Integer linear programming problems with vector-formed objectives and its application in workflow net analysis

doi:10.13196/j.cims.2017.05.004

›› 2017, Vol. 23 ›› Issue (第5期): 947-954.DOI: 10.13196/j.cims.2017.05.004

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Integer linear programming problems with vector-formed objectives and its application in workflow net analysis

Online:2017-05-31 Published:2017-05-31
Supported by:
Project supported by the National Natural Science Foundation,China(No.61602279,61472229),the Science & Technology Development Fund of Shandong Province,China(No.2014GGX101035,2016ZDJS02A11),the Shandong Provincial Natural Science Fondation,China (No.BS2014DX013,ZR2015FM013),the Open Project Foundation of the Key Laboratory of Embedded System and Service Computing of Ministry of Education in Tongji University,China(No.ESSCKF201403),the Shandong Provincial Postdoctoral Innovation Project,China(No.201603056),and the SDUST Research Fund,China(No.2015TDJH102).

向量目标整数线性规划问题及其在工作流网分析中的应用

包云霞^1,2,鲁法明^1,3+,王艳晓¹,段华²,林泽东¹

1.山东科技大学计算机科学与工程学院
2.山东科技大学数学与系统科学学院
3.同济大学嵌入式系统与服务计算教育部重点实验室

基金资助:
国家自然科学基金资助项目(61602279,61472229);山东省科技发展计划资助项目(2014GGX101035,2016ZDJS02A11);山东省自然科学基金资助项目(BS2014DX013,ZR2015FM013);同济大学嵌入式系统与服务计算教育部重点实验室开放课题资助项目 (ESSCKF201403);山东省博士后创新专项资金资助项目(201603056);山东科技大学领军人才与优秀科研团队计划资助项目(2015TDJH102)。

Abstract

Abstract: To solve a special kind of integer programming problems for reachability analysis and invariant computation of workflow nets,the definition and the standard model of Integer Linear Programming (ILP) problems with vector-formed objectives were presented by summarizing and abstracting these special problems.On the basis of the traditional ILP solving methods,a new type of branch and bound method was introduced to compute all the optimization solutions of positive-definite ILP problems.Both the decomposition approach with invariants and the properly end property of workflow nets were attributed to the solution of ILP problems with vector-formed objectives.The application of the proposed method in workflow net analysis was illustrated with two specific examples.

Key words: integer programming, Petri nets, workflow net, branch and bound method

摘要： 为了求解一类特殊的整数规划问题以对工作流网进行可达性分析和不变量计算,将该类问题进行归纳和抽象,提出向量目标整数线性规划问题的概念和标准模型;在传统整数规划问题求解方法的基础上,针对一类正定的向量目标整数线性规划问题设计了一种新的分支定界算法,以求取全部最优解;将工作流网不变量分解与恰当终结性验证等问题转换为前述向量目标整数规划问题,结合实例说明了该方法在工作流网性质分析中的应用。

关键词: 整数规划, Petri网, 工作流网, 分支定界法

CLC Number:

TP301

包云霞,鲁法明,王艳晓,段华,林泽东. 向量目标整数线性规划问题及其在工作流网分析中的应用[J]. 计算机集成制造系统, 2017, 23(第5期): 947-954.

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Integer linear programming problems with vector-formed objectives and its application in workflow net analysis

向量目标整数线性规划问题及其在工作流网分析中的应用

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