Solving the 0-1 Knapsack Problem by Using Tissue P System With Cell Division

Abstract

Membrane computing is a kind of distributed and parallel computing model inspired by a biological cell mechanism. The maximum parallelism of membrane computing improves the computational efficiency of its computational model. In this paper, a tissue P system named Π KP is proposed to solve the 0-1 knapsack problem, which is one of the classic NP-hard problems. Π KP could obtain the accurate solutions of knapsack problem and points out the number of accurate solutions, which mainly consists of three stages: first, generate all the solutions of knapsack problem by a cell division; then calculate the weights and total values in all the candidate membranes, which will be kept or dissolved according to the restriction of knapsack problem; and check out the final solutions. The instances are executed on a membrane simulator named UPSimulator, and the result of the experiments shows the whole searching procedure by the rules and proves the correctness and efficiency of the system.Fundamental Research Funds for the Central Universities (China) 2019CDXYJSJ002