An asynchronous P system with branch and bound for solving the knapsack problem

Membrane computing, which is a computational model based on cell activity, has considerable attention as a new computation paradigm. In general membrane computing, computationally hard problems have been solved in a polynomial number of steps using an exponential number of membranes. However, reduction of the number of membranes must be considered in order to make a P system a more realistic model.In the present paper, we propose an asynchronous P system for the 0/1 knapsack problem using branch and bound, which is a well-known optimization technique. The proposed P system solves the knapsack problem with n items and works in O(n2
ⁿ
) sequential steps or O(n
²
) parallel steps.In addition, the numbers of membranes used in the proposed P system are evaluated by computational simulation. The experimental results show the validity and efficiency of the proposed P system.