Using a bank of binary Hopfield networks as constraints solver in hybrid algorithms

This paper proposes the use of a bank of Hopfield networks to solve a class of constraints which appear in combinatorial optimization problems. Specifically, we deal with problems which constraints’ structure can be represented by a binary matrix C, and can be separated in independent substructures. We show that a bank of Hopfield networks can solve these constraints, and also can be easily hybridized with a global search algorithm, such as simulated annealing, to obtain a final solution to the problem. We apply our approach to the solution of a famous logic-type puzzle, the light-up puzzle, where we report improvements over a branch and bound algorithm, and to an important problem which arises in electronic control: the so-called Crossbar Switch Problem.