A parallel hybrid optimization algorithm for fitting interatomic potentials

In this work we present the parallel implementation of a hybrid global optimization algorithm assembled specifically to tackle a class of time consuming interatomic potential fitting problems. The resulting objective function is characterized by large and varying execution times, discontinuity and lack of derivative information. The presented global optimization algorithm corresponds to an irregular, two-level execution task graph where tasks are spawned dynamically. We use the OpenMP tasking model to express the inherent parallelism of the algorithm on shared-memory systems and a runtime library which implements the execution environment for adaptive task-based parallelism on multicore clusters. We describe in detail the hybrid global optimization algorithm and various parallel implementation issues. The proposed methodology is then applied to a specific instance of the interatomic potential fitting problem for the metal titanium. Extensive numerical experiments indicate that the proposed algorithm achieves the best parallel performance. In addition, its serial implementation performs well and therefore can also be used as a general purpose optimization algorithm.

[1]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[2]  Raymond Ros,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Experimental Setup , 2009 .

[3]  Herbert F. Wang,et al.  Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook , 1971 .

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

[5]  Janez Puhan,et al.  A new asynchronous parallel global optimization method based on simulated annealing and differential evolution , 2011, Appl. Soft Comput..

[6]  Jan Mayer,et al.  A numerical evaluation of preprocessing and ILU-type preconditioners for the solution of unsymmetric sparse linear systems using iterative methods , 2009, TOMS.

[7]  Thomas F. Coleman,et al.  A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing , 1993, J. Glob. Optim..

[8]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[9]  Charles E. Augarde,et al.  Simulation-based calibration of geotechnical parameters using parallel hybrid moving boundary particle swarm optimization , 2009 .

[10]  Weihang Zhu,et al.  Nonlinear optimization with a massively parallel Evolution Strategy-Pattern Search algorithm on graphics hardware , 2011, Appl. Soft Comput..

[11]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[12]  Johansson,et al.  Elastic constants of hexagonal transition metals: Theory. , 1995, Physical review. B, Condensed matter.

[13]  Anne Auger,et al.  Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009 , 2010, GECCO '10.

[14]  R. Lewontin.  ‘The Selfish Gene’ , 1977, Nature.

[15]  Rong Chen,et al.  A novel parallel hybrid intelligence optimization algorithm for a function approximation problem , 2012, Comput. Math. Appl..

[16]  Kevin Kok Wai Wong,et al.  Classification of adaptive memetic algorithms: a comparative study , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[18]  M. Noel,et al.  A new gradient based particle swarm optimization algorithm for accurate computation of global minimum , 2012, Appl. Soft Comput..

[19]  Fabio Schoen,et al.  Local search based heuristics for global optimization: Atomic clusters and beyond , 2012, Eur. J. Oper. Res..

[20]  K. V. Price,et al.  Differential evolution: a fast and simple numerical optimizer , 1996, Proceedings of North American Fuzzy Information Processing.

[21]  Baixin Liu,et al.  Interatomic potentials of the binary transition metal systems and some applications in materials physics , 2008 .

[22]  Yoshiaki Shimizu,et al.  A Parallel Computing Scheme for Large-Scale Logistics Network Optimization Enhanced by Discrete Hybrid PSO , 2009 .

[23]  Dimitris G. Papageorgiou,et al.  MEMPSODE: comparing particle swarm optimization and differential evolution within a hybrid memetic global optimization framework , 2012, GECCO '12.

[24]  John E. Dennis,et al.  Direct Search Methods on Parallel Machines , 1991, SIAM J. Optim..

[25]  Vassilios V. Dimakopoulos,et al.  Task-parallel global optimization with application to protein folding , 2011, 2011 International Conference on High Performance Computing & Simulation.

[26]  André van der Hoek,et al.  A Parallel Global Optimization Method for Solving Molecular Cluster and Polymer Conformation Problems , 1995, PPSC.

[27]  Raj Srinivasan,et al.  RPC: Remote Procedure Call Protocol Specification Version 2 , 1995, RFC.

[28]  Thomas Stützle,et al.  Evaluating Las Vegas Algorithms: Pitfalls and Remedies , 1998, UAI.

[29]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[30]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[31]  A R Plummer,et al.  Introduction to Solid State Physics , 1967 .

[32]  Pablo Moscato,et al.  Memetic algorithms: a short introduction , 1999 .

[33]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[34]  A. Müller.  The Structure of Metals , 1881, The American journal of dental science.

[35]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[36]  Dario Izzo,et al.  A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation , 2010, ArXiv.

[37]  Dimitris G. Papageorgiou,et al.  MEMPSODE: an empirical assessment of local search algorithm impact on a memetic algorithm using noiseless testbed , 2012, GECCO '12.

[38]  J. Dennis,et al.  Direct Search Methods on Parallel Machines , 1991 .

[39]  Konstantinos E. Parsopoulos,et al.  UPSO: A Unified Particle Swarm Optimization Scheme , 2019, International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004).

[40]  Michael N. Vrahatis,et al.  Memetic particle swarm optimization , 2007, Ann. Oper. Res..

[41]  Vassilios V. Dimakopoulos,et al.  High-Performance Numerical Optimization on Multicore Clusters , 2011, Euro-Par.

[42]  Michael N. Vrahatis,et al.  MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches , 2012, Comput. Phys. Commun..