Splitting for optimization

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. HighlightsMotivated 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.

[1]  Xu Wei-bin A Modified Artificial Bee Colony Algorithm , 2011 .

[2]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[3]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[4]  KarabogaDervis,et al.  A powerful and efficient algorithm for numerical function optimization , 2007 .

[5]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[6]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[7]  Dervis Karaboga,et al.  A quick artificial bee colony (qABC) algorithm and its performance on optimization problems , 2014, Appl. Soft Comput..

[8]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[9]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[10]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[11]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[12]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[13]  Dirk P. Kroese,et al.  The Cross Entropy Method: A Unified Approach To Combinatorial Optimization, Monte-carlo Simulation (Information Science and Statistics) , 2004 .

[14]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[15]  Dirk P. Kroese,et al.  Efficient Monte Carlo simulation via the generalized splitting method , 2012, Stat. Comput..

[16]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[17]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[18]  Thomas Stützle,et al.  Ant Colony Optimization , 2009, EMO.

[19]  Dirk P. Kroese,et al.  Handbook of Monte Carlo Methods , 2011 .

[20]  Zdravko Botev The Generalized Splitting method for Combinatorial Counting and Static Rare-Event Probability Estimation , 2009 .

[21]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[22]  Masao Fukushima,et al.  Evolution Strategies Learned with Automatic Termination Criteria , 2006 .

[23]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).