Membrane algorithms are a class of distributed and parallel algorithms inspired by the structure and behavior of living cells. Many attractive features of living cells have already been abstracted as operators to improve the performance of algorithms. In this work, inspired by the function of biological neuron cells storing information, we consider a memory mechanism by introducing memory modules into a membrane algorithm. The framework of the algorithm consists of two kinds of modules (computation modules and memory modules), both of which are arranged in a ring neighborhood topology. They can store and process information, and exchange information with each other. We test our method on a knapsack problem to demonstrate its feasibility and effectiveness. During the process of approaching the optimum solution, feasible solutions are evolved by rewriting rules in each module, and the information transfers according to directions defined by communication rules. Simulation results showed that the performance of membrane algorithms with memory cells is superior to that of algorithms without memory cells for solving a knapsack problem. Furthermore, the memory mechanism can prevent premature convergence and increase the possibility of finding a global solution.
Membrane algorithms （MAs）, which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.
