PARCO: Learning Parallel Autoregressive Policies for Efficient Multi-Agent Combinatorial Optimization

Multi-agent combinatorial optimization problems such as routing and scheduling have great practical relevance but present challenges due to their NP-hard combinatorial nature, hard constraints on the number of possible agents, and hard-to-optimize objective functions. This paper introduces PARCO (Parallel AutoRegressive Combinatorial Optimization), a novel approach that learns fast surrogate solvers for multi-agent combinatorial problems with reinforcement learning by employing parallel autoregressive decoding. We propose a model with a Multiple Pointer Mechanism to efficiently decode multiple decisions simultaneously by different agents, enhanced by a Priority-based Conflict Handling scheme. Moreover, we design specialized Communication Layers that enable effective agent collaboration, thus enriching decision-making. We evaluate PARCO in representative multi-agent combinatorial problems in routing and scheduling and demonstrate that our learned solvers offer competitive results against both classical and neural baselines in terms of both solution quality and speed. We make our code openly available at https://github.com/ai4co/parco.

Formulating and solving integrated order batching and routing in multi-depot AGV-assisted mixed-shelves warehouses

Different retail and e-commerce companies are facing the challenge of assembling large numbers of time-critical picking orders that include both single-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 both single-line and multi-line orders (saving up to 67% on driving distances for AGVs). Our variable neighborhood search algorithm provides close-to-optimal solutions within an acceptable computational time.