Learned enclosure method for experimental EIT data

Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary measurements is nonlinear and highly ill-posed, making it difficult to solve accurately. In recent years, there has been growing interest in combining analytical methods with machine learning to solve inverse problems. In this paper, we propose a method for estimating the convex hull of inclusions from boundary measurements by combining the enclosure method proposed by Ikehata with neural networks. We demonstrate its performance using experimental data. Compared to the classical enclosure method with least squares fitting, the learned convex hull achieves superior performance on both simulated and experimental data.

Deep Reinforcement Learning for Multi-Truck Vehicle Routing Problems with Multi-Leg Demand Routes

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these techniques have been quite successful for relatively simple problem instances, there are still under-researched and highly complex VRP variants for which no effective RL method has been demonstrated. In this work we focus on one such VRP variant, which contains multiple trucks and multi-leg routing requirements. In these problems, demand is required to move along sequences of nodes, instead of just from a start node to an end node. With the goal of making deep RL a viable strategy for real-world industrial-scale supply chain logistics, we develop new extensions to existing encoder-decoder attention models which allow them to handle multiple trucks and multi-leg routing requirements. Our models have the advantage that they can be trained for a small number of trucks and nodes, and then embedded into a large supply chain to yield solutions for larger numbers of trucks and nodes. We test our approach on a real supply chain environment arising in the operations of Japanese automotive parts manufacturer Aisin Corporation, and find that our algorithm outperforms Aisin's previous best solution.

Reinforcement Learning for Multi-Truck Vehicle Routing Problems

Vehicle routing problems and other combinatorial optimization problems have been approximately solved by reinforcement learning agents with policies based on encoder-decoder models with attention mechanisms. These techniques are of substantial interest but still cannot solve the complex routing problems that arise in a realistic setting which can have many trucks and complex requirements. With the aim of making reinforcement learning a viable technique for supply chain optimization, we develop new extensions to encoder-decoder models for vehicle routing that allow for complex supply chains using classical computing today and quantum computing in the future. We make two major generalizations. First, our model allows for routing problems with multiple trucks. Second, we move away from the simple requirement of having a truck deliver items from nodes to one special depot node, and instead allow for a complex tensor demand structure. We show how our model, even if trained only for a small number of trucks, can be embedded into a large supply chain to yield viable solutions.

Quantum Neural Networks for a Supply Chain Logistics Application

Problem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate-scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical-quantum algorithms have potential, however, to achieve good performance on much larger problem instances. We investigate one such hybrid algorithm on a problem of substantial importance: vehicle routing for supply chain logistics with multiple trucks and complex demand structure. We use reinforcement learning with neural networks with embedded quantum circuits. In such neural networks, projecting high-dimensional feature vectors down to smaller vectors is necessary to accommodate restrictions on the number of qubits of NISQ hardware. However, we use a multi-head attention mechanism where, even in classical machine learning, such projections are natural and desirable. We consider data from the truck routing logistics of a company in the automotive sector, and apply our methodology by decomposing into small teams of trucks, and we find results comparable to human truck assignment.

Short Quantum Circuits in Reinforcement Learning Policies for the Vehicle Routing Problem

Quantum computing and machine learning have potential for symbiosis. However, in addition to the hardware limitations from current devices, there are still basic issues that must be addressed before quantum circuits can usefully incorporate with current machine learning tasks. We report a new strategy for such an integration in the context of attention models used for reinforcement learning. Agents that implement attention mechanisms have successfully been applied to certain cases of combinatorial routing problems by first encoding nodes on a graph and then sequentially decoding nodes until a route is selected. We demonstrate that simple quantum circuits can used in place of classical attention head layers while maintaining performance. Our method modifies the networks used in [1] by replacing key and query vectors for every node with quantum states that are entangled before being measured. The resulting hybrid classical-quantum agent is tested in the context of vehicle routing problems where its performance is competitive with the original classical approach. We regard our model as a prototype that can be scaled up and as an avenue for further study on the role of quantum computing in reinforcement learning.