Conformational Space Annealing explained: A general optimization algorithm, with diverse applications

Abstract Many problems in science and engineering can be formulated as optimization problems. One way to solve these problems is to develop tailored problem-specific approaches. As such development is challenging, an alternative is to develop good generally-applicable algorithms. Such algorithms are easy to apply, typically function robustly, and reduce development time. Here we provide a description for one such algorithm called Conformational Space Annealing (CSA) along with its python version, PyCSA. We previously applied it to many optimization problems including protein structure prediction and graph community detection. To demonstrate its utility, we have applied PyCSA to two continuous test functions, namely Ackley and Eggholder functions. In addition, in order to provide complete generality of PyCSA to any types of an objective function, we demonstrate the way PyCSA can be applied to a discrete objective function, namely a parameter optimization problem. Based on the benchmarking results of the three problems, the performance of CSA is shown to be better than or similar to the most popular optimization method, simulated annealing. For continuous objective functions, we found that, L-BFGS-B was the best performing local optimization method, while for a discrete objective function Nelder–Mead was the best. The current version of PyCSA can be run in parallel at the coarse grained level by calculating multiple independent local optimizations separately. The source code of PyCSA is available from http://lee.kias.re.kr .

[1]  Hongyi Zhou,et al.  Distance‐scaled, finite ideal‐gas reference state improves structure‐derived potentials of mean force for structure selection and stability prediction , 2002, Protein science : a publication of the Protein Society.

[2]  Seung-Yeon Kim,et al.  An efficient molecular docking using conformational space annealing , 2005, J. Comput. Chem..

[3]  Julian Lee,et al.  Unbiased global optimization of Lennard-Jones clusters for N < or =201 using the conformational space annealing method. , 2003, Physical review letters.

[4]  Jorge Nocedal,et al.  Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization” , 2011, TOMS.

[5]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[6]  Keehyoung Joo,et al.  Multiple sequence alignment by conformational space annealing. , 2008, Biophysical journal.

[7]  Steven P Gross,et al.  Modularity optimization by conformational space annealing. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  A. Sali,et al.  Statistical potential for assessment and prediction of protein structures , 2006, Protein science : a publication of the Protein Society.

[9]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[10]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[11]  Yang Zhang,et al.  A Novel Side-Chain Orientation Dependent Potential Derived from Random-Walk Reference State for Protein Fold Selection and Structure Prediction , 2010, PloS one.

[12]  S. Takada,et al.  On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction , 2002 .

[13]  A. Liwo,et al.  Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[14]  New optimization method for conformational energy calculations on polypeptides: Conformational space annealing , 1997 .

[15]  Bindu Nanduri,et al.  HPIDB - a unified resource for host-pathogen interactions , 2010, BMC Bioinformatics.

[16]  Keehyoung Joo,et al.  All‐atom chain‐building by optimizing MODELLER energy function using conformational space annealing , 2009, Proteins.

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

[18]  S. Nash.  Newton-Type Minimization via the Lanczos Method , 1984 .

[19]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[20]  H. Scheraga,et al.  Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Jorge Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[22]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[23]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[24]  Lee,et al.  New Monte Carlo algorithm: Entropic sampling. , 1993, Physical review letters.

[25]  Jooyoung Lee,et al.  Ab initio materials design using conformational space annealing and its application to searching for direct band gap silicon crystals , 2016, Comput. Phys. Commun..

[26]  Y. Sugita,et al.  Multidimensional replica-exchange method for free-energy calculations , 2000, cond-mat/0009120.

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

[28]  András Fiser,et al.  New statistical potential for quality assessment of protein models and a survey of energy functions , 2010, BMC Bioinformatics.

[29]  B. M. Fulk.  MATH , 1992 .

[30]  J. Skolnick,et al.  GOAP: a generalized orientation-dependent, all-atom statistical potential for protein structure prediction. , 2011, Biophysical journal.

[31]  Richard Bonneau,et al.  An improved protein decoy set for testing energy functions for protein structure prediction , 2003, Proteins.

[32]  Finding multiple reaction pathways via global optimization of action , 2017, Nature communications.

[33]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[34]  Wang,et al.  Replica Monte Carlo simulation of spin glasses. , 1986, Physical review letters.

[35]  Yang Zhang,et al.  Scoring function for automated assessment of protein structure template quality , 2004, Proteins.