  Optimization problems are ubiquitous in various industrial settings, and
multi-knapsack optimization is one recurrent task faced daily by several
industries. The advent of quantum computing has opened a new paradigm for
computationally intensive tasks, with promises of delivering better and faster
solutions for specific classes of problems. This work presents a comprehensive
study of quantum computing approaches for multi-knapsack problems, by
investigating some of the most prominent and state-of-the-art quantum
algorithms using different quantum software and hardware tools. The performance
of the quantum approaches is compared for varying hyperparameters. We consider
several gate-based quantum algorithms, such as QAOA and VQE, as well as quantum
annealing, and present an exhaustive study of the solutions and the estimation
of runtimes. Additionally, we analyze the impact of warm-starting QAOA to
understand the reasons for the better performance of this approach. We discuss
the implications of our results in view of utilizing quantum optimization for
industrial applications in the future. In addition to the high demand for
better quantum hardware, our results also emphasize the necessity of more and
better quantum optimization algorithms, especially for multi-knapsack problems.
