<p>Quantum algorithms are of great interest due to their possible use in optimization problems. In particular, variational algorithms that utilize classical counterparts to optimize parameters hold promise for use in currently existing devices. However, convergence stagnation phenomena pose a challenge for such algorithms. Seeking to avoid such difficulties, we present a framework based on circuits with variable topology utilizing two approaches: one based on an evolutionary method known from the literature, and the other employing an introduction of an ansatz with a circuital structure inspired by the physics of the Hamiltonian related to the problem, considering an evolutionary term combined with a flexible circuit configuration inspired by the trotterization procedure in a digitalized version. The efficiency of the proposed framework was tested on several instances of the set partitioning problem. The two approaches were compared with the Variational Quantum Eigensolver in noisy and non-noisy scenarios. We also tested and compared the framework with the Quantum Approximate Optimization Algorithm for instances of the problem considering noisy. The results demonstrated that optimization using circuits with variable topology presented very encouraging outcomes. This framework circumvents the need for classical optimizers and, as a consequence, this procedure based on circuits with variable topology indicates an interesting path in the search for algorithms to solve integer optimization problems targeting efficient applications in larger-scale scenarios.</p>