A new bionic method inspired by DNA computation to solve the hamiltonian path problem

DNA computing is a method of applying interactions among biological macromolecules to realize parallel computation, which has the extensive foreground of application. However, it is usually time consuming and expensive to validate the accuracy of DNA computing algorithms experimentally. Therefore, to reduce the cost of experiments, it is necessary to develop mathematical models for computer simulations before carrying out the corresponding DNA computing experimental work. With the mathematical theory of Yuanjian, the paper firstly models the experimental processes of DNA computing, namely the Yuanjian model, to solve the Hamiltonian Path Problem (HPP). Then, an encoding rule is given from the view of mathematics. With the improvement of the Yuanjian model presented above, a generalized Yuanjian model for solving the multi-node HPP is derived. The simulations verify the effectiveness of the proposed model which can be applied as a new bionic algorithm to solve the HPP for any size digraph. Furthermore, the presented Yuanjian model provides a model reference for DNA computing technology, which highlights the prospect of mathematical models in reducing the experiment cost for DNA computing algorithms.

[1]  J. Fournier.  Graph theory and applications : with exercises and problems , 2009 .

[2]  Clifford R. Johnson,et al.  Solution of a 20-Variable 3-SAT Problem on a DNA Computer , 2002, Science.

[3]  Qiang Zhang,et al.  A RGB image encryption algorithm based on DNA encoding and chaos map , 2009, Comput. Electr. Eng..

[4]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[5]  Witold Pedrycz,et al.  DNA approach to solve clustering problem based on a mutual order , 2008, Biosyst..

[6]  Stephen J. H. Yang,et al.  Applying DNA computation to intractable problems in social network analysis , 2010, Biosyst..

[7]  Xiyu Liu,et al.  A CLIQUE algorithm using DNA computing techniques based on closed-circle DNA sequences , 2011, Biosyst..

[8]  P D Kaplan,et al.  DNA solution of the maximal clique problem. , 1997, Science.

[9]  Zhang Xun-cai.  Encryption scheme research based on DNA technology , 2009 .

[10]  E. Keinan,et al.  A molecular cryptosystem for images by DNA computing. , 2012, Angewandte Chemie.

[11]  Hassan Basri,et al.  Object identification using DNA computing algorithm , 2012, 2012 IEEE Congress on Evolutionary Computation.

[12]  Zhaocai Wang,et al.  Solving the Minimum Vertex Cover Problem with DNA Molecules in Adleman-Lipton Model , 2014 .

[13]  Pan Linqiang,et al.  A new approach based on PSO algorithm to find good computational encoding sequences , 2007 .

[14]  E. Shapiro,et al.  An autonomous molecular computer for logical control of gene expression , 2004, Nature.

[15]  Liu Xiangrong.  A DNA Algorithm for Comparative Modeling of Protein Structure , 2009 .

[16]  Hong-Chao Zhao,et al.  An Improved DNA Computing Method for Elevator Scheduling Problem , 2012, ICPCA/SWS.

[17]  M. A. Vega-Rodriguez,et al.  DNA sequence design for reliable DNA computing by using a multiobjective approach , 2012, 2012 IEEE 13th International Symposium on Computational Intelligence and Informatics (CINTI).

[18]  Chun‐Liang Lin,et al.  System Identification and Control Using DNA Computing Algorithms , 2022 .

[19]  Jules Moreau,et al.  Molecular Computation by DNA Hairpin Formation , 2000 .

[20]  Yiming Zhang,et al.  Solving traveling salesman problem in the Adleman-Lipton model , 2012, Appl. Math. Comput..

[21]  Fumiaki Tanaka,et al.  Design of nucleic acid sequences for DNA computing based on a thermodynamic approach , 2005, Nucleic acids research.

[22]  Linqiang Pan,et al.  A hybrid quantum chaotic swarm evolutionary algorithm for DNA encoding , 2009, Comput. Math. Appl..

[23]  Chung-Wei Yeh,et al.  Molecular solutions to the binary integer programming problem based on DNA computation. , 2006, Bio Systems.

[24]  Majid Darehmiraki,et al.  Molecular solution to the 0-1 knapsack problem based on DNA computing , 2007, Appl. Math. Comput..

[25]  Junzo Watada,et al.  SELECTION OF AN OPTIMAL SUITABLE PROJECT MANAGEMENT APPROACH THROUGH DNA COMPUTING-BASED CLUSTERING , 2013 .

[26]  Jianhua Qin,et al.  A microfluidic DNA computing processor for gene expression analysis and gene drug synthesis. , 2009, Biomicrofluidics.

[27]  Majid Babaei,et al.  A novel text and image encryption method based on chaos theory and DNA computing , 2012, Natural Computing.