基于时间Petri网的并行测试研究
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摘要
并行测试技术是ATS (Auto Test System)在进一步降低测试的时间、削减测试的成本的趋势下新兴的一项技术，它正以不可比拟的优势成为下一代ATS发展的热点。在运用并行测试技术时，要求分析系统执行过程中可能产生的冲突和竞争情况，特别是如何生成并行测试序列一直是一个复杂的、难于优化的NP难题。Petri网作为一种图形化建模工具，可以很直观的表示系统并发、异步等系统常见现象，而引入时间Petri网，可以更便捷地描述实时系统。因此，进一步发展并行测试技术理论和拓宽并行测试应用领域的关键在于：如何建立准确、可靠的并行测试时间Petri网模型，并在所建模型的基础上，探讨并行测试的任务调度算法。
本文在探讨时间Petri网构建过程中的约简步骤，并深入分析现今并行测试任务模型不足的基础上，提出了一种基于时间Petri网的并行测试建模方法。为说明该方法的应用步骤，选用一雷达接收机的实例建立相应的时间Petri网，并对其进行了动态性质分析。在此基础上，详细研究了群智能的各类优化算法，结合时间Petri网的特点和现有并行调度算法的局限，提出了一种基于遗传—蚁群算法的时间Petri网变迁序列求解算法，针对一雷达接收机的具体实例，快速地求得了最优调度方案。仿真实验表明，与现有研究成果相比，本文所提出的算法效率更高，具有重要的实用价值。
Parallel test technique is a new technique arising under the tendency of reducing test time and lowing test cost, which is becoming hot spot of the next ATS for unparalleled advantage. The parallel test system requires the analysis of competition and conflict in run time, Worse more, the optimized parallel test task scheduling sequence has been a complicated and difficult NP problem.Petri net, as a graphical modeling tool, which can represent concurrence, asynchrony in intuitive way, has been widely used in various fields. At the same time, the introduction of Timed Petri net can be more convenient to describe the real-time system. Therefore, the key of further development of the theory of parallel test technology, and broaden the application of parallel test is how to establish an accurate and reliable Timed Petri net model for parallel test, and to study parallel test task scheduling algorithm on the basis of the model activity.
In this article, based on discussing the procedure of simplifying a TPN model and analyzing the shortage of current parallel test model, proposed a modeling method for parallel test based on Timed Petri net. In order to explain the method for application of steps, used an instance of radar receiver to establish the corresponding Timed Petri net, also studied the dynamic nature of the model. On this basis, a detailed study of various optimization algorithms of swarm intelligence combined the characteristics of Timed Petri net with the limitations of existing parallel scheduling algorithms, an algorithm of exploring transition sequence of Timed Petri net based on genetic-ant colony algorithm is originally proposed. The optimal scheduling can be found in a very short period of time was presented in terms of an example on a radar receiver. Simulated experiment shows that compared with the existing research results, the given algorithm has important practical value for more efficiency.
本文在探讨时间Petri网构建过程中的约简步骤，并深入分析现今并行测试任务模型不足的基础上，提出了一种基于时间Petri网的并行测试建模方法。为说明该方法的应用步骤，选用一雷达接收机的实例建立相应的时间Petri网，并对其进行了动态性质分析。在此基础上，详细研究了群智能的各类优化算法，结合时间Petri网的特点和现有并行调度算法的局限，提出了一种基于遗传—蚁群算法的时间Petri网变迁序列求解算法，针对一雷达接收机的具体实例，快速地求得了最优调度方案。仿真实验表明，与现有研究成果相比，本文所提出的算法效率更高，具有重要的实用价值。
Parallel test technique is a new technique arising under the tendency of reducing test time and lowing test cost, which is becoming hot spot of the next ATS for unparalleled advantage. The parallel test system requires the analysis of competition and conflict in run time, Worse more, the optimized parallel test task scheduling sequence has been a complicated and difficult NP problem.Petri net, as a graphical modeling tool, which can represent concurrence, asynchrony in intuitive way, has been widely used in various fields. At the same time, the introduction of Timed Petri net can be more convenient to describe the real-time system. Therefore, the key of further development of the theory of parallel test technology, and broaden the application of parallel test is how to establish an accurate and reliable Timed Petri net model for parallel test, and to study parallel test task scheduling algorithm on the basis of the model activity.
In this article, based on discussing the procedure of simplifying a TPN model and analyzing the shortage of current parallel test model, proposed a modeling method for parallel test based on Timed Petri net. In order to explain the method for application of steps, used an instance of radar receiver to establish the corresponding Timed Petri net, also studied the dynamic nature of the model. On this basis, a detailed study of various optimization algorithms of swarm intelligence combined the characteristics of Timed Petri net with the limitations of existing parallel scheduling algorithms, an algorithm of exploring transition sequence of Timed Petri net based on genetic-ant colony algorithm is originally proposed. The optimal scheduling can be found in a very short period of time was presented in terms of an example on a radar receiver. Simulated experiment shows that compared with the existing research results, the given algorithm has important practical value for more efficiency.
引文
[1] William A Ross. The Impact of Next Generation Test Technology on Aviation Maintenance[C].IEEE, AUTOTESTCON 2003,2-9.
[2] Anderson J L. High Performance Missile Testing (next generation test Systems) [C].IEEE, AUTOTESTCON 2003,19-27.
[3]肖明清,朱小平,夏锐.并行测试技术综述[J].空军工程大学学报,2005,6(3):22-25.
[4]肖良清,乐晓波.时间Petri网与遗传—蚁群算法相结合的并行测试研究[J].系统仿真学报,2009,21(23):7648-7654.
[5]张涌,钱乐秋,王渊峰.基于扩展有限状态机测试中测试输入数据自动选取的研究[J].计算机学报,2003,26(10):1295-1303.
[6]陈奥,边泽强,孟晓风.基于信号参数集最小距离的并行测试任务调度算法[J].系统仿真学报,2006,18(9):2409-2411.
[7]李昕,沈士团,路辉.基于图染色理论的并行测试任务调度算法[J].北京航空航天大学学报,2007,33(9):1068-1071.
[8]胡瑜.基于有色Petri网理论的并行自动测试系统建模研究[D]:[电子科技大学博士学位论文].成都,电子科技大学,2003.
[9] Jochen Rivoir.Parallel Test Reduces Cost of Test More Effectively Than Just a Cheap Tester Electronics [J].IEEE, Electronics Manufacturing Technology Sysmposium, IEEE, 2004, 263-272.
[10] Jiajing Zhou, Chen Meng, Minghu Zou.A Task Scheduling Algorithm Of Single Processor Parallel Test System [C].IEEE, International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, 2007, 627-632.
[11]周春光,梁艳春.计算智能[M].长春:吉林大学出版社,2001, 1: 15-146.
[12]夏锐,肖明清,程进军.基于混合遗传退火算法的并行测试任务调度优化[J].系统仿真学报,2007,19(15):3564-3567.
[13]梁旭,李行善,于劲松.基于遗传算法的并行测试调度算法研究[J].电子测量与仪器学报,2009,23(2):19-24.
[14]付新华,肖明清,夏锐.基于蚁群算法的并行测试任务调度[J].系统仿真学报,2008,20(16):4352-4356.
[15]袁崇义.Petri网原理[M].北京:电子工业出版社,2005,3:18-184.
[16] Rangsarit Vanijjirattikhan, David Kaber, Mo-Yuen Chow et al.Timed Petri Net Modeling and Simulation of a High-Throughput Biological Screening Process[C].IEEE, Conference on Automation Science and Engineering, 2007,442-447.
[17] Li Xiaoou, Lara-Rosano F.Adaptive Fuzzy Petri Nets for Dynamic Knowledge Representation and Inference [J].Expert Systems with Applications, 2000, 19(3):235-241.
[18]刘舟,朱齐丹,朱伟等.面向对象Petri网在舰炮武器系统建模中的研究[J].系统仿真学报,2005,17(6):1343-1346.
[19]陈奥,孟晓风,边泽强.基于Petri网的并行测试程序运行管理模型[J].计算机工程与设计,2008,29(4):833-835.
[20]陈奥,孟晓风,边泽强.基于Petri网的并行自动测试系统资源分配模型与仿真[J].系统仿真学报,2008,20(12):3277-3279.
[21]吴晓华,雷航.基于随机Petri网测试的序列生成系统[J].微电子学与计算机,2006,23(11):99-101.
[22]韩咚,陈波.基于时间Petri网的多处理机的调度算法[J].计算机技术与发展,2007,17(6):15-17.
[23]马敏,陈光禹,陈东义.基于Petri网和模拟退火遗传算法的并行测试研究[J].仪器仪表学报,2007,28(2):331-336.
[24]胡文江,高永兵,樊瑞民等.基于Web服务的工作流执行优化方法探讨[J].计算机技术与发展,2009,19(6):156-159.
[25]黄光球,张斌.基于变迁可靠性的随机Petri网最优路径序列寻找[J].系统工程与电子技术,2009,31(1):187-194.
[26]宋巍,窦万春,刘茜萍.时间约束Petri网及其可调度性分析与验证[J].软件学报,2007,18(1):11-20.
[27]肖军,邓海鸿,高允锋等.基于时间Petri网的工作流建模及时间性能分析[J].吉林大学学报,2009,27(1):104-112.
[28]李勇,曹广益,朱新坚.一种基于单亲遗传算法的Petri网发射路径求解[J],系统仿真学报,2005,17(1):203-206.
[29] Adamyan A,He D. Sequential failure analysis using counters of Petri net models[J].IEEE Transactions on Systems, Man and Cybernetics, Part A,2003,33(1):1-11.
[30] Tsai JJP, Yang SJ, Chang WH.Timing Constraint Petri Nets and Their Applications to Schedulability Analysis of Real-Time System Specifications [J].IEEE, on Software Engineering 1995, 21(1):32-49.
[31] Berthomieu B, Diaz M.Modeling and Verification of Time Dependent Systems Using Time Petri Nets [J].IEEE, on Software Engineering 1991, 17(3):259-272.
[32]张广胜,吴哲辉,逄玉叶.基于时间Petri网的密码协议分析[J].系统仿真学报,2003,15:11-16.
[33]黄源,钟艳如,陈洺均.基于时间Petri网的嵌入式系统软硬件划分方法[J].微计算机信息,2008,24(3):26-28.
[34] Lin C.Stochastic Petri Nets and Performance Evaluation for System [M].北京:清华大学出版社,2005,2:10-78.
[35]谭冠政,肖如健.基于Petri网的工作流时间动态预测及验证[J].计算机测量与控制,2007,15(12):1801-1803.
[36]丁建立,陈坦坦,徐涛.基于时间Petri网的航班延误链式反应模型构建[J].系统仿真学报,2008,20(14):3888-3891.
[37]王振江,刘云.基于时间Petri网的铁通调度指挥系统建模与分析[J].北京电子科技学院学报,2006,14(2):19-22.
[38]叶阳东,杜彦花,高军伟等.时间Petri网的时间知识推理算法及在铁路智能运输系统中的应用[J].铁道学报,2002,24(5):5-10.
[39]张志伟,邓江沙.模糊时间Petri网应用[J].阜阳师范学院学报,2006,23(3) :65-67.
[40] Figueiredo J C A, Perkusich A.Fault and Timing Analysis in Real- Time Distributed Systems: A Fuzzy Time Petri-Net-Based Approach. Intl.J. Fuzzy Sets and Systems.1996.83 (3):143-168.
[41]高梅梅,吴智铭.模糊时间Petri网的时间推理及其在过程检测中的应用[J].控制与决策,2001,16(3):371-373.
[42]李涛,钟诗胜.基于着色时间Petri网的工作流模型及其性能分析[J].计算机辅助设计与图形学学报,2006,18(6):824-831.
[43]陈艾,周学海,王峰等.面向能耗优化的容错实时系统任务调度模型研究[J].小型微型计算机系统,2007,28(11):2056-2061.
[44]林闯.随机Petri网的分解与压缩技术[J].软件学报,1997, 8(7): 541 -548.
[45]田立勤,林闯,周文江.随机Petri网模型中变迁的串、并联性能等价化简技术[J].电子学报,2002,30(8):1134-1137.
[46]刘鸿,林闯,吴建平.一种紧同步随机Petri网模型的性能分析方法[J].软件学报,2003,14(6):1029-1036.
[47]杨怀洲,李增智.一组编制模式下组合Web服务模型的约简规则与算法[J].西安交通大学学报,2009,43(6):20-23.
[48]王培良,赵义军,叶志宝.Petri网的并分解[J].控制理论与应用,2001,18(1):116-118.
[49]夏锐,肖明清,朱小平等.并行测试技术在自动测试系统中的应用[J].计算机测量与控制,2005,13(1):7-10.
[50]卓家靖,孟晨.并行测试系统的任务分解和任务过程模型[J].电子测量技术,2008,31(8):109-112.
[51]高立娥,康凤举,刘卫东等.基于时间Petri网的实时多任务调度方法研究[J].系统仿真学报,2006,18(11):3075-3077.
[52]李鹏,董聪.基于实数编码的广义遗传算法及其在优化问题中的应用[J].控制与决策,2002,17(4):487-490.
[53]田小梅,龚静.实数编码遗传算法的评述[J].湖南环境生物职业技术学院学报,2005,11(1):25-31.
[54]张志顺,胡勇刚,赵宏伟等.基于改进形式的遗传算法研究[J].微电子学,2002,32(4):273-275.
[55]田小梅,郑金华,李合军.基于父个体相似度的自适应遗传算法[J].计算机工程与应用,2005,31(18):61-63.
[56]聂冲,王维平,赵雯等.基于学习算子的自学习遗传算法设计[J].计算机仿真,2006,23(9):168-171.
[57]吴养会,王乃信,刘瀛洲.多种群竞争遗传算法及其性能分析[J].西北农业科技大学学报,2005,33(4):154-156.
[58]蔡良伟,李霞.一种带融合操作的实数多种群遗传算法[J].计算机工程与应用,2005,31(13):61-63.
[59]王文义,任刚.多种群退火贪婪混合遗传算法[J].计算机工程与应用, 2005,31(23):60-62.
[60] Suresh Chandra Satapathy,Venkatesh Katari, Rohit Parimi et al.A New Approach of Integrating PSO & Improved GA for Clustering with Parallel and Transitional Technique[C].IEEE,Third International Conference on Natural Computation,2007.
[61]周远晖,陆玉昌,石纯一.基于克服过早收敛的自适应并行遗传算法[J].清华大学学报,1998,38(3):93-95.
[62]吴佳英,李平,胡宁静等.一种改进多亲遗传算法的并行模型研究[J].计算机工程,2007,33(5):190-192.
[63]吴庆洪,张纪会,徐心和.具有变异特征的蚁群算法[J].计算机研究与发展,1999,36(10):1240-1245.
[64]王颖,谢剑英.一种自适应蚁群算法及其仿真研究[J].系统仿真学报,2002,14(1):31-33.
[65]冯远静,冯祖仁,彭勤科.一类自适应蚁群算法及其收敛性分析[J].控制理论与应用,2005,22(5):713-717.
[66]陈烨.带杂交算子的蚁群算法[J].计算机工程,2001,28(12):74-76.
[67]段海滨,王道波,于秀芬.蚁群算法的研究现状及其展望[J].中国工程科学,2007,9(2):98-102.
[68]翁国栋.蚁群算法与遗传算法对TSP的一种融合[J].福建电脑, 2006,(2):115-116.
[2] Anderson J L. High Performance Missile Testing (next generation test Systems) [C].IEEE, AUTOTESTCON 2003,19-27.
[3]肖明清,朱小平,夏锐.并行测试技术综述[J].空军工程大学学报,2005,6(3):22-25.
[4]肖良清,乐晓波.时间Petri网与遗传—蚁群算法相结合的并行测试研究[J].系统仿真学报,2009,21(23):7648-7654.
[5]张涌,钱乐秋,王渊峰.基于扩展有限状态机测试中测试输入数据自动选取的研究[J].计算机学报,2003,26(10):1295-1303.
[6]陈奥,边泽强,孟晓风.基于信号参数集最小距离的并行测试任务调度算法[J].系统仿真学报,2006,18(9):2409-2411.
[7]李昕,沈士团,路辉.基于图染色理论的并行测试任务调度算法[J].北京航空航天大学学报,2007,33(9):1068-1071.
[8]胡瑜.基于有色Petri网理论的并行自动测试系统建模研究[D]:[电子科技大学博士学位论文].成都,电子科技大学,2003.
[9] Jochen Rivoir.Parallel Test Reduces Cost of Test More Effectively Than Just a Cheap Tester Electronics [J].IEEE, Electronics Manufacturing Technology Sysmposium, IEEE, 2004, 263-272.
[10] Jiajing Zhou, Chen Meng, Minghu Zou.A Task Scheduling Algorithm Of Single Processor Parallel Test System [C].IEEE, International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, 2007, 627-632.
[11]周春光,梁艳春.计算智能[M].长春:吉林大学出版社,2001, 1: 15-146.
[12]夏锐,肖明清,程进军.基于混合遗传退火算法的并行测试任务调度优化[J].系统仿真学报,2007,19(15):3564-3567.
[13]梁旭,李行善,于劲松.基于遗传算法的并行测试调度算法研究[J].电子测量与仪器学报,2009,23(2):19-24.
[14]付新华,肖明清,夏锐.基于蚁群算法的并行测试任务调度[J].系统仿真学报,2008,20(16):4352-4356.
[15]袁崇义.Petri网原理[M].北京:电子工业出版社,2005,3:18-184.
[16] Rangsarit Vanijjirattikhan, David Kaber, Mo-Yuen Chow et al.Timed Petri Net Modeling and Simulation of a High-Throughput Biological Screening Process[C].IEEE, Conference on Automation Science and Engineering, 2007,442-447.
[17] Li Xiaoou, Lara-Rosano F.Adaptive Fuzzy Petri Nets for Dynamic Knowledge Representation and Inference [J].Expert Systems with Applications, 2000, 19(3):235-241.
[18]刘舟,朱齐丹,朱伟等.面向对象Petri网在舰炮武器系统建模中的研究[J].系统仿真学报,2005,17(6):1343-1346.
[19]陈奥,孟晓风,边泽强.基于Petri网的并行测试程序运行管理模型[J].计算机工程与设计,2008,29(4):833-835.
[20]陈奥,孟晓风,边泽强.基于Petri网的并行自动测试系统资源分配模型与仿真[J].系统仿真学报,2008,20(12):3277-3279.
[21]吴晓华,雷航.基于随机Petri网测试的序列生成系统[J].微电子学与计算机,2006,23(11):99-101.
[22]韩咚,陈波.基于时间Petri网的多处理机的调度算法[J].计算机技术与发展,2007,17(6):15-17.
[23]马敏,陈光禹,陈东义.基于Petri网和模拟退火遗传算法的并行测试研究[J].仪器仪表学报,2007,28(2):331-336.
[24]胡文江,高永兵,樊瑞民等.基于Web服务的工作流执行优化方法探讨[J].计算机技术与发展,2009,19(6):156-159.
[25]黄光球,张斌.基于变迁可靠性的随机Petri网最优路径序列寻找[J].系统工程与电子技术,2009,31(1):187-194.
[26]宋巍,窦万春,刘茜萍.时间约束Petri网及其可调度性分析与验证[J].软件学报,2007,18(1):11-20.
[27]肖军,邓海鸿,高允锋等.基于时间Petri网的工作流建模及时间性能分析[J].吉林大学学报,2009,27(1):104-112.
[28]李勇,曹广益,朱新坚.一种基于单亲遗传算法的Petri网发射路径求解[J],系统仿真学报,2005,17(1):203-206.
[29] Adamyan A,He D. Sequential failure analysis using counters of Petri net models[J].IEEE Transactions on Systems, Man and Cybernetics, Part A,2003,33(1):1-11.
[30] Tsai JJP, Yang SJ, Chang WH.Timing Constraint Petri Nets and Their Applications to Schedulability Analysis of Real-Time System Specifications [J].IEEE, on Software Engineering 1995, 21(1):32-49.
[31] Berthomieu B, Diaz M.Modeling and Verification of Time Dependent Systems Using Time Petri Nets [J].IEEE, on Software Engineering 1991, 17(3):259-272.
[32]张广胜,吴哲辉,逄玉叶.基于时间Petri网的密码协议分析[J].系统仿真学报,2003,15:11-16.
[33]黄源,钟艳如,陈洺均.基于时间Petri网的嵌入式系统软硬件划分方法[J].微计算机信息,2008,24(3):26-28.
[34] Lin C.Stochastic Petri Nets and Performance Evaluation for System [M].北京:清华大学出版社,2005,2:10-78.
[35]谭冠政,肖如健.基于Petri网的工作流时间动态预测及验证[J].计算机测量与控制,2007,15(12):1801-1803.
[36]丁建立,陈坦坦,徐涛.基于时间Petri网的航班延误链式反应模型构建[J].系统仿真学报,2008,20(14):3888-3891.
[37]王振江,刘云.基于时间Petri网的铁通调度指挥系统建模与分析[J].北京电子科技学院学报,2006,14(2):19-22.
[38]叶阳东,杜彦花,高军伟等.时间Petri网的时间知识推理算法及在铁路智能运输系统中的应用[J].铁道学报,2002,24(5):5-10.
[39]张志伟,邓江沙.模糊时间Petri网应用[J].阜阳师范学院学报,2006,23(3) :65-67.
[40] Figueiredo J C A, Perkusich A.Fault and Timing Analysis in Real- Time Distributed Systems: A Fuzzy Time Petri-Net-Based Approach. Intl.J. Fuzzy Sets and Systems.1996.83 (3):143-168.
[41]高梅梅,吴智铭.模糊时间Petri网的时间推理及其在过程检测中的应用[J].控制与决策,2001,16(3):371-373.
[42]李涛,钟诗胜.基于着色时间Petri网的工作流模型及其性能分析[J].计算机辅助设计与图形学学报,2006,18(6):824-831.
[43]陈艾,周学海,王峰等.面向能耗优化的容错实时系统任务调度模型研究[J].小型微型计算机系统,2007,28(11):2056-2061.
[44]林闯.随机Petri网的分解与压缩技术[J].软件学报,1997, 8(7): 541 -548.
[45]田立勤,林闯,周文江.随机Petri网模型中变迁的串、并联性能等价化简技术[J].电子学报,2002,30(8):1134-1137.
[46]刘鸿,林闯,吴建平.一种紧同步随机Petri网模型的性能分析方法[J].软件学报,2003,14(6):1029-1036.
[47]杨怀洲,李增智.一组编制模式下组合Web服务模型的约简规则与算法[J].西安交通大学学报,2009,43(6):20-23.
[48]王培良,赵义军,叶志宝.Petri网的并分解[J].控制理论与应用,2001,18(1):116-118.
[49]夏锐,肖明清,朱小平等.并行测试技术在自动测试系统中的应用[J].计算机测量与控制,2005,13(1):7-10.
[50]卓家靖,孟晨.并行测试系统的任务分解和任务过程模型[J].电子测量技术,2008,31(8):109-112.
[51]高立娥,康凤举,刘卫东等.基于时间Petri网的实时多任务调度方法研究[J].系统仿真学报,2006,18(11):3075-3077.
[52]李鹏,董聪.基于实数编码的广义遗传算法及其在优化问题中的应用[J].控制与决策,2002,17(4):487-490.
[53]田小梅,龚静.实数编码遗传算法的评述[J].湖南环境生物职业技术学院学报,2005,11(1):25-31.
[54]张志顺,胡勇刚,赵宏伟等.基于改进形式的遗传算法研究[J].微电子学,2002,32(4):273-275.
[55]田小梅,郑金华,李合军.基于父个体相似度的自适应遗传算法[J].计算机工程与应用,2005,31(18):61-63.
[56]聂冲,王维平,赵雯等.基于学习算子的自学习遗传算法设计[J].计算机仿真,2006,23(9):168-171.
[57]吴养会,王乃信,刘瀛洲.多种群竞争遗传算法及其性能分析[J].西北农业科技大学学报,2005,33(4):154-156.
[58]蔡良伟,李霞.一种带融合操作的实数多种群遗传算法[J].计算机工程与应用,2005,31(13):61-63.
[59]王文义,任刚.多种群退火贪婪混合遗传算法[J].计算机工程与应用, 2005,31(23):60-62.
[60] Suresh Chandra Satapathy,Venkatesh Katari, Rohit Parimi et al.A New Approach of Integrating PSO & Improved GA for Clustering with Parallel and Transitional Technique[C].IEEE,Third International Conference on Natural Computation,2007.
[61]周远晖,陆玉昌,石纯一.基于克服过早收敛的自适应并行遗传算法[J].清华大学学报,1998,38(3):93-95.
[62]吴佳英,李平,胡宁静等.一种改进多亲遗传算法的并行模型研究[J].计算机工程,2007,33(5):190-192.
[63]吴庆洪,张纪会,徐心和.具有变异特征的蚁群算法[J].计算机研究与发展,1999,36(10):1240-1245.
[64]王颖,谢剑英.一种自适应蚁群算法及其仿真研究[J].系统仿真学报,2002,14(1):31-33.
[65]冯远静,冯祖仁,彭勤科.一类自适应蚁群算法及其收敛性分析[J].控制理论与应用,2005,22(5):713-717.
[66]陈烨.带杂交算子的蚁群算法[J].计算机工程,2001,28(12):74-76.
[67]段海滨,王道波,于秀芬.蚁群算法的研究现状及其展望[J].中国工程科学,2007,9(2):98-102.
[68]翁国栋.蚁群算法与遗传算法对TSP的一种融合[J].福建电脑, 2006,(2):115-116.