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Particle swarm optimisation for the design of two-connected networks with bounded rings

The particle swarm optimisation (PSO) is a stochastic population-based global optimisation technique modelled on the social behaviour of bird flocks or fish schooling. This paper investigates the use of PSO for designing minimum cost two-connected networks such that the shortest cycle to which each edge belongs to does not exceed a given length. PSO is a relatively new metaheuristic in which particles were originally designed to handle a continuous solution space. Given that the topological network design problem is a highly constrained discrete combinatorial optimisation, we modify the particle position representation and the particle velocity update rule by introducing an oscillating mechanism to better adapt a standard PSO for the problem. We provide numerical results based on randomly generated graphs found in the literature and compare the solution quality with that of tabu search and genetic algorithms. An empirical study for network sizes up to 30 nodes and a comparison with tabu search and genetic algorithms shows the potential of using PSO for the problem. To the best of our knowledge, this is the first attempt to implement particle swarm optimisation for the aforementioned problem.