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A Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems: QOPTLib

Core Concepts
QOPTLib is a quantum computing oriented benchmark for combinatorial optimization problems, comprising 40 instances across four well-known problems: Traveling Salesman Problem, Vehicle Routing Problem, one-dimensional Bin Packing Problem, and Maximum Cut Problem.
QOPTLib is a benchmark for evaluating quantum computing algorithms on combinatorial optimization problems. It includes 40 instances across four problems: Traveling Salesman Problem (TSP), Vehicle Routing Problem (VRP), one-dimensional Bin Packing Problem (1dBPP), and Maximum Cut Problem (MCP). The TSP dataset consists of 10 instances ranging from 4 to 25 nodes, derived from well-known TSPLib instances. The VRP dataset has 10 instances with 4 to 8 nodes, based on the Augerat CVRP benchmark. The 1dBPP dataset includes 10 randomly generated instances with 3 to 14 packages and bin capacities of 10, 12, or 15. The MCP dataset has 10 instances with 10 to 300 nodes, randomly generated. The problem sizes were selected to be computationally addressable by current quantum computers, including both small toy instances and more complex, yet approachable, cases. The authors conducted a preliminary experiment using two DWAVE solvers: the pure quantum Advantage system6.1 and the hybrid LeapHybridBQMSampler. The results provide a baseline for future research on quantum optimization algorithms.
The total cost of the optimal route for the wi4 TSP instance is 6700. The best solution found for the BPP 3 instance uses 2 bins. The best solution found for the MaxCut 10 instance has a cut value of 25.
"QOPTLib constitutes the first effort to provide users a general-purpose dataset." "Our main intention with this is to establish a preliminary baseline, hoping to inspire other researchers to beat these outcomes with newly proposed quantum-based algorithms."

Deeper Inquiries

How can QOPTLib be extended to include more real-world optimization problems beyond the four covered in this study

To extend QOPTLib to include more real-world optimization problems beyond the four covered in this study, several steps can be taken: Identifying Relevant Real-World Problems: Researchers can start by identifying a diverse range of real-world optimization problems that are commonly encountered in various industries such as logistics, supply chain management, finance, healthcare, and telecommunications. Research and Literature Review: Conduct a thorough literature review to understand the current state-of-the-art solutions, challenges, and benchmarks for these real-world optimization problems. This will help in selecting problems that are both relevant and challenging for quantum computing. Problem Formulation: Once the real-world optimization problems are identified, they need to be formulated in a way that is suitable for quantum computing. This may involve adapting existing problem formulations or creating new formulations that leverage the strengths of quantum algorithms. Instance Generation: Develop a methodology for generating problem instances for the selected real-world optimization problems. These instances should vary in size and complexity to provide a comprehensive testbed for quantum solvers. Validation and Testing: Validate the generated instances by comparing the solutions obtained from quantum algorithms with known optimal or near-optimal solutions. This will ensure the effectiveness and reliability of the benchmark. Open Access and Collaboration: Make the extended QOPTLib dataset openly accessible to the research community to encourage collaboration, benchmarking, and the development of new quantum optimization algorithms for real-world problems. By following these steps, QOPTLib can be expanded to encompass a wider range of real-world optimization problems, providing researchers with a valuable resource for testing and advancing quantum computing solutions in practical applications.

What are the potential limitations or biases in the random generation of the MCP instances, and how could they be addressed

The random generation of Maximum Cut Problem (MCP) instances in QOPTLib may introduce potential limitations or biases that could impact the validity and reliability of the benchmark. Some of these limitations and biases include: Biased Graph Structures: The random generation process may unintentionally bias the generated graphs towards certain structures or characteristics, leading to instances that do not represent a diverse range of real-world scenarios. Limited Diversity: Random generation may result in instances that are not sufficiently diverse in terms of graph size, edge weights, or connectivity patterns, limiting the generalizability of the benchmark. Lack of Real-World Relevance: The randomly generated instances may not accurately reflect the complexities and constraints present in real-world MCP applications, potentially reducing the practical utility of the benchmark. To address these limitations and biases, the following strategies can be implemented: Diverse Generation Algorithms: Utilize a variety of generation algorithms, such as preferential attachment, small-world networks, or scale-free networks, to create instances with different structural properties and complexities. Incorporate Real-World Data: Integrate real-world data or scenarios into the instance generation process to ensure that the generated instances closely resemble practical MCP applications. Validation and Sensitivity Analysis: Conduct sensitivity analysis and validation tests to assess the impact of the random generation process on the performance of quantum solvers. This can help identify and mitigate any biases or limitations in the benchmark. By implementing these strategies, the random generation of MCP instances in QOPTLib can be enhanced to provide a more robust and representative benchmark for evaluating quantum optimization algorithms.

Given the rapid advancements in quantum hardware, how might the problem sizes and characteristics of QOPTLib need to evolve over time to remain relevant and challenging for the research community

As quantum hardware continues to advance rapidly, the problem sizes and characteristics of QOPTLib will need to evolve to remain relevant and challenging for the research community. Some key considerations for the evolution of QOPTLib include: Scaling Problem Sizes: With the increasing qubit counts and connectivity of quantum processors, QOPTLib should include larger problem instances to leverage the capabilities of advanced quantum hardware. This will enable researchers to explore more complex optimization problems and algorithms. Incorporating Hybrid Approaches: As hybrid quantum-classical solvers become more prevalent, QOPTLib should include instances that are suitable for both pure quantum and hybrid approaches. This will facilitate the evaluation and comparison of different solver types on a common benchmark. Dynamic Problem Generation: Implement a dynamic instance generation process that adapts to the capabilities of the latest quantum hardware. This can involve generating instances with varying levels of complexity and size to challenge the performance of quantum solvers across different platforms. Community Feedback and Collaboration: Regularly seek feedback from the research community and collaborate with experts in quantum optimization to ensure that QOPTLib remains aligned with the latest advancements and challenges in the field. This iterative approach will help QOPTLib stay relevant and valuable for researchers. By incorporating these considerations and adapting to the evolving landscape of quantum computing, QOPTLib can continue to serve as a comprehensive and cutting-edge benchmark for combinatorial optimization problems in the quantum computing domain.