Particle swarm exchange algorithms with applications in generating optimal model-discrimination designs

Exchange-type algorithms have been commonly used to construct optimal designs. As these algorithms may converge to a local optimum, the typical procedure requires the use of several randomly chosen initial designs. Thus, the search for the optimal design can be conducted by performing several independent optimizations. We propose a general framework that combines exchange algorithms with particle swarm intelligence techniques. The main strategy is to represent each initial design as a particle and make the algorithm share information from various converging paths from those initial designs. This amounts to conducting one coordinated optimization instead of several independent optimizations. The proposed general algorithm is called the particle swarm exchange (PSE) algorithm. We compare the performance of PSE with those of two commonly used exchange algorithms–the columnwise-pairwise (CP) exchange algorithm of Li and Wu (1997) for designs with structural requirements and the coordinate exchange algorithm of Meyer and Nachtsheim (1995) for designs without such requirements. In the context of model-robust discriminating designs, we demonstrate that PSE typically performs as well as or, very often, better than the corresponding pure exchange algorithms.