Splitting for optimization

• Motivated by the splitting algorithm for rare-event simulation, we introduce a novel global optimization method for continuous optimization that is both very fast and accurate, called Splitting for Continuous Optimization (SCO).
• The idea is to adaptively sample a collection of particles on a sequence of level sets, such that at each level the elite set of particles is “split” into better performing offspring. The particles are generated from a multivariate normal distribution with independent components, via a Gibbs sampler.
• We compared the performance of SCO with that of the Differential Evolutionary (DE) and Artificial Bee colony (ABC) algorithms through two sets of numerical experiments based on a widely used suite of test functions. From the results, it can be concluded that SCO is competitive with both DE and ABC algorithm on this test suite.

The splitting method is a well-known method for rare-event simulation, where sample paths of a Markov process are split into multiple copies during the simulation, so as to make the occurrence of a rare event more frequent. Motivated by the splitting algorithm we introduce a novel global optimization method for continuous optimization that is both very fast and accurate. Numerical experiments demonstrate that the new splitting-based method outperforms known methods such as the differential evolution and artificial bee colony algorithms for many bench mark cases.