免疫算法和模拟退火算法求解TSP问题的研究
摘要
旅行商问题是一个经典的组合优化问题，也是一个NP难问题。它在实际中的应用却非常广泛。历年来，人们一直努力地寻找一种既有高质量的解，又能快速收敛的近似算法。数学发展的重要手段之一就是用新方法解决老问题。最近二十年，许多仿生计算技术悄然兴起，它随着计算机科学的发展同步成长起来。于是，这个古老问题的研究又重新注入了新的活力；由于模拟退火算法简单易行，从而使它的应用范围极为广泛，并且已在众多领域得到了实际应用，且经常用于解决工程上的寻优；生物免疫系统是一个高度进化的生物系统，它具有高度自适应、高度分布性、自组织等特性。它能够有效识别入侵的抗原并清除抗原，并保持机体的稳定。人工免疫算法正是借鉴生物免疫系统信息处理机制的基础上发展起来的智能信息处理技术。由于人工免疫算法具备模式识别、学习和记忆的能力，因此它成为了一种科学及工程领域中信息处理和问题求解范式，由此也开辟了计算智能研究的新领域。
本文的工作主要集中在以下几个方面：
介绍了生物免疫的一些基本概念、系统组成、功能及原理；简单分析了人工免疫系统的研究内容、研究现状及基本理论；然后，对现已被提出的一些免疫算法和模拟退火算法的基本结构和流程进行了研究和分析。
其次，在深入分析了模拟退火算法基础上，提出一种温度可控的求解TSP问题的模拟退火算法，通过对CHN144以及标准的TSPLIB中不同国家的城市的数据进行测试，测试结果表明：该算法很容易收敛到问题的最优解。
然后，在理解和掌握生物免疫系统的基本概念和工作原理后，针对免疫原理提出了求解TSP问题的免疫算法并进行了实现和实验。实验表明：该算法能够求得很好的解。
最后，在深入研究免疫算法和模拟退火算法之后，本文提出了一种新的免疫模拟退火算法，并将其应用于求解典型的NP问题——TSP问题，同时进行了仿真实验，通过对标准的TSPLIB中的PR1002的数据进行测试，该算法具有良好的性能。
Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem and NP-hard. But it is applied in abroad field in practice. In the past, people have been struggling to seek a new method that has not only high quality but also fast convergence rate all the while. One of the important methods in mathematic processing is solving the old problem using updating standard. In the past twenty years, many technologies of bionic algorithms spring up quietly. And pullulate companied with the developing of computer science synchronously. So a kind of new energy was emitted to the study of TSP. The simulated annealing algorithm is simple and easy to implement, so it has been used in every broad fields. It is used in solving engineering optimal problems. The vertebrate immune system is a highly evolutionary system, which is highly adaptive, highly distributed and self-organizing. It can effectively recognize the antigens and kill them rapidly to protect the stability of the body. The Artificial Immune System (AIS) is an intelligent information processing technology that is based on the mechanism of the vertebrate immune system. As a novel branch of computational intelligence, AIS has strong capabilities of pattern recognition, learning and associative memory, hence it is natural to view AIS as a powerful information processing and problem-solving paradigm in both the scientific and engineering fields.
In this paper, some topics are mainly talked about:
Some basic concepts, framework, functions and principles of the biological immune system are introduced. Then the research range, research status and basic theory of the artificial immune system and simulated annealing algorithm are simply analyzed.
Secondly, we deeply analyze the mechanism of simulated annealing algorithm, then the paper proposes a simulated annealing algorithm based on controllable temperature parameter for solving TSP. By testing the data of CHN144 and benchmark TSPLIB, the experiments show that the algorithm is easy to find out the best answer.
Thirdly, after understanding some basic concepts and some principles of the vertebrate immune system, an immune algorithm is proposed and realized on the basis of immune principal. By testing it, the algorithm obtains a good solution.
Finally, we do the research on immune algorithm and simulated annealing algorithm, and a new immune simulated annealing algorithm for TSP is proposed on the basis of simulated annealing algorithm and immune algorithm. By testing the data of PR1002, the experiences show that the algorithm has a good performance.
本文的工作主要集中在以下几个方面：
介绍了生物免疫的一些基本概念、系统组成、功能及原理；简单分析了人工免疫系统的研究内容、研究现状及基本理论；然后，对现已被提出的一些免疫算法和模拟退火算法的基本结构和流程进行了研究和分析。
其次，在深入分析了模拟退火算法基础上，提出一种温度可控的求解TSP问题的模拟退火算法，通过对CHN144以及标准的TSPLIB中不同国家的城市的数据进行测试，测试结果表明：该算法很容易收敛到问题的最优解。
然后，在理解和掌握生物免疫系统的基本概念和工作原理后，针对免疫原理提出了求解TSP问题的免疫算法并进行了实现和实验。实验表明：该算法能够求得很好的解。
最后，在深入研究免疫算法和模拟退火算法之后，本文提出了一种新的免疫模拟退火算法，并将其应用于求解典型的NP问题——TSP问题，同时进行了仿真实验，通过对标准的TSPLIB中的PR1002的数据进行测试，该算法具有良好的性能。
Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem and NP-hard. But it is applied in abroad field in practice. In the past, people have been struggling to seek a new method that has not only high quality but also fast convergence rate all the while. One of the important methods in mathematic processing is solving the old problem using updating standard. In the past twenty years, many technologies of bionic algorithms spring up quietly. And pullulate companied with the developing of computer science synchronously. So a kind of new energy was emitted to the study of TSP. The simulated annealing algorithm is simple and easy to implement, so it has been used in every broad fields. It is used in solving engineering optimal problems. The vertebrate immune system is a highly evolutionary system, which is highly adaptive, highly distributed and self-organizing. It can effectively recognize the antigens and kill them rapidly to protect the stability of the body. The Artificial Immune System (AIS) is an intelligent information processing technology that is based on the mechanism of the vertebrate immune system. As a novel branch of computational intelligence, AIS has strong capabilities of pattern recognition, learning and associative memory, hence it is natural to view AIS as a powerful information processing and problem-solving paradigm in both the scientific and engineering fields.
In this paper, some topics are mainly talked about:
Some basic concepts, framework, functions and principles of the biological immune system are introduced. Then the research range, research status and basic theory of the artificial immune system and simulated annealing algorithm are simply analyzed.
Secondly, we deeply analyze the mechanism of simulated annealing algorithm, then the paper proposes a simulated annealing algorithm based on controllable temperature parameter for solving TSP. By testing the data of CHN144 and benchmark TSPLIB, the experiments show that the algorithm is easy to find out the best answer.
Thirdly, after understanding some basic concepts and some principles of the vertebrate immune system, an immune algorithm is proposed and realized on the basis of immune principal. By testing it, the algorithm obtains a good solution.
Finally, we do the research on immune algorithm and simulated annealing algorithm, and a new immune simulated annealing algorithm for TSP is proposed on the basis of simulated annealing algorithm and immune algorithm. By testing the data of PR1002, the experiences show that the algorithm has a good performance.
引文
[1]Mitsumoto N, Fukuda T, Shimojima K.Micro Autonomous Robotic System and Biologically Inspired Immune Swarm Stratew as a Vlulti Agent Robotic System. Proceeding the 1995 IEEE International Conference on Robotics and Automation. Nagoya, Japan. 1995.p.2187-2192.
[2]Messmate N,Fukuda T,Shimojima K. Control of the Distributed Autonomous Robotic System Based on the Biologically Inspired Immunological Architecture Proceedine the 1997 IEEE International Conference on Robotics and Automation.Albuquerque, NM, USA, 1997. p..3551-3556.
[3]Segel L A. Immune Svstem as a Prototype of Autonomous Decentralized Systems. Proceeding of the 1997 IEEE International Conference on System. Man and Cybernetics, Orlando FL, USA, 1997.p.875-884.
[4]Takahashi K, Yamada T. Application of an Immune Feedback Mechanism to Control Systems. JSME International Journal. Series C, Vol.41, No.2,1998.p.184-191.
[5]Ishida Y, Mizessyn F. Learning Algorithms on an Immune Network Model: Application to Sensor Diagnosis. Proceeding International Conference Neural Networks, China. 1992, pp.33-38.
[6]Ishida Y. An Immune Nenvork Model and Its Applications to Process Diagnosis Systems and Computers( in Japanese). 1993. Vol.24, No.6.p.38-45.
[7]Ishiguru A,Watanabe Y.,Uorooka Y.Distributed Diagnosis System Combining the Immune Network and Learning Lector Quantization. Proceeding 1995 IEEE 21~(st) International Electronics. Control and Instrumentation, Orlando,FL,USA. 1995.p.1531 — 1536.
[8]Hunt J E, Cooke D E.Learning L'sing an Artif cial Immune System. Journal of Network and Computer Applications. 1996. Voll9.p.l89-212.
[9]Dasgupta D, Attoh-Okine N.Immunity-based System:A Survey. Proceeding 1997 IEEE International Conference on System and Cybernetics. Orlando. FL, USA, 1997.p.869-874.
[10]Forrest S, Javornik B,Smith R, Perelson A S. Using Genetic Algorithms to Explore Pattern Recognition in the Immune System. Evolutionary Computation. 1993,Vol.l. No.3.p.191-211..
[11]McCoy D F, Devarajan V. Artificial Immune System and .Aerial Image Segmentation. Proceeding 1997 IEEE International Conference on Systems. Man and Cvbemetics.Orlando. FL. USA. 199 7. p.879-884.
[12]Chun J S ,Cho D H, Kim MK.A Study on Comparison Between Immune Algorithm and the Other Algorithm in Motor Design. Proceeding ISAP'97 International on Intelligent System Application to Power Systems. Seoul, South Korea. 1997. p.588-592.
[13] Chun J S, Kim M K. Jung H.K. Shape optimi_ation of Electromagnetic Drives L.sing Immune Algorithm. IEEE Trans on Maanetics. 1997. Vol.33. No.2. p.1876-1879.
[14]Hajela P,Lee P J.Constrained Genetic Search Iria Schema.Adaptation:An Immune Network Solution. Structural Optimization. 1996. Vol.12. No. 1.p.11-15.
[15]Ishiguro A,Kondo T,Watanabe.An Evolutionary Construction of Immune Network-Based Behavior Alrbitration mechanism for Autonomous Mobile Robot.Trans of the Institute of Electrical Engineers of Japan(Series C). 1997. Vol.117, No.7.p.867- 873.
[16]Tazawa L, Koakutsu S, Hirata H .An Optimization Method Based on the Immune Proceeding Society 1996 World Congress on Neural Networks. International Neural Meeting, San Diego, CA. USA. 1996. p.1045-1049.
[17]Hunt J E, Cookie D E.An Adaptive. Distributed Learning System. Based on the Immune System. Proceeding 1996 IEEE International Conference on Neural Networks,Washington, DC, USA. 1996.p.519-523.
[18]D'haeseleer P, Forrest S, Herman P. An Immunological Approach to Change Detection: Algorithms, Analysis and Applications. Proceeding IEEE Symposium on Research in Security and Privacy, Oakland. CA, USA. 1996.p.110-119.
[19]Kephart J O etal. Biological Inspired Defenses Against Computer Viruses. Proceeding 14~(th) International Joint Conference Artificial Intelligence. San Mateo. CA, USA.p.986-996.
[20]Dasgupta D. Artificial Neural Networks and Artificial Immune Systems: Similarities and Differences. In: Proceedings of the IEEE SMC, 1997.p. 873-878.
[21]Jerne N K. Towards a Network Theory of the Immune System. Annual Immunology. 1974.p.373-389.
[22]Farmer J D, Packard N H, Perelson A S. The Immune System, Adaption, and Machine Learning. Physica 22D. 1986.p.187-204.
[23]Perelson A S. Immune Network Theory. Immuneological review. 1986.No.10.p.536-551.
[24] Bersini H, Varela F J. Hints for Adaptive Problem Solving Gleaned from Immune Networks. In Proc the First Workshop on Parallel Problem Solving from Nature.1990.p.343-354.
[25]Verla F J,Stewart J. Dynamics of a Class of Immune Network. Global Stability of Idiotype Interactions. J. Theoretical Biology. 1990.p.93-101.
[26] Kephart J O. A biologically inspired immune system for computer, in R. A. Brooks and P. Maes, eds., Artificial Life Ⅳ. Proc. of the 4th International Workshop on the Synthesis and Simulation of Living Systems, MIT Press 1994. p.130-139.
[27] 张海峰，梁意文，代文．计算机免疫识别规则的演化挖掘．计算机工程．2001(11)，102-103
[28] 梁意文，汪朝霞，刘冬梅．基于食物链的计算机免疫多识别器协同识别模型．计算机工程与应用．2002，No5．p．147-149．
[29] 戴志锋，何军．一种基于主机分布式安全扫描的计算机免疫系统模型．计算机应用．2001，No10．p．24-26．
[30] 张慧敏，何军，黄厚宽．一个基于免疫的网络入侵检测模型．计算机工程与应用．2002，No6．p．159-160．
[31] 白晓冰，曹阳，张维明等．基于人工免疫模型的网络入侵检测系统，计算机工程与应用．2002，No9．p．133-135．
[32] 姜梅，丁秋林．一种基于生物免疫系统的计算机抗病毒新技术．计算机应用研究．2001(6)，No6．p．69-71．
[33] 张彦超，王文东．一种基于免疫原理的网络入侵检测模型．计算机工程与应用2002，No10．p．159-161．
[34] 李涛．计算机免疫学[M]．北京：电子工业大学出版社，2004．
[35] 康立山，谢云，尤矢勇，罗祖华．非数值并行算法(第一册)模拟退火算法[M]．北京：科学出版社，1997．
[36] 标准的TSP测试库的网址为：http://www.iwr.uniheidelberg.de/groups/comopt/software/TSPLIB95/tsp/．
[37] 陈慰峰．医学免疫学．北京：人民出版社，2001．
[38] Dasgupta D, Forrest S. Artificial Immune Systems in Industrial Applications. In Dasgupta D (Ed.) 1999 Artificial Immune Systems and Their Applications, Springer-Vedag. p.105-113.
[39] Nasaroui O, Gonzalez F, Dasgupta D. The Fuzzy Artificial Immune System: Motivations, Basic Concepts, and Application to Clustering and Web Profiling. Proceedings of the 2002 IEEE International Conference on, Vol. 1, 12-17 May 2002. p. 711-716.
[40] Kevin P, Zydallis J B, et al. Extending the Computer Defense Immune System: Network Intrusion Detection with a 1Vlultiobjective Evolutionary Programming Approach. In Jonathan Timmis and Peter J. Bentley, editors, First International Conference on Artificial Immune Systems (ICARIS'2002). University of Kent at Canterbury, UK, September 2002 ISBN 1-902671-32-5.p., 12-21.
[41] Kaers J, Wheeler R, Verrelst H. The effect of Antibody Morphology on Non-self Detection. J. Timmis, et al. (Eds.): ICARIS 2003, LNCS 2787, 2003. p.285-295
[42] Canhanm R, Jackson A H, Tyrrell A.Robot Error Detection Using Artifiicial Tmmune System. Evolvable Hardware, Proceedings, NASA/DOD Conference on, July 2003.p.91-100.
[43] Esponda F, Forrest S, Helman P. A Formal Framework for Positive and Negative Detection Schemes. IEEE Transactions on systems, Man, And Cybernetics-Part B: Cyemetics, 2003.p.78-81.
[44]Forrest S,Hofmeyr s, Somayaji A. Computer Immunology. Communications of the ACM,40(10), 1997.p. 88-96.
[45] De Castro L N, Von Zuben F J. The Clonal Selection Algorithm with Engineering Applications. In: Proceedings of GECCO'00 Workshop on Artificial Immune Systems and Their Applications, 2000.p. 36-37.
[46]Jang-Sung Chun, Hyun-Kyo Jung, Song-Yop Hahn. A study on comparison of optimizationperformances between immune algorithm and other heuristic algorithms. Magnetic, 1998, Vol34,No5.p. 2972-2975.
[47]Shyh-Jier Huang. Enhancement of thermal unit commitment using immune algorithms based optimization approaches. Electrical Power and Energy System, 1999, No21.p.245-252.
[48]Shyh-Jier Huang. An immune-based optimization method to capacitor placement in a radial distribution system. IEEE Transactions on Power Delivery, 2000, Voll5,No2.p. 744-749.
[49]Endoh S,Toma N,Yamada K. Immune algorithm for n-TSP.In: Proceedings of IEEE International Conference on Systems Man and Cybernetics, 1998,No4.p. 3844-3849
[50]Kim J,Bentley P J. Towards an Artificial Immune System for NetworkIntrusion Detection: An Investigation of Dynamic Clonal Selection, Proceedings of Congress on Evolutionary Computation. 2002.p.1015-1020.
[2]Messmate N,Fukuda T,Shimojima K. Control of the Distributed Autonomous Robotic System Based on the Biologically Inspired Immunological Architecture Proceedine the 1997 IEEE International Conference on Robotics and Automation.Albuquerque, NM, USA, 1997. p..3551-3556.
[3]Segel L A. Immune Svstem as a Prototype of Autonomous Decentralized Systems. Proceeding of the 1997 IEEE International Conference on System. Man and Cybernetics, Orlando FL, USA, 1997.p.875-884.
[4]Takahashi K, Yamada T. Application of an Immune Feedback Mechanism to Control Systems. JSME International Journal. Series C, Vol.41, No.2,1998.p.184-191.
[5]Ishida Y, Mizessyn F. Learning Algorithms on an Immune Network Model: Application to Sensor Diagnosis. Proceeding International Conference Neural Networks, China. 1992, pp.33-38.
[6]Ishida Y. An Immune Nenvork Model and Its Applications to Process Diagnosis Systems and Computers( in Japanese). 1993. Vol.24, No.6.p.38-45.
[7]Ishiguru A,Watanabe Y.,Uorooka Y.Distributed Diagnosis System Combining the Immune Network and Learning Lector Quantization. Proceeding 1995 IEEE 21~(st) International Electronics. Control and Instrumentation, Orlando,FL,USA. 1995.p.1531 — 1536.
[8]Hunt J E, Cooke D E.Learning L'sing an Artif cial Immune System. Journal of Network and Computer Applications. 1996. Voll9.p.l89-212.
[9]Dasgupta D, Attoh-Okine N.Immunity-based System:A Survey. Proceeding 1997 IEEE International Conference on System and Cybernetics. Orlando. FL, USA, 1997.p.869-874.
[10]Forrest S, Javornik B,Smith R, Perelson A S. Using Genetic Algorithms to Explore Pattern Recognition in the Immune System. Evolutionary Computation. 1993,Vol.l. No.3.p.191-211..
[11]McCoy D F, Devarajan V. Artificial Immune System and .Aerial Image Segmentation. Proceeding 1997 IEEE International Conference on Systems. Man and Cvbemetics.Orlando. FL. USA. 199 7. p.879-884.
[12]Chun J S ,Cho D H, Kim MK.A Study on Comparison Between Immune Algorithm and the Other Algorithm in Motor Design. Proceeding ISAP'97 International on Intelligent System Application to Power Systems. Seoul, South Korea. 1997. p.588-592.
[13] Chun J S, Kim M K. Jung H.K. Shape optimi_ation of Electromagnetic Drives L.sing Immune Algorithm. IEEE Trans on Maanetics. 1997. Vol.33. No.2. p.1876-1879.
[14]Hajela P,Lee P J.Constrained Genetic Search Iria Schema.Adaptation:An Immune Network Solution. Structural Optimization. 1996. Vol.12. No. 1.p.11-15.
[15]Ishiguro A,Kondo T,Watanabe.An Evolutionary Construction of Immune Network-Based Behavior Alrbitration mechanism for Autonomous Mobile Robot.Trans of the Institute of Electrical Engineers of Japan(Series C). 1997. Vol.117, No.7.p.867- 873.
[16]Tazawa L, Koakutsu S, Hirata H .An Optimization Method Based on the Immune Proceeding Society 1996 World Congress on Neural Networks. International Neural Meeting, San Diego, CA. USA. 1996. p.1045-1049.
[17]Hunt J E, Cookie D E.An Adaptive. Distributed Learning System. Based on the Immune System. Proceeding 1996 IEEE International Conference on Neural Networks,Washington, DC, USA. 1996.p.519-523.
[18]D'haeseleer P, Forrest S, Herman P. An Immunological Approach to Change Detection: Algorithms, Analysis and Applications. Proceeding IEEE Symposium on Research in Security and Privacy, Oakland. CA, USA. 1996.p.110-119.
[19]Kephart J O etal. Biological Inspired Defenses Against Computer Viruses. Proceeding 14~(th) International Joint Conference Artificial Intelligence. San Mateo. CA, USA.p.986-996.
[20]Dasgupta D. Artificial Neural Networks and Artificial Immune Systems: Similarities and Differences. In: Proceedings of the IEEE SMC, 1997.p. 873-878.
[21]Jerne N K. Towards a Network Theory of the Immune System. Annual Immunology. 1974.p.373-389.
[22]Farmer J D, Packard N H, Perelson A S. The Immune System, Adaption, and Machine Learning. Physica 22D. 1986.p.187-204.
[23]Perelson A S. Immune Network Theory. Immuneological review. 1986.No.10.p.536-551.
[24] Bersini H, Varela F J. Hints for Adaptive Problem Solving Gleaned from Immune Networks. In Proc the First Workshop on Parallel Problem Solving from Nature.1990.p.343-354.
[25]Verla F J,Stewart J. Dynamics of a Class of Immune Network. Global Stability of Idiotype Interactions. J. Theoretical Biology. 1990.p.93-101.
[26] Kephart J O. A biologically inspired immune system for computer, in R. A. Brooks and P. Maes, eds., Artificial Life Ⅳ. Proc. of the 4th International Workshop on the Synthesis and Simulation of Living Systems, MIT Press 1994. p.130-139.
[27] 张海峰，梁意文，代文．计算机免疫识别规则的演化挖掘．计算机工程．2001(11)，102-103
[28] 梁意文，汪朝霞，刘冬梅．基于食物链的计算机免疫多识别器协同识别模型．计算机工程与应用．2002，No5．p．147-149．
[29] 戴志锋，何军．一种基于主机分布式安全扫描的计算机免疫系统模型．计算机应用．2001，No10．p．24-26．
[30] 张慧敏，何军，黄厚宽．一个基于免疫的网络入侵检测模型．计算机工程与应用．2002，No6．p．159-160．
[31] 白晓冰，曹阳，张维明等．基于人工免疫模型的网络入侵检测系统，计算机工程与应用．2002，No9．p．133-135．
[32] 姜梅，丁秋林．一种基于生物免疫系统的计算机抗病毒新技术．计算机应用研究．2001(6)，No6．p．69-71．
[33] 张彦超，王文东．一种基于免疫原理的网络入侵检测模型．计算机工程与应用2002，No10．p．159-161．
[34] 李涛．计算机免疫学[M]．北京：电子工业大学出版社，2004．
[35] 康立山，谢云，尤矢勇，罗祖华．非数值并行算法(第一册)模拟退火算法[M]．北京：科学出版社，1997．
[36] 标准的TSP测试库的网址为：http://www.iwr.uniheidelberg.de/groups/comopt/software/TSPLIB95/tsp/．
[37] 陈慰峰．医学免疫学．北京：人民出版社，2001．
[38] Dasgupta D, Forrest S. Artificial Immune Systems in Industrial Applications. In Dasgupta D (Ed.) 1999 Artificial Immune Systems and Their Applications, Springer-Vedag. p.105-113.
[39] Nasaroui O, Gonzalez F, Dasgupta D. The Fuzzy Artificial Immune System: Motivations, Basic Concepts, and Application to Clustering and Web Profiling. Proceedings of the 2002 IEEE International Conference on, Vol. 1, 12-17 May 2002. p. 711-716.
[40] Kevin P, Zydallis J B, et al. Extending the Computer Defense Immune System: Network Intrusion Detection with a 1Vlultiobjective Evolutionary Programming Approach. In Jonathan Timmis and Peter J. Bentley, editors, First International Conference on Artificial Immune Systems (ICARIS'2002). University of Kent at Canterbury, UK, September 2002 ISBN 1-902671-32-5.p., 12-21.
[41] Kaers J, Wheeler R, Verrelst H. The effect of Antibody Morphology on Non-self Detection. J. Timmis, et al. (Eds.): ICARIS 2003, LNCS 2787, 2003. p.285-295
[42] Canhanm R, Jackson A H, Tyrrell A.Robot Error Detection Using Artifiicial Tmmune System. Evolvable Hardware, Proceedings, NASA/DOD Conference on, July 2003.p.91-100.
[43] Esponda F, Forrest S, Helman P. A Formal Framework for Positive and Negative Detection Schemes. IEEE Transactions on systems, Man, And Cybernetics-Part B: Cyemetics, 2003.p.78-81.
[44]Forrest S,Hofmeyr s, Somayaji A. Computer Immunology. Communications of the ACM,40(10), 1997.p. 88-96.
[45] De Castro L N, Von Zuben F J. The Clonal Selection Algorithm with Engineering Applications. In: Proceedings of GECCO'00 Workshop on Artificial Immune Systems and Their Applications, 2000.p. 36-37.
[46]Jang-Sung Chun, Hyun-Kyo Jung, Song-Yop Hahn. A study on comparison of optimizationperformances between immune algorithm and other heuristic algorithms. Magnetic, 1998, Vol34,No5.p. 2972-2975.
[47]Shyh-Jier Huang. Enhancement of thermal unit commitment using immune algorithms based optimization approaches. Electrical Power and Energy System, 1999, No21.p.245-252.
[48]Shyh-Jier Huang. An immune-based optimization method to capacitor placement in a radial distribution system. IEEE Transactions on Power Delivery, 2000, Voll5,No2.p. 744-749.
[49]Endoh S,Toma N,Yamada K. Immune algorithm for n-TSP.In: Proceedings of IEEE International Conference on Systems Man and Cybernetics, 1998,No4.p. 3844-3849
[50]Kim J,Bentley P J. Towards an Artificial Immune System for NetworkIntrusion Detection: An Investigation of Dynamic Clonal Selection, Proceedings of Congress on Evolutionary Computation. 2002.p.1015-1020.