Journal of Software:2011.22(6):1267-1280

(大连理工大学 计算机科学与技术学院,辽宁 大连 116023)
Solving Chinese Postman Problem on Time Varying Network with Timed Automata
TAN Guo-Zhen,SUN Jing-Hao,WANG Bao-Cai,YAO Wei-Hong
(School of Computer Science and Technology, Dalian University of Technology, Dalian 116023, China)
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Received:July 09, 2010    Revised:March 29, 2011
> 中文摘要: 基于时间自动机理论,提出了时间窗、时间依赖服务代价以及时间依赖旅行时间这3 类时变网络中国邮路问题的统一建模的语义模型和求解方法.首先,将中国邮路问题可行解条件和时变参数与时间自动机联系起来,建立了3 类问题的统一时间自动机系统(timed automata system,简称TAS)模型;然后,将时变网络中国邮路问题归结为TAS 模型上的一系列可达性判定问题,并利用形式化验证算法给出了有效的求解方法.由于TAS 模型中存在O(|A|+|AR|+1)个时间自动机,限制了问题求解规模.为此,通过扩展时间自动机语义,提出了TAS 模型中的时间自动机合并策略,进而将TAS 模型转换为一个广义时间自动机(GTA)模型.基于GTA 模型,利用UPPAAL 工具对9 组、共54 个随机算例进行实验.实验结果表明,该方法在求解精度上明显优于运筹学领域的方法.
Abstract:This work presents timed automata as a natural tool for solving Chinese postman problems on time varying network. This study shows that the optimal Chinese tour can be equivalently casted as the shortest run in this automaton system, which can be obtained efficiently by solving a series of decision problems for reachability. A composition strategy is then proposed to adapt to the current model, such that the number of timed automaton is reduced from O(|A|+|AR|+1) to O(1). Computational results show that the improved model can solve small-sized instances optimally, and that it can obtain a better gap between the lower bound and upper bound than the ones obtained by the cutting plane and column generation algorithms.
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基金项目:国家自然科学基金(60873256); 国家重点基础研究发展计划(973)(2005CB321904) 国家自然科学基金(60873256); 国家重点基础研究发展计划(973)(2005CB321904)
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TAN Guo-Zhen,SUN Jing-Hao,WANG Bao-Cai,YAO Wei-Hong.Solving Chinese Postman Problem on Time Varying Network with Timed Automata.Journal of Software,2011,22(6):1267-1280