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运筹学学报 >

2016 , Vol. 20 >Issue 1: 61 - 74

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.01.006

运筹学

数学规划与约束规划整合下的多目标分组排序问题研究

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  • 1. 暨南大学应急管理学院，广州 510632

收稿日期: 2014-11-19

  网络出版日期: 2016-03-15

基金资助

国家自然科学基金(No. 71401062)；广东省自然科学基金(No. s2013010014179)

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Integration of mathematical programming with constraint programming for multi-objective planning and scheduling

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  • 1. School of Emergency Management, Jinan University, Guangzhou 510632, China

Received date: 2014-11-19

  Online published: 2016-03-15

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摘要

分组排序问题属于NP-难题, 单纯的数学规划模型或约束规划模型都无法在有效时间内解决相当规模的此类问题. 控制成本、缩短工期和减少任务延迟是排序问题的三个基本目标, 在实际工作中决策者通常需要兼顾三者, 并在 三者之间进行权衡. 多目标分组排序问题 的研究增强了排序问题的实际应用价值, 有利于帮助决策者处理复杂的多目标环境. 然而, 多目标的引入也增加了问题求解难度, 针对数学规划擅长寻找最优, 约束规划擅长排序的特点, 将两类方法整合起来, 提出一个基于Benders分解算法, 极大提高了此类问题的求解 效率.

关键词： 多目标分组排序; 数学规划; 约束规划; Benders分解算法

本文引用格式

龚晶 . 数学规划与约束规划整合下的多目标分组排序问题研究[J]. 运筹学学报, 2016 , 20(1) : 61 -74 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.006

Abstract

Planning and scheduling, a NP-hard problem, can be viewed as a decision-making process of allocating limited resources to tasks over time with the goal of optimizing a certain objective. Neither mathematical programming nor constraint programming can solve it in the reasonable time. Minimum cost, minimum makespan and minimum tardiness are three classical objectives for this problem. The requirements from a real world application might be that several goals need to be achieved simultaneously. Based on Benders decomposition approach, this paper proposed an algorithm integrating  mathematical programming and constraint programming for solving multi-objective planning and scheduling.

Key words：  multiple-objective planning and scheduling; mathematical programming; constraint programming; Benders decomposition

参考文献

[1] Lustig I J, Puget J F. Program does not equal program: Constraint programming and its relationship to mathematical programming [J]. Interfaces, 2001, 31: 29-53.
[2] 宋继伟, 唐加福. 基于离散粒子群优化的轧辊热处理调度方法 [J].  管理科学学报, 2010, 13(6): 44-53.
[3] 宋莉波, 徐学军, 孙延明, 等. 基一种求解柔性工作车间调度问题的混合遗传算法 [J]. 管理科学学报, 2010, 13(11): 49--54.
[4] Pinedo M.  Plannig and Scheduling in Manufacturing and Services [M]. New York: Springer, 2009.
[5] Hentenryck P V, Perron L, Puget J F. Search and strategies in OPL [J]. ACM Transactions on Computational Logic, 2000, 1: 282-315.
[6] Heipcke S. Comparing constraint programming and mathematical programming approaches to discrete optimization - the change problem [J]. Journal of Operational Research Society, 1999, 50: 581-595.
[7] Rodesek R, Wallace M G, Hajian M T. A new approach to integrating mixed integer programming and constraint logic programming [J]. Annals of Operational Research, 1999, 86: 63-87.
[8] Hooker J N. A search-infer-and-relax framework for integration solution methods [J]. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems(CPAIOR), LNCS, 2005, 3524: 243-257.
[9] Kim H J, Hooker J N. Solving fixed-charge network flow problems with a hybrid optimization and constraint programming approach [J].  Annals of Operations Research, 2002, 115: 95-124.
[10] 冯欣, 唐立新, 王梦光. BAB算法中集成CPT求解job-shop调度问题 [J]. 管理科学学报, 2005, 8(3): 81-89.
[11] Benders J F. Partitioning procedures for solving mixed-variables programming problems [J]. Numerische Mathematick, 1962, 4: 238-252.
[12] Geoffrion A M. Generalized benders decompostion [J]. Journal of optimization theory and application, 1972, 10: 237-260.
[13] Hooker J N.  Logic-based Methods for Optimization: Combining Optimization and Constraint Satisfaction [M]. New York: John Wiley, 2000.
[14] Jain V, Grossmann I E. Algorithms for hybrid MILP/CP models for a class of optimization problems [J].  INFORMS Journal on Computing, 2001, 13: 258-276.
[15] Harjunkoski I, Grossmann I E. Decomposition techniques for multistage scheduling problems using mixed-integer and constraint programming methods [J]. Computers and Chemical Engineering, 2002, 26: 1533-1552.
[16] Maravelias C T, Grossmann I E. A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants [J]. Computers and Chemical Engineering, 2004,  28: 1921-1949.
[17] Coban E,  Hooker J  N. Single facility scheduling by logic-based Benders decomposition [J]. Annals of Operations Research, 2013, 210(1): 245-272.
[18] Hooker J N. Planning and scheduling by logic-based benders decomposition [J]. Operations Research, 2007, 55(3): 588-602.
[19] Lin S W, Ying K C. A multi-point simulated annealing heuristic for solving multiple objective unrelated parallel machine scheduling problems [J]. International Journal of Production Research, 2015, 53(4): 1065-1076.
[20] Fernandez-Viagasa V, Framinana J  M. A bounded-search iterated greedy algorithm for the distributed permutation flow-shop scheduling problem [J]. International Journal of Production Research, 2015, 53(4): 1111-1123.
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