A large population island framework for the unconstrained binary quadratic problem

The unconstrained binary quadratic problem is an NP-hard problem and has applications in many fields. Recently, the problem has attracted much interest in the field of quantum optimization, as it is directly related to the Ising problem in physics and the development of quantum computers. However, effectively solving large instances of this problem remains a major challenge for existing solution methods. To advance the state of the art in solving the problem on a large scale, we propose an evolutionary algorithm with a very large population organized in different islands and integrating a new pairing and recombination method to produce promising offspring in each generation. Numerous experiments are conducted to evaluate the effects of different pairing strategies, crossovers, and migration topologies. This research has led to the discovery of new bounds for difficult instances of the maximum cut problem, which has been transformed using the binary quadratic formulation.