Varying dimensional particle swarm optimization

A new algorithm, varying dimensional particle swarm optimization (VD-PSO), is proposed for entities with varying-dimensional components and each component assumes continuous-valued parameters. Such problems are distinct from current benchmark problems where the dimension of the particles is fixed. One well-studied application of VD-PSO is probability density estimation by Gaussian Mixture Models. A particle in VD-PSO includes a discrete number as the number of components and a set of real-valued component parameters. The number of components varies according to a random scheme, which dictates how many sets of components remain or expand. The component parameters are matched up supporting a linked update. Three other methods, the last two of which are also proposed by us as intuitive attempts to solve the varying dimensional problems, are compared with VD-PSO: 1. binary-headered PSO, 2. exhaustive PSO, 3. discrete-headered PSO. Simulations on known data with specified components show that VD-PSO provides a competitive density estimation to the exhaustive PSO, but spends the least wall-clock-time among all algorithms, almost 12% of the exhaustive PSO, while the binary-headered PSO or discrete-headered PSO do not achieve similar performance, because the binary-headered PSO is adversely affected by the dummy parameters, and the discrete-headered PSO makes too many dimension variations before the parameters are well tuned. The new VD-PSO algorithm is a viable and efficient solution to varying dimensional optimization problems.