--This work explores the application of hybrid quantum-classical algorithms to optimize robotic inspection trajectories derived from Computer-Aided Design (CAD) models in industrial settings. By modeling the task as a 3D variant of the Traveling Salesman Problem--incorporating incomplete graphs and open-route constraints--this study evaluates the performance of two D-Wave-based solvers against classical methods such as GUROBI and Google OR-T ools. Results across five real-world cases demonstrate competitive solution quality with significantly reduced computation times, highlighting the potential of quantum approaches in automation under Industry 4.0. Advances in quantum computing are enabling problem-solving capabilities at a scale beyond brute-force classical simulation [1]. As hardware improves--with more qubits, lower error rates, and faster execution--quantum algorithm research is advancing through both theory and experimentation.

The development of advanced quantum-classical algorithms is among the most prominent strategies in quantum computing. Numerous hybrid solvers have been introduced recently. Many of these methods are created ad hoc to address specific use cases. However, several well-established schemes are frequently utilized to address optimization problems. In this context, D-Wave launched the Hybrid Solver Service in 2020, offering a portfolio of methods designed to accelerate time-to-solution for users aiming to optimize performance and operational processes. Recently, a new technique has been added to this portfolio: the Nonlinear-Program Hybrid Solver. This paper describes this solver and evaluates its performance through a benchmark of 45 instances across three combinatorial optimization problems: the Traveling Salesman Problem, the Knapsack Problem, and the Maximum Cut Problem. To facilitate the use of this relatively unexplored solver, we provide details of the implementation used to solve these three optimization problems.