DNA计算中的编码设计优化算法
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摘要
DNA计算是以DNA分子和生物酶等为载体,以生化反应作为“信息处理工具的”一种崭新的计算模式。由于DNA计算所具有的巨并行性、海量存储以及低能耗等优点,DNA计算显示了巨大的生命力。但生化反应中由于各种外界因素以及编码本身的缺陷,会存在非特异性杂交,这种随机性为后续计算进程带来了很大的不确定性,严重的可能会导致生化反应不可控,进而造成计算失败,有效的编码设计能够提高DNA计算的可靠性。
本文重点研究了DNA编码问题,研究重点主要集中在如何设计出可以减少不合法反应的DNA编码序列集合。介绍了DNA编码的相关约束条件,并进行数学建模,研究现有流行的智能进化算法。在此基础上提出两种DNA编码的优化算法。本文的主要工作包括：
1.分析DNA计算中编码序列设计的影响因素、总结了现有研究主要考虑的六个数学约束条件：H-measure约束、连续性约束、相似度约束、发夹结构约束、解链温度、GC含量。建立一套基于以上六个约束条件的多目标评价体系的DNA编码序列组合优化模型,设计出了适应度函数Fitness的具体实现。
2.提出一种基于离散粒子群的DNA编码优化方法(简称DPSO)。根据DNA编码问题离散量的特点,对DPSO算法粒子的位置、速度等量及运算规则进行了重新定义,满足了六种约束条件,引入基于权重的适应度函数来评价DNA序列集合,并设计出了DPSO算法的具体实现。经实验验证,DPSO算法大大降低了计算复杂度,并且参数设置和调整非常方便。
3.提出一种基于文化粒子群(cultural-based PSO, CBPSO)的DNA编码序列优化方法。种群空间利用了DPSO的快速演化能力,通过接收精英个体送入信念空间。同时利用文化算法模型中的遗传操作,对个体选择,交叉,变异等,影响种群空间的粒子来增加DPSO群体多样性和全局搜索能力。并设计出CBPSO的具体实现,经实验验证得到了较高质量的DNA编码序列,验证算法的有效性。
4.用Java实现了DNA计算编码设计系统。系统架构采取了五层框架,分别是表现层,算法层,约束层,对象层,数据库层,层和层之间松散耦合。其框架是灵活的,可扩展的。经实验证明,GPSDS可以帮助验证不同的DNA编码优化算法模型。
DNA computing is a brand news computing mode which is based on DNA molecular and biological enzyme and uses biochemical reaction as its information processing tool. By nature of the advantages of great parallelity, huge storage ability and low power costs, DNA computing reveals its glorious prosperity. As a branch of DNA computing, DNA coding means designing the initial database of DNA computing. Designing of effective DNA code will remarkably improve the reliability of DNA computing.
The paper discusses DNA coding and the main focus is on the decreasing of illegal code sequences. To achieve the DNA coding, the paper briefly introduces the thermodynamics and biology restrictions. And then, mathematic model is designed for the restrictions respectively. Moreover, some evolution algorithms are researched. Based on the research mentioned above, two optimal approaches for DNA coding are designed. The structure of the paper is as follows:
1. The main restrictions which have influences on the DNA codes designing are studied. Six mathematic restrictions are discussed respectively. There are H-measure, Continuity, Similarity, Hairpin, Tm as well as GC content. Based on six restrictions mentioned above, an optimal model for DNA coding with a multiple aims evaluation system is established. In the paper, the evaluation system is realized as Fitness function.
2. An optimal algorithm for DNA coding named discrete particle swarm optimization (DPSO) is researched. First, the location and velocity updating rule is derived according to the DNA coding restrictions and the characteristic of discrete value. And then, in order to evaluate the performance of DNA consequence set, a fitness function based on the six restrictions as well as their respective power is designed. The DPSO algorithm is realized in chapter four. And in contrast with traditional genetic algorithm, the DPSO algorithm remarkably decreases the computing complexity, also, it's very convenient to set and adjust the parameters.
3. A more optimal algorithm for DNA coding named cultural-based PSO (CBPSO) is designed. The population space adopts the DPSO and makes use of its rapid evolvement attribute, and sends elite individual to the belief space. Meanwhile, the belief space adopts the genetic operations which is including the selection, crossover and variation operation. The belief space will influences the population space to guide the population space and increase the diversity of the population space as well as the global search ability. Through the realization of the CBPSO algorithm, DNA code sequence with higher quality is derived.
4. A General-Purpose Sequence Design System is designed and realized using JAVA language. The system structure contains five layers:behavior layer, algorithm layer, restriction layer, object layer and database layer, and those layers are loose coupled with each other. The good traits contribute to an agile, extendable and general-purposed system. Through the realization of the GPSDS system, different optimal model for DNA coding can be implemented, and the respective DNA code sequence acquired.
本文重点研究了DNA编码问题,研究重点主要集中在如何设计出可以减少不合法反应的DNA编码序列集合。介绍了DNA编码的相关约束条件,并进行数学建模,研究现有流行的智能进化算法。在此基础上提出两种DNA编码的优化算法。本文的主要工作包括：
1.分析DNA计算中编码序列设计的影响因素、总结了现有研究主要考虑的六个数学约束条件：H-measure约束、连续性约束、相似度约束、发夹结构约束、解链温度、GC含量。建立一套基于以上六个约束条件的多目标评价体系的DNA编码序列组合优化模型,设计出了适应度函数Fitness的具体实现。
2.提出一种基于离散粒子群的DNA编码优化方法(简称DPSO)。根据DNA编码问题离散量的特点,对DPSO算法粒子的位置、速度等量及运算规则进行了重新定义,满足了六种约束条件,引入基于权重的适应度函数来评价DNA序列集合,并设计出了DPSO算法的具体实现。经实验验证,DPSO算法大大降低了计算复杂度,并且参数设置和调整非常方便。
3.提出一种基于文化粒子群(cultural-based PSO, CBPSO)的DNA编码序列优化方法。种群空间利用了DPSO的快速演化能力,通过接收精英个体送入信念空间。同时利用文化算法模型中的遗传操作,对个体选择,交叉,变异等,影响种群空间的粒子来增加DPSO群体多样性和全局搜索能力。并设计出CBPSO的具体实现,经实验验证得到了较高质量的DNA编码序列,验证算法的有效性。
4.用Java实现了DNA计算编码设计系统。系统架构采取了五层框架,分别是表现层,算法层,约束层,对象层,数据库层,层和层之间松散耦合。其框架是灵活的,可扩展的。经实验证明,GPSDS可以帮助验证不同的DNA编码优化算法模型。
DNA computing is a brand news computing mode which is based on DNA molecular and biological enzyme and uses biochemical reaction as its information processing tool. By nature of the advantages of great parallelity, huge storage ability and low power costs, DNA computing reveals its glorious prosperity. As a branch of DNA computing, DNA coding means designing the initial database of DNA computing. Designing of effective DNA code will remarkably improve the reliability of DNA computing.
The paper discusses DNA coding and the main focus is on the decreasing of illegal code sequences. To achieve the DNA coding, the paper briefly introduces the thermodynamics and biology restrictions. And then, mathematic model is designed for the restrictions respectively. Moreover, some evolution algorithms are researched. Based on the research mentioned above, two optimal approaches for DNA coding are designed. The structure of the paper is as follows:
1. The main restrictions which have influences on the DNA codes designing are studied. Six mathematic restrictions are discussed respectively. There are H-measure, Continuity, Similarity, Hairpin, Tm as well as GC content. Based on six restrictions mentioned above, an optimal model for DNA coding with a multiple aims evaluation system is established. In the paper, the evaluation system is realized as Fitness function.
2. An optimal algorithm for DNA coding named discrete particle swarm optimization (DPSO) is researched. First, the location and velocity updating rule is derived according to the DNA coding restrictions and the characteristic of discrete value. And then, in order to evaluate the performance of DNA consequence set, a fitness function based on the six restrictions as well as their respective power is designed. The DPSO algorithm is realized in chapter four. And in contrast with traditional genetic algorithm, the DPSO algorithm remarkably decreases the computing complexity, also, it's very convenient to set and adjust the parameters.
3. A more optimal algorithm for DNA coding named cultural-based PSO (CBPSO) is designed. The population space adopts the DPSO and makes use of its rapid evolvement attribute, and sends elite individual to the belief space. Meanwhile, the belief space adopts the genetic operations which is including the selection, crossover and variation operation. The belief space will influences the population space to guide the population space and increase the diversity of the population space as well as the global search ability. Through the realization of the CBPSO algorithm, DNA code sequence with higher quality is derived.
4. A General-Purpose Sequence Design System is designed and realized using JAVA language. The system structure contains five layers:behavior layer, algorithm layer, restriction layer, object layer and database layer, and those layers are loose coupled with each other. The good traits contribute to an agile, extendable and general-purposed system. Through the realization of the GPSDS system, different optimal model for DNA coding can be implemented, and the respective DNA code sequence acquired.
引文
[1]许进,张雷.DNA计算机原理、进展及难点(Ⅰ)生物计算系统及其在图论中的应用.计算机学报,2003,26(1)：1-11
[2]Adleman. L. Molecular computation of solution to combinatorial problems. Science,1994, 266(11):1021-1024
[3]Sakamoto K, Gouzu H, Komiya K, et al. Molecular computation by DNA hairpin formation. Science,2000,288(5469):1223-1226
[4]Paun G, Rozenberg G, Salomaa A. DNA computing:new computing paradigms. Springer. Berlin.1998
[5]王延峰.DNA计算中的编码理与方法研究：[博士学位论文].武汉：华中科技大学,2007,35-48
[6]刘西奎.DNA计算和遗传算法的编码与几个优化模型的研究：[博士学位论文].武汉：华中科技大学,2003,15-23
[7]Lipton R J.DNA solution of hard computational problems. Science,1995,268(5210): 542-545
[8]Guamieri F, Fliss M, Bancroft C.Making DNA add. Science,1996,273(5272):220-223
[9]Ouyang Q, Kaplan P D, Liu S, et al. DNA solution of the maximal clique problem. Science,1997,278 (17):446-449
[10]Head T, Rozenberg G, Bladergroen R B, et al. Computing with DNA by operating on plasmids. BioSystems,2000,57:87-93
[11]Liu Q, Wang L, Frutos A, et al. DNA computing on surfaces. Nature,2000,403(13): 175-178
[12]Sakamoto K, Gouzu H, Komiya K,et al.Molecular computation by DNA hairpin formation.Science,2000,288(5469):1223-1226
[13]Benenson Y, PazElizur T, Adar R,et al.Programmable and autonomous computing machine made of biomolecules. Nature,2001,414(6862):430-434
[14]Braich R S, Chelyapov N, Johnson C. Solution of a 20-variable 3-SAT problem on a DNA computer. Science,2002,296(5567):499-502
[15]Benenson Y, Gil B, Ben-Dor U,et al.An autonomous molecular computer for logical control of gene expression.Nature,2004,429(6990):423-429
[16]贺林,李秀霞,师咏勇,等.运行于磁珠表面的可编程DNA计算机.科学通报,2003,48(23)：2422-2427
[17]赵健,钱璐璐,刘强,等.基于线性自组装的DNA加法.科学通报,2006,51(21)：2485-2489
[18]许进,强小利,方刚,等.一种图顶点着色DNA计算机模型.科学通报,2006,51(4)：480-487
[19]许进,范月科.经典Ramsey数DNA计算模型(Ⅰ)：位序列计算模型.计算机学报,2008,31(12)：2073.2080
[20]许进,范月科.经典Ramsey数DNA计算模型(Ⅱ)：基于位序列的DNA计算模型.计算机学报,2008,31(12)：2081-2089
[21]Frutos A G. Demonstration of a word design strategy for DNA computing on surface. Nucleic Acids Research,1997,25(23):4748-4757
[22]Arita M. The power of sequence design in DNA computing. The 4th International Conference on Computational Intelligence and Multimedia Applications,2001:163-167
[23]Braich R S, Johnson C, Rothemund P W K,et al.Solution of a satisfy problem on a gel-based DNA computer.The 6th International Workshop on DNA based Computing. London:Springer-verlag,2001:27-42
[24]Tulpan D C, Hoos H H, Condon A E. Stochastic local search algorithms for DNA word design.LNCS 2568:DNA8,2003:229-241
[25]Feldkamp U, Banzhaf W, Rauhe H. A DNA Sequence Compiler. In:Proceedings of 6th DIMACS Workshop on DNA Based Computers,2000
[26]Baum E. DNA sequences useful for computation. DIMACS Series in Discrete Mathematics and Theoretical Computer Science,1996,27:122-127
[27]Deaton, R. C. Murphy, M. Garzon, etc. Good encodings for DNA-based solutions to combinatorial problems. DNA Based Computers Ⅱ, DIMACS, American Mathematical Society,1998, vol.44,247-258
[28]Deaton R, Murphy R C, Garzon M, et al. Genetic search of reliable encodings for DNA-based computation. In:Kozon J R, Goldberg D E, Fogel D B, et al. Editors, Proceedings of the 1st Annual Conference on Genetic Programming, Princeton University,1996,9-15
[29]Arita M, Nishikawa A, Hagiya M, et al. Improving sequence design for DNA computing. In:Whitley D, Goldberg D E, Cant E, Editors, Proceedings of the Genetic and Evolutionary Computation Conference, Las Vegas USA,2000,875-852
[30]Marathe A, Condon A E, Corn R M. On combinatorial DNA word design. In: Proceedings of 5th DIMACS Workshop on DNA Based Computers, Cambridge. MA. USA,1999,75-89
[31]Zhang K, Pan L Q, Xu J. A global heuristically search algorithm for DNA encoding. Progress in Natural Science,2007,17 (6):745-749
[32]Tanaka F, Nakatsugawa M, Yamamoto M, et al. Developing support system for Sequence design in DNA computing. In:Preliminary Proceedings of 7th international Workshop on DNA-Based Computers,2001,340-349
[33]Cui G Z, Niu Y Y, Wang Y F, et al. A new approach based on PSO algorithm to find good computational encoding sequences. Progress in Natural Science,2007,17 (6): 712-716
[34]Wang W, Zheng X D, Zhang Q. The optimization of DNA encodings based on GA/SA algorithm. Progress in Natural Science,2007,17 (6):739-744
[35]Xiao J H, Xu J, Geng X T, et al. Multi-objective carrier chaotic evolutionary Algorithm for DNA sequences design. Progress in Natural Science,2007,17(12):1515-1520
[36]Kawashimo S, Ono H, Sadakane K. Dynamic neighborhood searches for Thermo dynamically designing DNA sequence. DNA 13,2008,4848:130-139
[37]Tri Basuki Kurniawan, Noor Khafifah Khalid, Zuwairie Ibrahim,,et al. An Ant Colony System for DNA Sequence Design Based on Thermo dynamics, The 4th IASTEAD International Conference on Advances in Computer Science and Technology (ACST 2008),2-4 April 2008, Langkawi, Malaysia, pp.144-149
[38]Noor Khafifah Khalid, Tri Basuki Kurniawan, Zuwairie Ibrahim, etc. A Model to Optimize DNA Sequences Based on Particle Swarm Optimization, Asia International Conference on Modeling and Simulation, Kuala Lumpur, Malaysia,13-15 May 2008, pp. 34-539
[39]Kim D, Shin S Y, Lee I H, et al. NACST/Seq:A sequences design system with multi-objective optimization. Lecture Notes in Computer Science,2003,2568:242-251
[40]Arita M, Kobayashi S. DNA sequence design using templates. New Generation Computer,2002,20 (3):263-278
[41]Feldkamp U, Banzhaf W, Rauhe H. DNA sequences generator:a program for the construction of DNA sequences. In:Jonoska N, Seeman N C, Editors, Proceedings of the 7th International Workshop on DNA Based Computers, University of South Florida, 2001,179-188
[42]Hartemink A J, Gifford D K, Khodor J. Automated constraint-based nucleotide sequence selection for DNA computation. In:Proceedings of 4th Annual DIMACS Workshop on DNA-Based Computers, University of Pennsylvania, Baltimore,1998
[43]Salomaa, A. Paun, G. Rozenberg, G. DNA计算：一种新的计算模式.许进,王淑栋,潘林强.1.北京：清华大学出版社,2004,21-85
[44]肖建华.仿生型DNA计算编码算法研究：[博士学位论文].武汉：华中科技大学, 2008
[45]朱翔鸥.DNA计算编码研究及其算法实现：[硕士学位论文].杭州：浙江工业大学,2005
[46]刘宏坤.DNA计算在NP问题中的应用及程序模拟：[硕士学位论文].长春：吉林大学,2006
[47]Garzon M, Deaton R, Neathery P, et al. On the encoding problem for DNA computing. In:Proceedings of 3rd DIMACS Workshop on DNA-base Computer, University of Pennsylvania, Baltimore,1997,230-237
[48]Garzon M H, Deaton R J. Codeword design and information encoding in DNA ensembles. Natural Computing,2004,3 (3):253-292
[49]Santalucia J. A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. In:Proceedings of Natl. Acad. Science,1998, 1460-1465
[50]Zoya I., Israael M., Karl-Heinz Z.DNA计算模型.郗方,王淑栋,强小利.1.北京：清华大学出版社,2010,43-53
[51]Santaucia J, Allawi H T, Seneviratne P A. Improved nearest-neighbor parameters for predicting DNA duplex stability. Biochemistry,1996,35 (11):3555-3562
[52]许世明,张强.基于遗传粒子群算法的DNA编码优化.计算机工程,2008,34(1)：218-220
[53]Shin S Y, Lee I H, Kim D, et al. Multi-objective evolutionary optimization of DNA sequences for reliable DNA computing. IEEE Transactions on Evolutionary Computation,2005,9 (2):143-158
[54]Wang W, Zheng X D, Zhang Q, et al. The optimization of DNA encodings based on GA/SA algorithm. Progress in Natural Science,2007,17 (6):739-744
[55]Jianhua Xiao, Jin Xu, Zhihua Chen, Kai Zhang, Linqiang Pan, A hybrid quantum chaotic swarm evolutionary algorithm for DNA encoding, Computers & Mathematics with Applications, v.57 n.11-12, p.1949-1958, June,2009
[56]Kennedy J, Eberhart R C, Shi Y. Swarm Intelligence. San Francisco:Morgan Kaufman Publishers,2001
[57]Reynolds R G. An Introduction to Cultural Algorithms. Proceedings of the Third Annual Conference on Evolutionary Programming, World Scientific. River Edge, New Jersey: 1994:131-139
[58]齐仲纪,刘漫丹.文化算法研究.计算机技术与发展,2008,18(5)：126-130
[59]Yan-Feng Wang, Ying Niu, Guang-Zhao Cui. An Efficient Genetic Algorithm Based on the Cultural Algorithm Applied to DNA Codewords Design.In:The 3rd International Conference, Bio-Inspired Computing:Theories and Applications, Adelaide,2008, 262-268
[2]Adleman. L. Molecular computation of solution to combinatorial problems. Science,1994, 266(11):1021-1024
[3]Sakamoto K, Gouzu H, Komiya K, et al. Molecular computation by DNA hairpin formation. Science,2000,288(5469):1223-1226
[4]Paun G, Rozenberg G, Salomaa A. DNA computing:new computing paradigms. Springer. Berlin.1998
[5]王延峰.DNA计算中的编码理与方法研究：[博士学位论文].武汉：华中科技大学,2007,35-48
[6]刘西奎.DNA计算和遗传算法的编码与几个优化模型的研究：[博士学位论文].武汉：华中科技大学,2003,15-23
[7]Lipton R J.DNA solution of hard computational problems. Science,1995,268(5210): 542-545
[8]Guamieri F, Fliss M, Bancroft C.Making DNA add. Science,1996,273(5272):220-223
[9]Ouyang Q, Kaplan P D, Liu S, et al. DNA solution of the maximal clique problem. Science,1997,278 (17):446-449
[10]Head T, Rozenberg G, Bladergroen R B, et al. Computing with DNA by operating on plasmids. BioSystems,2000,57:87-93
[11]Liu Q, Wang L, Frutos A, et al. DNA computing on surfaces. Nature,2000,403(13): 175-178
[12]Sakamoto K, Gouzu H, Komiya K,et al.Molecular computation by DNA hairpin formation.Science,2000,288(5469):1223-1226
[13]Benenson Y, PazElizur T, Adar R,et al.Programmable and autonomous computing machine made of biomolecules. Nature,2001,414(6862):430-434
[14]Braich R S, Chelyapov N, Johnson C. Solution of a 20-variable 3-SAT problem on a DNA computer. Science,2002,296(5567):499-502
[15]Benenson Y, Gil B, Ben-Dor U,et al.An autonomous molecular computer for logical control of gene expression.Nature,2004,429(6990):423-429
[16]贺林,李秀霞,师咏勇,等.运行于磁珠表面的可编程DNA计算机.科学通报,2003,48(23)：2422-2427
[17]赵健,钱璐璐,刘强,等.基于线性自组装的DNA加法.科学通报,2006,51(21)：2485-2489
[18]许进,强小利,方刚,等.一种图顶点着色DNA计算机模型.科学通报,2006,51(4)：480-487
[19]许进,范月科.经典Ramsey数DNA计算模型(Ⅰ)：位序列计算模型.计算机学报,2008,31(12)：2073.2080
[20]许进,范月科.经典Ramsey数DNA计算模型(Ⅱ)：基于位序列的DNA计算模型.计算机学报,2008,31(12)：2081-2089
[21]Frutos A G. Demonstration of a word design strategy for DNA computing on surface. Nucleic Acids Research,1997,25(23):4748-4757
[22]Arita M. The power of sequence design in DNA computing. The 4th International Conference on Computational Intelligence and Multimedia Applications,2001:163-167
[23]Braich R S, Johnson C, Rothemund P W K,et al.Solution of a satisfy problem on a gel-based DNA computer.The 6th International Workshop on DNA based Computing. London:Springer-verlag,2001:27-42
[24]Tulpan D C, Hoos H H, Condon A E. Stochastic local search algorithms for DNA word design.LNCS 2568:DNA8,2003:229-241
[25]Feldkamp U, Banzhaf W, Rauhe H. A DNA Sequence Compiler. In:Proceedings of 6th DIMACS Workshop on DNA Based Computers,2000
[26]Baum E. DNA sequences useful for computation. DIMACS Series in Discrete Mathematics and Theoretical Computer Science,1996,27:122-127
[27]Deaton, R. C. Murphy, M. Garzon, etc. Good encodings for DNA-based solutions to combinatorial problems. DNA Based Computers Ⅱ, DIMACS, American Mathematical Society,1998, vol.44,247-258
[28]Deaton R, Murphy R C, Garzon M, et al. Genetic search of reliable encodings for DNA-based computation. In:Kozon J R, Goldberg D E, Fogel D B, et al. Editors, Proceedings of the 1st Annual Conference on Genetic Programming, Princeton University,1996,9-15
[29]Arita M, Nishikawa A, Hagiya M, et al. Improving sequence design for DNA computing. In:Whitley D, Goldberg D E, Cant E, Editors, Proceedings of the Genetic and Evolutionary Computation Conference, Las Vegas USA,2000,875-852
[30]Marathe A, Condon A E, Corn R M. On combinatorial DNA word design. In: Proceedings of 5th DIMACS Workshop on DNA Based Computers, Cambridge. MA. USA,1999,75-89
[31]Zhang K, Pan L Q, Xu J. A global heuristically search algorithm for DNA encoding. Progress in Natural Science,2007,17 (6):745-749
[32]Tanaka F, Nakatsugawa M, Yamamoto M, et al. Developing support system for Sequence design in DNA computing. In:Preliminary Proceedings of 7th international Workshop on DNA-Based Computers,2001,340-349
[33]Cui G Z, Niu Y Y, Wang Y F, et al. A new approach based on PSO algorithm to find good computational encoding sequences. Progress in Natural Science,2007,17 (6): 712-716
[34]Wang W, Zheng X D, Zhang Q. The optimization of DNA encodings based on GA/SA algorithm. Progress in Natural Science,2007,17 (6):739-744
[35]Xiao J H, Xu J, Geng X T, et al. Multi-objective carrier chaotic evolutionary Algorithm for DNA sequences design. Progress in Natural Science,2007,17(12):1515-1520
[36]Kawashimo S, Ono H, Sadakane K. Dynamic neighborhood searches for Thermo dynamically designing DNA sequence. DNA 13,2008,4848:130-139
[37]Tri Basuki Kurniawan, Noor Khafifah Khalid, Zuwairie Ibrahim,,et al. An Ant Colony System for DNA Sequence Design Based on Thermo dynamics, The 4th IASTEAD International Conference on Advances in Computer Science and Technology (ACST 2008),2-4 April 2008, Langkawi, Malaysia, pp.144-149
[38]Noor Khafifah Khalid, Tri Basuki Kurniawan, Zuwairie Ibrahim, etc. A Model to Optimize DNA Sequences Based on Particle Swarm Optimization, Asia International Conference on Modeling and Simulation, Kuala Lumpur, Malaysia,13-15 May 2008, pp. 34-539
[39]Kim D, Shin S Y, Lee I H, et al. NACST/Seq:A sequences design system with multi-objective optimization. Lecture Notes in Computer Science,2003,2568:242-251
[40]Arita M, Kobayashi S. DNA sequence design using templates. New Generation Computer,2002,20 (3):263-278
[41]Feldkamp U, Banzhaf W, Rauhe H. DNA sequences generator:a program for the construction of DNA sequences. In:Jonoska N, Seeman N C, Editors, Proceedings of the 7th International Workshop on DNA Based Computers, University of South Florida, 2001,179-188
[42]Hartemink A J, Gifford D K, Khodor J. Automated constraint-based nucleotide sequence selection for DNA computation. In:Proceedings of 4th Annual DIMACS Workshop on DNA-Based Computers, University of Pennsylvania, Baltimore,1998
[43]Salomaa, A. Paun, G. Rozenberg, G. DNA计算：一种新的计算模式.许进,王淑栋,潘林强.1.北京：清华大学出版社,2004,21-85
[44]肖建华.仿生型DNA计算编码算法研究：[博士学位论文].武汉：华中科技大学, 2008
[45]朱翔鸥.DNA计算编码研究及其算法实现：[硕士学位论文].杭州：浙江工业大学,2005
[46]刘宏坤.DNA计算在NP问题中的应用及程序模拟：[硕士学位论文].长春：吉林大学,2006
[47]Garzon M, Deaton R, Neathery P, et al. On the encoding problem for DNA computing. In:Proceedings of 3rd DIMACS Workshop on DNA-base Computer, University of Pennsylvania, Baltimore,1997,230-237
[48]Garzon M H, Deaton R J. Codeword design and information encoding in DNA ensembles. Natural Computing,2004,3 (3):253-292
[49]Santalucia J. A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. In:Proceedings of Natl. Acad. Science,1998, 1460-1465
[50]Zoya I., Israael M., Karl-Heinz Z.DNA计算模型.郗方,王淑栋,强小利.1.北京：清华大学出版社,2010,43-53
[51]Santaucia J, Allawi H T, Seneviratne P A. Improved nearest-neighbor parameters for predicting DNA duplex stability. Biochemistry,1996,35 (11):3555-3562
[52]许世明,张强.基于遗传粒子群算法的DNA编码优化.计算机工程,2008,34(1)：218-220
[53]Shin S Y, Lee I H, Kim D, et al. Multi-objective evolutionary optimization of DNA sequences for reliable DNA computing. IEEE Transactions on Evolutionary Computation,2005,9 (2):143-158
[54]Wang W, Zheng X D, Zhang Q, et al. The optimization of DNA encodings based on GA/SA algorithm. Progress in Natural Science,2007,17 (6):739-744
[55]Jianhua Xiao, Jin Xu, Zhihua Chen, Kai Zhang, Linqiang Pan, A hybrid quantum chaotic swarm evolutionary algorithm for DNA encoding, Computers & Mathematics with Applications, v.57 n.11-12, p.1949-1958, June,2009
[56]Kennedy J, Eberhart R C, Shi Y. Swarm Intelligence. San Francisco:Morgan Kaufman Publishers,2001
[57]Reynolds R G. An Introduction to Cultural Algorithms. Proceedings of the Third Annual Conference on Evolutionary Programming, World Scientific. River Edge, New Jersey: 1994:131-139
[58]齐仲纪,刘漫丹.文化算法研究.计算机技术与发展,2008,18(5)：126-130
[59]Yan-Feng Wang, Ying Niu, Guang-Zhao Cui. An Efficient Genetic Algorithm Based on the Cultural Algorithm Applied to DNA Codewords Design.In:The 3rd International Conference, Bio-Inspired Computing:Theories and Applications, Adelaide,2008, 262-268