Abstract
The minimization of the molecular potential energy function is one of the most important real-life problems which can help to predict the 3D structure of the protein by knowing the steady (ground) state of the molecules of the protein. In this paper, we propose a new hybrid algorithm between the social spider algorithm and the genetic algorithm in order to minimize a simplified model of the energy function of the molecule. We call the proposed algorithm by hybrid social spider optimization and genetic algorithm (HSSOGA). The HSSOGA comprises of three main steps. In the first step, we apply the social spider optimization algorithm to balance between the exploration and the exploitation processes in the proposed algorithm. In the second step, we use the dimensionality reduction process and the population partitioning process by dividing the population into subpopulations and applying the arithmetical crossover operator for each subpopulation order to increase the diversity of the search in the algorithm. In the last steps, we use the genetic mutation operator in the whole population to avoid the premature convergence and avoid trapping in local minima. The combination of three steps helps the proposed algorithm to solve the molecular potential energy function with different molecules size, especially when the problem dimension \(D>100\) with powerful performance. We test it on 13 large-scale unconstrained global optimization problems to investigate its performance on these functions. In order to investigate the efficiency of the proposed HSSOGA, we compare HSSOGA against eight benchmark algorithms when we minimize the potential energy function problem. The numerical experiment results show that the proposed algorithm is a promising and efficient algorithm and can obtain the global minimum or near global minimum of the large-scale optimization problems up to 1000 dimension and the molecular potential energy function of the simplified model with up to 200 degrees of freedom faster than the other comparative algorithms.
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References
Avils L (1997) Causes and consequences of cooperation and permanent-sociality in spiders. In: Choe BC (ed) The evolution of social behavior in insects and arachnids. Cambridge University Press, Cambridge, p 476498
Banharnsakun A, Achalakul T, Sirinaovakul B (2011) The best-so-far selection in Artificial Bee Colony algorithm. Appl Soft Comput 11:2888–2901
Bansal JC, Deep Shashi K, Katiyar VK (2010) Minimization of molecular potential energy function using particle swarm optimization. Int J Appl Math Mech 6(9):1–9
Barbosa HJC, Lavor C, Raupp FM (2005) A GA-simplex hybrid algorithm for global minimization of molecular potential energy function. Ann Oper Res 138:189–202
Cuevas E, Cienfuegos M, Zaldvar D, Prez-Cisneros M (2013) A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Syst Appl 40(16):6374–6384
De Jong KA (1985) Genetic algorithms: a 10 year perspective. In: International conference on genetic algorithms, pp 169–177
Deep K, Thakur M (2007a) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193(1):211–230
Deep K, Thakur M (2007b) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188(1):895–912
Deep K, Barak S, Katiyar VK, Nagar AK (2012) Minimization of molecular potential energy function using newly developed real coded genetic algorithms. Int J Optim Control Theor Appl (IJOCTA) 2(1):51–58
Draz̆ić M, Lavor C, Maculan N, Mladenović N (2008) Acontinuous variable neighborhood search heuristic for finding thethree-dimensional structure of a molecule. Eur JOper Res 185:1265–1273
Eric C, Yip KS (2008) Cooperative capture of large prey solves scaling challenge faced by spider societies. Proc Natl Acad Sci USA 105(33):11818–11822
Esmin AA, Lambert-Torres G, Alvarenga GB (2006) Hybrid evolutionary algorithm based on PSO and GA mutation. In: Proceedings of 6th international conference on hybrid intelligent systems, p 5762
Floudas CA, Klepeis JL, Pardalos PM (1999) Global optimization approaches in protein folding and peptide docking, DIMACS series in discrete metjematics and theoretical computer science. American Mathematical Society, Providence
Garcia S, Fernandez A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning, accuracy and interpretability. Soft Comput 13:959–977
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading
Grimaccia Gandelli F, Mussetta M, Pirinoli P, Zich RE (2007) Development and validation of different hybridization strategies between GA and PSO. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp 2782–2787
Grimaldi EA, Grimacia F, Mussetta M, Pirinoli P, Zich RE (2004) A new hybrid genetical swarm algorithm for electromagnetic optimization, In: Proceedings of international conference on computational electromagnetics and its applications, Beijing, China, pp 157–160
Hedar A, Ali AF, Hassan T (2011) Genetic algorithm and tabu search based methods for molecular 3D-structure prediction. Numer Algebra Control Optim 1(1):191–209
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Jian M, Chen Y (2006) Introducing recombination with dynamic linkage discovery to particle swarm optimization. In: Proceedings of the genetic and evolutionary computation conference, pp 85–86
Juang CF (2004) A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans Syst Man Cybern Part B Cybern 34:997–1006
Kovac̆ević-Vujc̆ić V, čangalović M, Draz̆ić M, Mladenović N (2004) VNS-based heuristics forcontinuous global optimization. In: Hoai An LT, Tao PD (eds) Modeling. Computation and optimization in information systems andmanagement sciences. Hermes Science, Oxford, pp 215–222
Krink T, Lvbjerg M (2002) The lifecycle model: combining particle swarm optimization, genetic algorithms and hill climbers. In: Proceedings of the parallel problem solving from nature, pp 621-630
Lavor C, Maculan N (2004) A function to test methods applied to global minimization of potential energy of molecules. Numer Algorithms 35:287–300
Maxence S (2010) Social organization of the colonial spider Leucauge sp. in the Neotropics: vertical stratification within colonies. J Arachnol 38:446–451
Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, Berlin
Pardalos PM, Shalloway D, Xue GL (1994) Optimization methods for computing global minima of nonconvex potential energy function. J Glob Optim 4:117–133
Pasquet A (1991) Cooperation and prey capture efficiency in a social spider, Anelosimus eximius (Araneae, Theridiidae). Ethology 90:121–133
Pogorelov A (1987) Geometry. Mir Publishers, Moscow
Robinson J, Sinton S, Samii Y.R (2002) Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In: Proceedings of the IEEE international symposium in Antennas and Propagation Society, pp 314–317
Sheskin DJ (2003) Handbook of parametric and nonparametric statistical procedures. CRC Press, Boca Raton
Settles M, Soule T (2005) Breeding swarms: a GA/PSO hybrid. In: Proceedings of Genetic and Evolutionary Computation Conference, pp 161–168
Wales DJ, Scheraga HA (1999) Global optimization of clusters, crystals and biomolecules. Science 285:1368–1372
Wang H, Sun H, Li C, Rahnamayan S, Jeng-shyang P (2013) Diversity enhanced particle swarm optimization with neighborhood. Inf Sci 223:119–135
Yang WY, Cao W, Chung T-S, Morris J (2005) Applied numerical methods using MATLAB. Wiley, Hoboken
Zar JH (1999) Biostatistical analysis. Prentice Hall, Englewood Cliffs
Acknowledgments
We are grateful to the anonymous reviewers for constructive feedback and insightful suggestions which greatly improved this article. The research of the first author is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The postdoctoral fellowship of the second author is supported by NSERC.
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Tawhid, M.A., Ali, A.F. A hybrid social spider optimization and genetic algorithm for minimizing molecular potential energy function. Soft Comput 21, 6499–6514 (2017). https://doi.org/10.1007/s00500-016-2208-9
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DOI: https://doi.org/10.1007/s00500-016-2208-9