GREEN-PSO: Conserving function evaluations in Particle Swarm Optimization

In the Particle Swarm Optimization (PSO) algorithm, the expense of evaluating the objective function can make it difficult, or impossible, to use this approach effectively; reducing the number of necessary function evaluations would make it possible to apply the PSO algorithm more widely. Many function approximation techniques have been developed that address this issue, but an alternative to function approximation is function conservation. We describe GREEN-PSO (GR-PSO), an algorithm that, given a fixed number of function evaluations, conserves those function evaluations by probabilistically choosing a subset of particles smaller than the entire swarm on each iteration and allowing only those particles to perform function evaluations. The "surplus" of function evaluations thus created allows a greater number of particles and/or iterations. In spite of the loss of information resulting from this more parsimonious use of function evaluations, GR-PSO performs as well as, or better than, the standard PSO algorithm on a set of six benchmark functions, both in terms of the rate of error reduction and the quality of the final solution.