Ordering samples along environmental gradients using particle swarm optimization

Due to the enormity of the solution space for sequential ordering problems, non-exhaustive heuristic techniques have been the focus of many research efforts, particularly in the field of operations research. In this paper, we outline an ecologically motivated problem in which environmental samples have been obtained along a gradient (e.g. pH), with which we desire to recover the sample order. Not only do we model the problem for the benefit of an optimization approach, we also incorporate hybrid particle swarm techniques to address the problem. The described method is implemented on a real dataset from which 22 biological samples were obtained along a pH gradient. We show that we are able to approach the optimal permutation of samples by evaluating only approximately 5000 solutions infinitesimally smaller than the 22! possible solutions.