In this work, we investigate the capabilities of a hybrid quantum-classical procedure to explore the solution space using the D-Wave 2000QTM quantum annealer device. Here, we study the ability of the quantum hardware to solve the number partitioning problem, a well-known NP-hard optimization model that poses some challenges typical of those encountered in real-world applications. This represents one of the most complex scenario in terms of qubits connectivity and, by increasing the input problem size, we analyze the scaling properties of the quantum-classical workflow. We find remarkable results in most instances of the model; for the most complex ones, we investigate further the D-Wave Hybrid suite. Specifically, we were able to find the optimal solutions even in the worst cases by fine-tuning the parameters that schedule the annealing time and allowing a pause in the annealing cycle.