A branch-and-bound algorithm (BB for short) is the most general technique to deal with various combinatorial optimization problems. Even if it is used, computation time is likely to increase exponentially. So we consider its parallelization to reduce it. It has been reported that the computation time of a parallel BB heavily depends upon node-variable selection strategies. And, in case of a parallel BB, it is also necessary to prevent increase in communication time. So, it is important to pay attention to how many and what kind of nodes are to be transferred (called sending-node selection strategy). In this paper, for the graph coloring problem, we propose some sending-node selection strategies for a parallel BB algorithm by adopting MPI for parallelization and experimentally evaluate how these strategies affect computation time of a parallel BB on a PC cluster network.

In a previous study about a combinatorial optimization problem solver using neural networks, since the Hopfield method, convergence to the optimum solution sooner and with more certainty is regarded as important. Namely, only static states are considered as the information. However, from a biological point of view, dynamical systems have attracted attention recently. Therefore, we propose a "dynamical" combinatorial optimization problem solver using hysteresis neural networks. In this paper, the proposed system is evaluated by the N-Queen problem.