, there are two open-source simulation frameworks in the literature, Alphabet Soup and RAWSim-O. However, the steps between simulation and real-world RMFS are not clear in the literature. Therefore, this paper aims to bridge this gap. The simulator is firstly transferred as core software. The core software is connected with an open-source ERP system, called Odoo, while it is also connected with real robots and stations through an XOR-bench. The XOR-bench enables the RMFS to be integrated with several mini-robots and mobile industrial robots in (removed) experiments for the purpose of research and education.

Laurin Luttmann, Lin Xie

Self-improvement has emerged as a state-of-the-art paradigm in Neural Combinatorial Optimization (NCO), where models iteratively refine their policies by generating and imitating high-quality solutions. Despite strong empirical performance, existing methods face key limitations. Training is computationally expensive, as policy updates require sampling numerous candidate solutions per instance to extract a single expert trajectory. More fundamentally, these approaches fail to exploit the structure of combinatorial problems involving the coordination of multiple agents, such as vehicles in min-max routing or machines in scheduling. By supervising on single-action trajectories, they fail to exploit agent-permutation symmetries, where distinct sequences of actions yield identical solutions, hindering generalization and the ability to learn coordinated behavior. We address these challenges by extending self-improvement to operate over joint multi-agent actions. Our model architecture predicts complete agent-task assignments jointly at each decision step. To explicitly leverage symmetries, we employ a set-prediction loss, which supervises the policy on multiple expert assignments for any given state. This approach enhances sample efficiency and the model's ability to learn coordinated behavior. Furthermore, by generating multi-agent actions in parallel, it drastically accelerates the solution generation phase of the self-improvement loop. Empirically, we validate our method on several combinatorial problems, demonstrating consistent improvements in the quality of the final solution and a reduced generation latency compared to standard self-improvement.

Lin Xie, Hanyi Li, Laurin Luttmann

Different retail and e-commerce companies are facing the challenge of assembling large numbers of time-critical picking orders that include both small-line and multi-line orders. To reduce unproductive picker working time as in traditional picker-to-parts warehousing systems, different solutions are proposed in the literature and in practice. For example, in a mixed-shelves storage policy, items of the same stock keeping unit are spread over several shelves in a warehouse; or automated guided vehicles (AGVs) are used to transport the picked items from the storage area to packing stations instead of human pickers. This is the first paper to combine both solutions, creating what we call AGV-assisted mixed-shelves picking systems. We model the new integrated order batching and routing problem in such systems as an extended multi-depot vehicle routing problem with both three-index and two-commodity network flow formulations. Due to the complexity of the integrated problem, we develop a novel variable neighborhood search algorithm to solve the integrated problem more efficiently. We test our methods with different sizes of instances, and conclude that the mixed-shelves storage policy is more suitable than the usual storage policy in AGV-assisted mixed-shelves systems for orders with different sizes of order lines (saving up to 62% on driving distances for AGVs). Our variable neighborhood search algorithm provides optimal solutions within an acceptable computational time.

Ruslan Krenzler, Lin Xie, Hanyi Li

In a robotic mobile fulfillment system, robots bring shelves, called pods, with storage items from the storage area to pick stations. At every pick station there is a person -- the picker -- who takes parts from the pod and packs them into boxes according to orders. Usually there are multiple shelves at the pick station. In this case, they build a queue with the picker at its head. When the picker does not need the pod any more, a robot transports the pod back to the storage area. At that time, we need to answer a question: "Where is the optimal place in the inventory to put this pod back?". It is a tough question, because there are many uncertainties to consider before answering it. Moreover, each decision made to answer the question influences the subsequent ones. The goal of this paper is to answer the question properly. We call this problem the Pod Repositioning Problem and formulate a deterministic model. This model is tested with different algorithms, including binary integer programming, cheapest place, fixed place, random place, genetic algorithms, and a novel algorithm called tetris.

Marius Merschformann, Lin Xie, Hanyi Li

This paper deals with a new type of warehousing system, Robotic Mobile Fulfillment Systems (RMFS). In such systems, robots are sent to carry storage units, so-called "pods", from the inventory and bring them to human operators working at stations. At the stations, the items are picked according to customers' orders. There exist new decision problems in such systems, for example, the reallocation of pods after their visits at work stations or the selection of pods to fulfill orders. In order to analyze decision strategies for these decision problems and relations between them, we develop a simulation framework called "RAWSim-O" in this paper. Moreover, we show a real-world application of our simulation framework by integrating simple robot prototypes based on vacuum cleaning robots.

Marius Merschformann, Lin Xie, Daniel Erdmann

This paper presents a collection of path planning algorithms for real-time movement of multiple robots across a Robotic Mobile Fulfillment System (RMFS). Robots are assigned to move storage units to pickers at working stations instead of requiring pickers to go to the storage area. Path planning algorithms aim to find paths for the robots to fulfill the requests without collisions or deadlocks. The state-of-the-art path planning algorithms, including WHCA*, FAR, BCP, OD&ID and CBS, were adapted to suit path planning in RMFS and integrated within a simulation tool to guide the robots from their starting points to their destinations during the storage and retrieval processes. Ten different layouts with a variety of numbers of robots, floors, pods, stations and the sizes of storage areas were considered in the simulation study. Performance metrics of throughput, path length and search time were monitored. Simulation results demonstrate the best algorithm based on each performance metric.