Combining tabu Hopfield network and estimation of distribution for unconstrained binary quadratic programming problem

Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. This paper combines a tabu Hopfield neural network (HNN) (THNN) with estimation of distribution algorithm (EDA), and thus a THNN–EDA is proposed for the UBQP. In the THNN, the tabu rule, instead of the original updating rule of the HNN, is used to govern the state transition or updating of neurons to search for the global minimum of the energy function. A probability vector in EDA model is built to characterize the distribution of promising solutions in the search space, and then the THNN is guided by the global search information in EDA model to search better solution in the promising region. Thus, the short term memory of the tabu mechanism in the THNN cooperates with the long term memory mechanism in the EDA to help the network escape from local minima. The THNN–EDA is tested on 21 UBQP benchmark problems with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. Simulation results show that the THNN–EDA is better than the other HNN based algorithms, and is better than or competitive with metaheuristic algorithms and state-of-the-art algorithms.