Abstract Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the “Optimizing the Production of Test Vehicles” use-case given in the BMW quantum computing challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like coin-or branch and cut and Gurobi solver. We conclude that the performance of the CQM solver is comparable to the classical solvers in optimizing the number of test vehicles, given the noise-prone quantum hardware. However, the CQM solver takes much more time, which prohibits obtaining useful quantum advantages. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.
Abstract Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the “Optimizing the Production of Test Vehicles” use-case given in the BMW quantum computing challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like coin-or branch and cut and Gurobi solver. We conclude that the performance of the CQM solver is comparable to the classical solvers in optimizing the number of test vehicles, given the noise-prone quantum hardware. However, the CQM solver takes much more time, which prohibits obtaining useful quantum advantages. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.
In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.
To increase efficiency in automotive manufacturing, newly produced vehicles can move autonomously from the production line to the distribution area. This requires an optimal placement of sensors to ensure full coverage while minimizing the number of sensors used. The underlying optimization problem poses a computational challenge due to its large-scale nature. Currently, classical solvers rely on heuristics, often yielding nonoptimal solutions for large instances, resulting in suboptimal sensor distributions and increased operational costs. We explore quantum computing methods that may outperform classical heuristics in the future. We implemented quantum annealing with D-Wave, transforming the problem into a quadratic unconstrained binary optimization formulation with one-hot and binary encoding. Hyperparameters like the penalty terms and the annealing time are optimized and the results are compared with default parameter settings. Our results demonstrate that quantum annealing is capable of solving instances derived from real-world scenarios. Through the use of decomposition techniques, we are able to scale the problem size further, bringing it closer to practical, industrial applicability. Through this work, we provide key insights into the importance of quantum annealing parametrization, demonstrating how quantum computing could contribute to cost-efficient, large-scale optimization problems once the hardware matures.
This study compares the performance of D-Wave’s two quantum-classical hybrid optimization solvers, which integrate quantum computing principles with classical optimization techniques to solve complex optimization problems. It focuses on the Binary Quadratic Model (BQM) solver, which encodes optimization problems using a binary quadratic formulation, and the Constrained Quadratic Model (CQM) solver, which can incorporate constraints into the model. The solvers were tested on five combinatorial optimization problems: Traveling Salesman Problem (TSP), Quadratic Knapsack Problem (QKP), Quadratic Assignment Problem (QAP), Weighted Max-Cut Problem (WMP), and Maximum Clique Problem (MCP). The goal is to quantify the accuracy of solutions compared to the optimal ones. Experiments on multiple instances with known optimal solutions examined solver behavior and solution quality. At default execution durations, the CQM solver generally outperforms BQM with lower error and higher consistency. Across all test problem instances in TSP, QKP, QAP, and WMP, the CQM solver achieved lower average absolute errors by 48.38, 27.83, 21.29, and 0.05 percentage points, respectively, compared to the BQM solver. An exception was found in MCP, where the BQM solver outperformed the CQM solver by 0.75 percentage points. These findings provide a guide for end users to understand the characteristics of the solvers and to select the appropriate solver for their specific optimization problems.
Motivated by recent efforts to develop quantum computing for practical, industrial-scale challenges, we demonstrate the effectiveness of state-of-the-art hybrid (not necessarily quantum) solvers in addressing the business-centric optimization problem of scheduling Automatic Guided Vehicles (AGVs). Some solvers can already leverage noisy intermediate-scale quantum (NISQ) devices. In our study, we utilize D-Wave hybrid solvers that implement classical heuristics with potential assistance from a quantum processing unit. This hybrid methodology performs comparably to existing classical solvers. However, due to the proprietary nature of the software, the precise contribution of quantum computation remains unclear. Our analysis focuses on a practical, business-oriented scenario: scheduling AGVs within a factory constrained by limited space, simulating a realistic production setting. Our approach maps a realistic AGVs problem onto one reminiscent of railway scheduling and demonstrates that the AGVs problem is better suited to quantum computing than its railway counterpart, the latter being denser in terms of the average number of constraints per variable. The main idea here is to highlight the potential usefulness of a hybrid approach for handling AGVs scheduling problems of practical sizes. We show that a scenario involving up to 21 AGVs, significant due to possible deadlocks, can be efficiently addressed by a hybrid solver in seconds.
The paper presents a quantum method to optimize the placement of sensors on the surface of a vehicle. The problem, as posted in the BMW Quantum Computing Challenge 2021, is to arrive at the optimal positions and configurations (type and orientation) of the sensors on the vehicle surface that maximizes coverage of the Region of Interest (RoI), while minimizing the total cost of the selected sensors. The dataset contains approximately 100,000 points in the RoI, with defined measures of criticality (ranging between 0 to 1), distributed over a volume of approximately 40,000 cubic metres around the vehicle. The types of sensors, their coverage parameters and costs are inputs to the problem.The optimization problem is decomposed and solved individually for each side of the vehicle, and the results for the entire vehicle are collated and presented in the paper. The approach considers a quadratic approximation to the maximum set-coverage formulation with the advantage of obtaining the optimal number of sensors as an output from the model itself. The resultant quadratic program is solved using quantum methods, as well as a standard, state-of-the-art Integer Quadratic Program (IQP) solver, respectively. The quadratic approximation consumes qubits that are linear in the number of total configurations and significantly reduces the number of decision variables required in an Ising formulation of the problem.The quantum and classical methods are found to perform on par with each other. A detailed comparison of the results is presented in the paper. Given the combinatorial nature of the optimization problem, the classical approach may become intractable while solving the problem in an integrated manner (instead of solving individually for each side). Under such scenarios, there is a possibility to expect benefits by adopting the proposed strategies with the availability of large-sized quantum computers in the near future.
We present a quantum-based approach for the optimization of join orders in database applications. Our approach relies on a hybrid framework, where classical heuristics are combined with a quantum processor to accelerate the search over the set of solutions to a constrained problem. By taking advantage of a previously introduced formulation of the join order optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem, we implement it using the Constrained Quadratic Model (CQM), a hybrid classical-quantum solver that interfaces classical heuristics with D-Wave’s quantum annealer. We show that even a generic implementation of this classical-quantum hybrid framework produces competitive results for the join order problem, suggesting that better-tailored hybrid solvers could produce a computational advantage.