Abstract-We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes the problem NP-hard. Our experiments show great improvements over the sub-optimal solutions of prior methods. Our new algorithms improve over our previously proposed algorithm in three ways. First, whereas the previous algorithm can be applied only to acyclic networks, our new method works also with networks with cycles. Second, we enrich the set of components used in the genetic algorithm, which improves the performance. Third, we develop a novel distributed framework. Combining distributed random network coding with our distributed optimization yields a network coding protocol where the resources used for coding are optimized in the setup phase by running our evolutionary algorithm at each node of the network. We demonstrate the effectiveness of our approach by carrying out simulations on a number of different sets of network topologies.

Abstract. We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes the problem NP-hard and, for our experiments, greatly improves on sub-optimal solutions of established methods. We compare two different genotype encodings, which tradeoff search space size with fitness landscape, as well as the associated genetic operators. Our finding favors a smaller encoding despite its fewer intermediate solutions and demonstrates the impact of the modularity enforced by genetic operators on the performance of the algorithm.

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Digital integrators (DIs) and digital differentiators (DDs) of second, third and fourth-order based on particle swarm optimisation (PSO) algorithm are presented. A modified particle swarm optimisation (MPSO) algorithm with reducing maximum velocity has been used to optimise the mean square error of the digital operators. Statistical and simulation results have been presented for comparing quality of optimal operators obtained by MPSO, genetic algorithm (GA), two variants of PSO and PSO-GA hybrid techniques. The results obtained for best solutions by the proposed algorithm are either superior or at par with the basic PSO variants and hybrid techniques. The proposed digital operators have also been simulated using MATLAB, and the results have been compared with that of existing DIs and DDs derived by different optimisation algorithms, to demonstrate the effectiveness of the use of proposed MPSO. The relative magnitude errors (dB) obtained for digital integrators and differentiators are as low as −40 and −35 dB, respectively, which are valid for almost the full band of normalised frequency.

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