SUMMARYThis paper presents a new multi-layered artificial immune system architecture using the ideas generated from the biological immune system for solving combinatorial optimization problems. The proposed methodology is composed of five layers. After expressing the problem as a suitable representation in the first layer, the search space and the features of the problem are estimated and extracted in the second and third layers, respectively. Through taking advantage of the minimized search space from estimation and the heuristic information from extraction, the antibodies (or solutions) are evolved in the fourth layer and finally the fittest antibody is exported. In order to demonstrate the efficiency of the proposed system, the graph planarization problem is tested. Simulation results based on several benchmark instances show that the proposed algorithm performs better than traditional algorithms.
In this article, we present a solution to the maximum clique problem using a gradient-ascent learning algorithm of the Hopfield neural network. This method provides a near-optimum parallel algorithm for finding a maximum clique. To do this, we use the Hopfield neural network to generate a near-maximum clique and then modify weights in a gradient-ascent direction to allow the network to escape from the state of near-maximum clique to maximum clique or better. The proposed parallel algorithm is tested on two types of random graphs and some benchmark graphs from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). The simulation results show that the proposed learning algorithm can find good solutions in reasonable computation time.
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