流程工业间歇生产调度中并行列队竞争算法的应用研究
|
摘要
流程工业是国民经济的重要基础工业。近年来,随着经济全球化的发展,传统流程工业受到了巨大的挑战。流程企业的经营环境更为复杂,市场竞争日趋激烈,每个企业都在寻求最佳的生产运营管理方案,以提高企业的生产经营效率,从而增强企业的竞争优势。生产调度是流程企业生产管理的核心,合理的生产调度不仅有助于提高企业的服务水平,而且还可以为企业带来显著的经济效益。目前,研究流程工业生产调度问题的瓶颈在于建模及求解的困难,现有的求解方法往往采用大量的整数变量和非线性关系式描述各种生产约束条件,致使所建立的模型规模庞大,求解难度高。当面临稍大规模的复杂调度问题时,一般的求解方法就很难在合理的时间内找到满意的调度方案。
本文对流程工业间歇生产调度问题进行了研究。提出了新的建模及求解方法,较好地解决了较大规模复杂调度问题的求解。主要研究工作包括以下几个方面的内容：
(1)将并行计算技术与列队竞争算法相结合,提出了一种求解大规模复杂优化问题的并行列队竞争算法。该算法采用有虚拟主节点的粗粒度并行模型作为基本并行框架,通过动态迁移拓扑、动态繁殖子代、多水平竞争等策略以实现局部搜索与全局搜索的对立统一。对典型测试函数的计算证实,并行列队竞争算法求解大规模优化问题的性能优于普通列队竞争算法。对复杂工程优化实例的求解表明,相对于文献中报道的一类进化算法,并行列队竞争算法具有更好的鲁棒性和求解质量。
(2)建立了有并行生产设备的单阶段多产品间歇生产调度优化模型,该模型将调度优化问题分解为订单生产安排和排序两个子问题。对订单的生产安排,通过引入启发式订单分配规则和柔性生产约束处理方法来完成。而对排序子问题,则是基于对订单生产顺序和订单分配规则的变异,用并行列队竞争算法来求解。实例计算表明,对小规模调度问题,本文所提出的方法可快速求得与文献中相同的最优解；对文献中有不同复杂约束条件的各种50份订单的较大规模调度问题,本文所求得的结果均优于文献中报道的结果。
(3)对有并行生产设备的多阶段多产品间歇生产调度问题进行了研究。提出了分级调度的新思想与正向-逆向订单分配策略,建立了该问题的调度优化模型。基于对订单生产序列实施的置换-反转混合变异策略和对订单分配规则实施的按比例分配搜索空间策略,用并行列队竞争算法对文献中有多种复杂约束条件与不同调度目标的问题进行了求解,结果表明：本文所提出的方法在求解文献中所有大于10份订单的调度问题时,都得到了优于文献所报道的解,并且解的质量随调度问题规模的增加而明显提高。
(4)对有并行生产设备的多目的间歇生产调度问题进行了研究。建立了以加权生产完成时间为调度目标,以所有订单生产步骤排序和订单各阶段所选用分配规则为决策变量的调度优化模型。在使用并行列队竞争算法求解时,提出了新的混合变异及迁移操作策略,有效地提高了算法的求解效率。对文献中实例的求解表明,本文所提出的方法同时适用于序贯多目的生产调度问题和有并行设备的多目的生产调度问题的求解,并且在求解有并行设备的复杂调度问题时得到了比文献更好的解。另外,对虚拟实例的求解证实,采用本文提出的调度目标与求解方法可得到即能满足客户需求,又能有效提高生产效率的调度方案。
(5)研究了涂料生产过程的调度问题。根据涂料企业生产实际提出了订单生产总时间和拖期总时间加权和最少的调度目标,并给合本文所提出的多阶段多产品调度问题的求解方法对一个涂料企业生调度的实例进行了求解,得到了既能最大限度满足顾客需求,又能最小化涂料订单生产总时间的优化调度方案。
Process industry is a major basic industry of national economy. In recent years, with the development of economic globalization, the traditional process industry is facing great challenges. With increasingly keen market competition and more complex business environment, each enterprise in process industry is searching for good solutions for production and operation to improve the efficiency of production operation, thereby enhance its own core competitive advantage. Production scheduling is the core content of enterprise management, and the reasonable production schedule not only can improve the service level of enterprises, but can bring significant economic benefits for enterprises. At present, the bottleneck problems for solving the production scheduling problem in process industry are modeling and optimization algorithms. The existing methods often used a large number of integer variables and nonlinear inequalities to represent various constraints in actual production, leading to large model size and computational intractable. Therefore, it is very difficult for the existing methods to obtain acceptable solutions to large-scale problems within reasonable time.
This thesis focuses on the batch production scheduling problems in process industry. New ways of modeling and algorithm are presented for solving the large-scale complex scheduling problems in batch plants effectively. The key problems addressed in the thesis are as follows.
Based on the combination of conventional line-up competition algorithm (CLCA) and parallel computing, a parallel line-up competition algorithm (PLCA) for solving large-scale complex optimization problems is proposed. An improved coarse-grained parallel model with virtual master node has been presented to implement the parallelization. A new dynamic migration topology, dynamic offspring reproduction scheme and multilevel competition model are employed to balance well global search and local search, leading to the rapid convergence of the proposed algorithm. Comparative study on a group of benchmark functions show that PLCA is superior to CLCA for solving large-scale problems. Computational results on several high-constrained real-life engineering design examples further demonstrate PLCA has good performance as well as good robustness compared with other evolutionary algorithms in literature.
A new model for single-stage multi-product scheduling problem (SMSP) in batch plants with parallel units is proposed. In this model the complex scheduling problem is decomposed into order assignment and order sequencing subproblems. The assignment subproblem is solved using a group of heuristic order assignment rule and flexible constraint handling strategies, while the sequencing subproblem is solved using parallel line-up competition algorithm that mutates the sequence of orders and the order assignment rule simultaneously to search the better solutions. Computational results on examples in literature show that the proposed approach can quickly obtain the same optimal solutions as obtained by the approaches in the literature for solving medium-scale and small-scale problems. However, for all 50-order problems with different complex constraints, the proposed approach has obtained better solutions than those of literature.
The multi-stage multi-product scheduling problem (MMSP) in batch plants with parallel units is studied. The decomposition scheduling method and forward-backward assignment strategy are proposed to solve the MMSP. In this basis, a new model for MMSP in batch plants with parallel units is presented. Based on a mixed swap-reverse mutation strategy for the order sequence and a proportion-based search space allocation strategy for the order assignment rules, PLC A is used to solve the high-constrained examples with different scheduling objectives in literature. Computational results indicate that the proposed approach has obtained the better solutions than those of the literature for all scheduling problems with more than 10 orders. Moreover, with the problem size increasing, the solutions obtained by the proposed approach are improved remarkably.
A new model for multi-purpose scheduling problem (MSP) in batch plants with parallel units is proposed. The objective function of this new model is the weighted production completion time, and the variables are sequence of order process steps and order assignment rules in each stage. To solving this model, more effective mixed mutation strategy and migration strategy are proposed to improve the performance of PLCA. Computational results on examples in literature show that the proposed approach is suitable for both sequential MSP and MSP with parallel units. Especially, for the complex MSP with parallel units, the proposed approach has obtained better results than those of the literature. On the other hand, the computational results on virtual examples show that a reasonable scheduling scheme that can meet the customer needs and improve production efficiency simultaneously can be obtained.
The scheduling problem in paint production process is studied. According to the actual situation in paint enterprise, a new weighted scheduling objective consisting of total completion time of orders and total tardiness is proposed. The approach for solving MMSP with parallel units is applied to the actual paint plant. And then scheduling schemes that can maximize customer satisfaction and minimize the total completion time of orders simultaneously can be obtained.
本文对流程工业间歇生产调度问题进行了研究。提出了新的建模及求解方法,较好地解决了较大规模复杂调度问题的求解。主要研究工作包括以下几个方面的内容：
(1)将并行计算技术与列队竞争算法相结合,提出了一种求解大规模复杂优化问题的并行列队竞争算法。该算法采用有虚拟主节点的粗粒度并行模型作为基本并行框架,通过动态迁移拓扑、动态繁殖子代、多水平竞争等策略以实现局部搜索与全局搜索的对立统一。对典型测试函数的计算证实,并行列队竞争算法求解大规模优化问题的性能优于普通列队竞争算法。对复杂工程优化实例的求解表明,相对于文献中报道的一类进化算法,并行列队竞争算法具有更好的鲁棒性和求解质量。
(2)建立了有并行生产设备的单阶段多产品间歇生产调度优化模型,该模型将调度优化问题分解为订单生产安排和排序两个子问题。对订单的生产安排,通过引入启发式订单分配规则和柔性生产约束处理方法来完成。而对排序子问题,则是基于对订单生产顺序和订单分配规则的变异,用并行列队竞争算法来求解。实例计算表明,对小规模调度问题,本文所提出的方法可快速求得与文献中相同的最优解；对文献中有不同复杂约束条件的各种50份订单的较大规模调度问题,本文所求得的结果均优于文献中报道的结果。
(3)对有并行生产设备的多阶段多产品间歇生产调度问题进行了研究。提出了分级调度的新思想与正向-逆向订单分配策略,建立了该问题的调度优化模型。基于对订单生产序列实施的置换-反转混合变异策略和对订单分配规则实施的按比例分配搜索空间策略,用并行列队竞争算法对文献中有多种复杂约束条件与不同调度目标的问题进行了求解,结果表明：本文所提出的方法在求解文献中所有大于10份订单的调度问题时,都得到了优于文献所报道的解,并且解的质量随调度问题规模的增加而明显提高。
(4)对有并行生产设备的多目的间歇生产调度问题进行了研究。建立了以加权生产完成时间为调度目标,以所有订单生产步骤排序和订单各阶段所选用分配规则为决策变量的调度优化模型。在使用并行列队竞争算法求解时,提出了新的混合变异及迁移操作策略,有效地提高了算法的求解效率。对文献中实例的求解表明,本文所提出的方法同时适用于序贯多目的生产调度问题和有并行设备的多目的生产调度问题的求解,并且在求解有并行设备的复杂调度问题时得到了比文献更好的解。另外,对虚拟实例的求解证实,采用本文提出的调度目标与求解方法可得到即能满足客户需求,又能有效提高生产效率的调度方案。
(5)研究了涂料生产过程的调度问题。根据涂料企业生产实际提出了订单生产总时间和拖期总时间加权和最少的调度目标,并给合本文所提出的多阶段多产品调度问题的求解方法对一个涂料企业生调度的实例进行了求解,得到了既能最大限度满足顾客需求,又能最小化涂料订单生产总时间的优化调度方案。
Process industry is a major basic industry of national economy. In recent years, with the development of economic globalization, the traditional process industry is facing great challenges. With increasingly keen market competition and more complex business environment, each enterprise in process industry is searching for good solutions for production and operation to improve the efficiency of production operation, thereby enhance its own core competitive advantage. Production scheduling is the core content of enterprise management, and the reasonable production schedule not only can improve the service level of enterprises, but can bring significant economic benefits for enterprises. At present, the bottleneck problems for solving the production scheduling problem in process industry are modeling and optimization algorithms. The existing methods often used a large number of integer variables and nonlinear inequalities to represent various constraints in actual production, leading to large model size and computational intractable. Therefore, it is very difficult for the existing methods to obtain acceptable solutions to large-scale problems within reasonable time.
This thesis focuses on the batch production scheduling problems in process industry. New ways of modeling and algorithm are presented for solving the large-scale complex scheduling problems in batch plants effectively. The key problems addressed in the thesis are as follows.
Based on the combination of conventional line-up competition algorithm (CLCA) and parallel computing, a parallel line-up competition algorithm (PLCA) for solving large-scale complex optimization problems is proposed. An improved coarse-grained parallel model with virtual master node has been presented to implement the parallelization. A new dynamic migration topology, dynamic offspring reproduction scheme and multilevel competition model are employed to balance well global search and local search, leading to the rapid convergence of the proposed algorithm. Comparative study on a group of benchmark functions show that PLCA is superior to CLCA for solving large-scale problems. Computational results on several high-constrained real-life engineering design examples further demonstrate PLCA has good performance as well as good robustness compared with other evolutionary algorithms in literature.
A new model for single-stage multi-product scheduling problem (SMSP) in batch plants with parallel units is proposed. In this model the complex scheduling problem is decomposed into order assignment and order sequencing subproblems. The assignment subproblem is solved using a group of heuristic order assignment rule and flexible constraint handling strategies, while the sequencing subproblem is solved using parallel line-up competition algorithm that mutates the sequence of orders and the order assignment rule simultaneously to search the better solutions. Computational results on examples in literature show that the proposed approach can quickly obtain the same optimal solutions as obtained by the approaches in the literature for solving medium-scale and small-scale problems. However, for all 50-order problems with different complex constraints, the proposed approach has obtained better solutions than those of literature.
The multi-stage multi-product scheduling problem (MMSP) in batch plants with parallel units is studied. The decomposition scheduling method and forward-backward assignment strategy are proposed to solve the MMSP. In this basis, a new model for MMSP in batch plants with parallel units is presented. Based on a mixed swap-reverse mutation strategy for the order sequence and a proportion-based search space allocation strategy for the order assignment rules, PLC A is used to solve the high-constrained examples with different scheduling objectives in literature. Computational results indicate that the proposed approach has obtained the better solutions than those of the literature for all scheduling problems with more than 10 orders. Moreover, with the problem size increasing, the solutions obtained by the proposed approach are improved remarkably.
A new model for multi-purpose scheduling problem (MSP) in batch plants with parallel units is proposed. The objective function of this new model is the weighted production completion time, and the variables are sequence of order process steps and order assignment rules in each stage. To solving this model, more effective mixed mutation strategy and migration strategy are proposed to improve the performance of PLCA. Computational results on examples in literature show that the proposed approach is suitable for both sequential MSP and MSP with parallel units. Especially, for the complex MSP with parallel units, the proposed approach has obtained better results than those of the literature. On the other hand, the computational results on virtual examples show that a reasonable scheduling scheme that can meet the customer needs and improve production efficiency simultaneously can be obtained.
The scheduling problem in paint production process is studied. According to the actual situation in paint enterprise, a new weighted scheduling objective consisting of total completion time of orders and total tardiness is proposed. The approach for solving MMSP with parallel units is applied to the actual paint plant. And then scheduling schemes that can maximize customer satisfaction and minimize the total completion time of orders simultaneously can be obtained.
引文
[1]赵小强,荣冈.流程工业生产调度问题综述[J].化工自动化及仪表,2004,31(6)：8-13.
[2]Kallrath J. Planning and scheduling in the process industry [J]. OR Spectrum,2002, 24(3):219-250.
[3]徐俊刚.流程企业生产调度方法与应用研究[D].中国科学院研究生院,2003.
[4]杨勇.化工批处理过程调度的建模与优化[D].浙江大学,2003.
[5]丁然.不确定条件下鲁棒性生产调度的研究[D].山东大学,2006.
[6]Rippin D W T. Batch process systems engineering:a retrospective and prospective review [J]. Computers and Chemical Engineering,1993,17(S1):1-13.
[7]Zimmermann H J. An application-oriented view of modeling uncertainty [J]. European Journal of Operational Research,2000,122(2):190-198.
[8]Garey M R, Johnson D S. A guide to the theory of NP-Completeness [J]. Computers and Intractability:Freeman, New York,1979.
[9]Voudouris V T, Grossmann I E. MILP model for scheduling and design of a special class of multipurpose batch plants [J]. Computers and Chemical Engineering,1996,20:1335-1360.
[10]Floudas C A, Lin X. Continuous-time versus discrete-time approaches for scheduling of chemical processes:a review [J]. Computers and Chemical Engineering,2004,28(11): 2109-2129.
[11]Carlos A. Mendez C A, Cerda J, Grossmann IE, et al. State-of-the-art review of optimization methods for short-term scheduling of batch processes [J]. Computers and Chemical Engineering,2006,30:913-946.
[12]Kondili E, Pantelides C C, Sargent R W H. A general algorithm for scheduling batch operations [J]. In:Proceeding of 3rd International Symposium on Process Systems Engineering. Sydney, Australia,1988,62-75.
[13]Pantelides C C. Unified frameworks for optimal process planning and scheduling [J]. In: Rippin, D. W.T. and Hale, J., Editors, Proc. Second Conf. on Foundations of Computer Aided Operations. CACHE Publications,1994.253-274.
[14]Crooks C. Synthesis of operating procedures for chemical plants [D].University of London. 1992.
[15]Majozi T, Zhu X X. A novel continuous-time MILP formulation for multipurpose batch plants 1-short-term scheduling [J]. Industrial and Engineering Chemistry Research,2001,40 (25):5935-5949.
[16]陈昌领.批处理过程计划调度的研究和应用[D].上海交通大学,2002.
[17]Bowman EH. The schedule-sequencing problem [J]. Operations Research,1959, 7(5):621-624.
[18]Kondili E, Pantelides C C, Sargent R W H. General algorithm for short-term scheduling of batch operations-I. MILP formulation [J]. Computers and Chemical Engineering,1993,17(2): 211-227.
[19]Shah N, Pantelides C C, Sargent R W H.A general algorithm for short-term scheduling of batch operations-II.Computational issues [J]. Computers and Chemical Engineering,1993, 17(2):229-244.
[20]Dedopoulos I T, Shah N. Optimal short-term scheduling of maintenance and production for multipurpose plants [J]. Industrial and Engineering Chemistry Research,1995,34:192-201.
[21]潘明.重要化工过程生产调度的数学建模与研究[D].华南理工大学,2008.
[22]Pinto J M, Grossmann I E. A continuous time mixed integer linear programming model for short term scheduling of multistage batch plants [J]. Industrial and Engineering Chemistry Research,1995,34(9):3037-3051.
[23]Pinto J M, Grossmann I E. An alternate MILP model for short-term scheduling of batch plants with preordering constraints [J]. Industrial and Engineering Chemistry Research,1996, 35(1):338-342.
[24]Moon S, Hrymak A N. Mixed-integer linear programming model for short-term scheduling of a special class of multipurpose batch plants [J]. Industrial and Engineering Chemistry Research,1999,38:2144-2150.
[25]Chen C, Liu C, Feng X and Shao H. Optimal short-term scheduling of multiproduct single-stage batch plants with parallel lines [J]. Industrial and Engineering Chemistry Research,2002,41(5):1249-1260.
[26]Sundaramoorthy A, Karimi I A. A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants [J]. Chemical Engineering Science,2005, 60:2679-2702.
[27]Dogan M E, Grossmann I E. Slot-based formulation for the short-term scheduling of multistage multiproduct batch plants with sequence-dependent changeovers [J]. Industrial and Engineering Chemistry Research,2008,47(4):1159-1183.
[28]Zhang X, Sargent R W H. The optimal operation of mixed production facilities. Part A. General formulation and some solution approaches for the solution [J]. Computers and Chemical Engineering,1996,20:897-904.
[29]Zhang X, Sargent R W H. The optimal operation of mixed production facilities-extensions and improvements [J]. Computers and Chemical Engineering,1998,22:1287-1295.
[30]Mockus L, Reklaitis G .V. Mathematical programming formulation for scheduling of batch operations based on nonuniform time discrimination [J]. Computers and Chemical Engineering,1997,21(10):1147-1156.
[31]Mockus L, Reklaitis G. V. Continuous time representation approach to batch and continuous process scheduling. Part 1.MINLP formulation [J]. Industrial and Engineering Chemistry Research,1999,38:197-203.
[32]Mockus L, Reklaitis G. V. Continuous time representation approach to batch and continuous process scheduling. Part 2.Computational issues [J]. Industrial and Engineering Chemistry Research,1999,38:204-210.
[33]Schilling G, Pantelides C C.A simple continuous-time process scheduling formulation and a novel solution algorithm [J]. Computers and Chemical Engineering,1996,20(S2): 1221-1226.
[34]Castro P, Barbosa-Povoa A, Matos H. An improved RTN continuous-time formulation for the short-term scheduling of multipurpose batch plants[J]. Industrial and Engineering Chemistry Research,2001,40 (9):2059-2068.
[35]Lee K H, Park H I, Lee I B. A novel nonuniform discrete time formulation for short-term scheduling of batch and continuous processes [J]. Industrial and Engineering Chemistry Research,2001,40 (22):4902-4911.
[36]Giannelos N F, Georgjadis M C.A simple new continuous-time formulation for short-term scheduling of multipurpose batch processes [J]. Industrial and Engineering Chemistry Research,2002,41:2178-2184.
[37]Maravelias C T, Grossmann I E. New general continuous-time state-task network formulation for short-term scheduling of multipurpose batch plants [J]. Industrial and Engineering Chemistry Research,2003,42 (13):3056-3074.
[38]Ierapetritou M G, Floudas C A. Effective continuous-time formulation for short-term scheduling.1. Multipurpose batch processes [J]. Industrial and Engineering Chemistry Research,1998,37 (11):4341-4359.
[39]Ierapetritou M G, Floudas C A. Effective continuous-time for short-term scheduling.2. Continuous and semicontinuous processes [J]. Industrial and Engineering Chemistry Research,1998,37:4360-4374.
[40]Ierapetritou M G, Floudas C A. Effective continuous-time for short-term scheduling.3. Multiple intermediate due dates [J]. Industrial and Engineering Chemistry Research,1999, 37:3446-3461.
[41]Lin X, Floudas C A. Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation [J]. Computers and Chemical Engineering, 2001,25(4-6):665-674.
[42]Janak S L, Lin X, Floudas C A. Enhanced continuous-time unit-specific event-based formulation for short-term scheduling of multipurpose batch processes:resource constraints and mixed storage policies [J]. Industrial and Engineering Chemistry Research,2004,43 (10):2516-2533.
[43]Shaik M A, Janak S L, Floudas C A. Continuous-time models for short-term scheduling of multipurpose batch plants:a comparative study [J]. Industrial and Engineering Chemistry Research,2006,45:6190-6209.
[44]Janak S L, Lin X, Floudas C A. A new robust optimization approach for scheduling under uncertainty:Ⅱ. Uncertainty with known probability distribution [J]. Computers and Chemical Engineering,2007,31(3):171-195.
[45]Mendez C A, Cerda J. Optimal scheduling of a resource-constrained multiproduct batch plant supplying intermediates to nearby end-product facilities [J]. Computers and Chemical Engineering,2000,2A:369-376.
[46]Mendez C A, Henning G P, Cerda J. Optimal scheduling of batch plants satisfying multiple product orders with different due-dates [J]. Computers and Chemical ngineering,2000,24: 2223-2245.
[47]Mendez C A, Henning G P, Cerda J. An MILP continuous time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities [J]. Computers and Chemical Engineering,2001,25:701-711.
[48]Hui C W, Gupta A, Harke A J van der Meulen. A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints [J]. Computers and Chemical Engineering,2000,24(12):2705-2717.
[49]Hui C W, Gupta A. A novel MILP formulation for short-term scheduling of multistage multi-product batch plants [J]. Computers and Chemical Engineering,2000,24(2-7): 1611-1617.
[50]Hui C W, Gupta A. A bi-index continuous-time mixed-integer linear programming model for single-stage batch scheduling with parallel unit [J]. Industrial and Engineering Chemistry Research,2001,40(25):5960-5967.
[51]Gupta S, Karimi I A. An improved MILP formulation for scheduling multiproduct multistage batch plants [J]. Industrial and Engineering Chemistry Research,2003,42:2365-2380.
[52]Castro P M, Grossmann I E. New continuous-time MILP model for the short-term scheduling of multistage batch plants [J]. Industrial and Engineering Chemistry Research, 2005,44,9175-9190.
[53]Liu Y, Karimi IA. Novel continuous-time formulations for scheduling multi-stage batch plants with identical parallel units [J]. Computers and Chemical Engineering,2007,31: 1671-1693.
[54]Xue Y F, Yuan J Q. Scheduling model for a multi-product batch plant using a pre-ordering approach [J]. Chemical Engineering and Technology,2008,31(3),433-439.
[55]Pan M, Qian Y, Li X X. A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants [J]. Chemical Engineering Science,2008,63:4313-4332.
[56]Wu D, Ierapetritou M G. Decomposition approaches for the efficient solution of short-term scheduling problems [J]. Computers and Chemical Engineering,2003,27,1261-1276.
[57]Wu D, Ierapetritou M G Lagrangean decomosition using an improved Nelder-Mead approach for langrangean multiplier update [J]. Computers and Chemical Engineering,2006, 30:778-789.
[58]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.
[59]Maravelias C T, Grossmann I E. Using MILP and CP for the scheduling of batch chemical processes [J]. Lecture Notes in Computer Science,2004,3011:1-20.
[60]Maravelias C T, Grossmann I E. A decomposition framework for the scheduling of single-and multi-stage processes [J]. Computers and Chemical Engineering,2006,30:407-420.
[61]Roe B, Papageorgiou L G, Shah N. A hybrid MILP/CLP slgorithm for multipurpose batch process scheduling [J]. Computers and Chemical Engineering,2005,29:1277-1291.
[62]Ku H M, Karrimi I A. An evaluation of simulated annealing for batch process scheduling [J]. Industrial and Engineering Chemistry Research,1991,30:163-169.
[63]Gelatt Jr C D, Kirkpatrick S, Vecchi M P. Optimization by simulation annealing[J]. Science, 1983,220:671-680.
[64]Holland J H. A daptation in national and artificial systems, Ann Arbor, The University of Michigen Press,1975.
[65]Do Jong K A. Analysis of the behavior of a class of genetic adaptive system [D]. University of Michigen, No.76-9381,1975.
[66]鄢烈祥.过程系统全局优化搜索新算法-列队竞争算法[D].北京化工大学,1998.
[67]Das H, Cummings P T, Levan M D. Scheduling of serial multiproduct batch processes via simulated annealing [J]. Computers and Chemical Engineering,1990,14:1351-1362.
[68]王举,袁希钢,陈中州.用于多产品间歇化工过程排序的模拟退火算法[J].化工学报,2000,51(6)：751-755.
[69]He Y, Hui C W. Genetic algorithm for large-size multi-stage batch plant scheduling [J]. Chemical Engineering Science,2007,62(5):1504-1523.
[70]He Y, Hui C W. Genetic algorithm based on heuristic rules for high-constrained large-size single-stage multi-product scheduling with parallel units [J]. Chemical Engineering and Processing:Process Intensification,2007,46(11):1175-1191.
[71]He Y, Hui C W. A rule-based genetic algorithm for the scheduling of single-stage multi-product batch plants with parallel units [J]. Computers and Chemical Engineering, 2008,32(12):3067-3083.
[72]孔令启,李玉刚,岳金彩,等.列队竞争算法求解多目的厂间歇过程调度问题.青岛科技大学学报(自然科学版),2006,27(5)：419-422.
[73]孔令启,岳金彩,李玉钢,等.列队竞争算法求解多产品间歇生产过程排序问题[J].计算机与应用化学,2007,24(7)：915-918.
[74]赵均,曹润生.发酵过程调度问题的约束指导模拟退火算法[J].浙江大学学报(工学版),2001,35(5)：487-491.
[75]Catherine A P, Leonardo B H, Philippe B, et al. A two-stage methodology for short-term batch plant scheduling:discrete-event simulation and genetic algorithm [J]. Computers and Chemical Engineering,1998,22(10):1461-1481.
[76]Wang K, Lohl T, Stobbe M, et al. A genetic algorithm for online-scheduling of a multiproduct polymer batch plant [J]. Computers and Chemical Engineering,2000,24(2-7): 393-400.
[77]Wu L Y, Hu Y D, Xu D M, et al. Solving batch production scheduling using genetic algorithm[J]. Computer Aided Chemical Engineering,2003,15(1):648-653.
[78]王健,陈丙珍,何小荣.并行计算在化工系统模拟与优化中的应用[J].化工学报,2002,53(5)：441-446.
[79]陈国良等编著.并行算法实践[M].北京：高等教育出版社,2004.1.
[80]Ananth Grama(美).并行计算导论[M].北京：机械工业出版社,2005.1.
[81]Cantu-Paz E. A survey of parallel genetic algorithm [J]. Caclulateurs Paralleles,1998, 10(2):141-171.
[82]Cantu-Paz E, Goldberg D E. Efficient parallel genetic algorithms:theory and practice [J]. Computer Methods in Applied. Mechanics and Engineering,2001,186:221-238.
[83]戴晓明,许超,龚向阳,等人.并行遗传算法收敛性分析及优化运算[J].计算机工程.2002,28(6)：92-95.
[84]Alba E., Luna F., Nebro A.J., et al, Parallel heterogeneous genetic algorithms for continuous optimization [J]. Parallel. Computer,2004,30:699-719.
[85]康立山,陈毓屏.解货担郎问题的异步并行模拟退火算法[J].自然科学进展,1991,3：246-252.
[86]Ram D J, Sreenivas T H, Subramaniam K G Parallel simulated annealing algorithms [J]. Journal of parallel and distributed computing,1996,37(2):207-212.
[87]Onbasoglu E., Ozdamar, L. Parallel simulated annealing algorithms in global optimization[J]. Journal of Global Optimization,2001,19:27-50.
[88]Schutte J F, Reinbolt J A, Fregly B J, et al, Parallel global optimization with particle swarm algorithm [J]. International Journal for Numerical Methods in Engineering,2004,61: 2296-2315.
[89]Koh B I, George A D, Haftka R T, et al. Parallel asynchronous particle swarm optimization [J]. International Journal for Numerical Methods in Engineering,2006,67:578-595.
[90]Chen H, Flann N. Parallel simulated annealing and genetic algorithms:a space of hybrid methods [J]. In:Y Davidor, H.P. Schwefel, R. Manner (Eds.), Proceedings of International Conference on Evolutionary Computation-PPSN III, Lecture Notes in Computer Science, Springer-Verlag, Berlin,1994,428-438.
[91]吴浩扬,常炳国,朱长纯,等人.基于模拟退火机制的多种群并行遗传算法[J].软件学报,2000,11(3)：416-420.
[92]Wang Z G, Wong Y S, Rahman M. Development of a parallel optimization method based on genetic simulated annealing algorithm [J]. Parallel Computing,2005,31:839-857.
[93]Lee C Y, Kim S J. Parallel genetic algorithms for the earliness-tardiness job scheduling problem with general penalty weights [J]. Computers and Industrial Engineering,1995,28(2): 231-243.
[94]Mayer M K. A network parallel genetic algorithm for the one machine sequencing problem[J]. Computers and Mathematics with Applications,1999,37(3):71-78.
[95]路飞,田国会,姜健.用基于模拟退火机制的多种群并行遗传算法解Job-Shop调度问题[J].山东工业大学学报,2001,31(4)：361-364.
[96]魏英姿,赵明扬.资源受限单机动态调度的并行GA算法研究[J].系统仿真学报,2005,17(4)：827-830.
[97]Gu J, Gu X, Gu M. A novel parallel quantum genetic algorithm for stochastic job shop scheduling [J]. Journal of Mathematical Analysis and Applications,2009,355(1):63-81.
[98]Yan L X, Ma DX. Global optimization of nonconvex nonlinear programs using line-up competition algorithm [J]. Computers and Chemical Engineering,2001,25:1601-1610.
[99]Sun D Y, Huang TC. Integrating controlled random search into the line-up competition algorithm to solve unsteady operation problems [J]. Industrial and Engineering Chemistry Research,2008,47:8869-8887.
[100]Sun D Y, Huang T C. The solutions of time-delayed optimal control problems by the use of modified line-up competition algorithm [J]. Journal of the Taiwan Institute of Chemical Engineers,2010,41(1):54-64.
[101]Yan L X. Solving combinatorial optimization problems with line-up competition algorithm [J]. Computers and Chemical Engineering,2003,27:251-258.
[102]鄢烈祥.用列队竞争算法解旅行商问题[J].运筹与管理,1999,8(3)：24-30.
[103]Yan L X, Shen K, Hu S H. Solving mixed integer nonlinear programming problems with line-up competition algorithm [J]. Computers and Chemical Engineering,2004, 28:2647-2657.
[104]鄢烈祥,麻德贤.全局优化搜索新算法—列队竞争算法(1)：解非线性和混合整数非线性规划问题[J].化工学报,1999,50(5)：663-670.
[105]鄢烈祥,胡晟华,麻德贤.锅炉蒸汽系统多操作周期的优化调度[J].化工学报,2003,(12).
[106]Adamidis P. Parallel evolutionary algorithms:a review, HERCMA'98,4th Hellenic-European Conference on Computer Mathematics and Its Applications, Athens, Greece,1998.
[107]Muhlenbein H, Schomisch M, Born J. The parallel genetic algorithm as function optimizer [J]. Parallel Computing,1991,17:619-632.
[108]Cohoon J P, Martin W N, Richards D S. Genetic algorithms and punctuated equilibria in VLSI [J]. In Schwefel H P, Manner R(Eds.), Proceedings of Parallel Problem Solving from Nature (PPSN 1),1st Workshop, Springer-Verlag, Berlin, Germany,1991, pp.134-144.
[109]Gordon V S, Whitney D. Serial and parallel genetic algorithms as function optimizers [J]. In Forrest S. (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA,1993, pp.177-183.
[110]Yao X, Liu Y, Lin G. Evolutionary programming made faster [J]. IEEE Transactions on Evolutionary Computation,1999,3:82-102.
[111]Lee C Y, Yao X. Evolutionary programming using mutations based on the Levy probability distribution [J]. IEEE Transactions on Evolutionary Computation,2004,8:1-13.
[112]Alba E. Parallel evolutionary algorithms can achieve super-linear performance [J]. Information Processing Letters,2002,82:7-13.
[113]Kumar V, Grama A, Gupta A, et al. Introduction to parallel computing-design and analysis of algorithms [M]. The Benjamin/Cummings Publishing Company, Inc., Redwood City, CA, 1994.
[114]Rao S S. Engineering optimization third ed. [M]. Wiley, New York,1996.
[115]Deb K. Optimal design of a welded beam via genetic algorithms [J], AIAA. J.1991, 29:2013-2015.
[116]Coello Coello C A. Use of a self-adaptive penalty approach for engineering optimization problems [J]. Computers and industrial engineering,2004,41:113-127.
[117]Coello Coello C A, Montes E M. Constraint-handling in genetic algorithms through the use of dominance-based tournament selection [J]. Advanced Engineering Materials,2003, 16:193-203.
[118]He Q, Wang L. An effective co-evolutionary particle swarm optimization for constrained engineering design problems [J]. Engineering Applications of Artificial Intelligence,2007, 20:89-99.
[119]Kannan B K, Kramer S N. An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design [J]. Journal of Mechanical Design, Transactions of the ASME,1994,116:318-20.
[120]Sandgren E. Nonlinear integer and discrete programming in mechanical design [J]. Journal of Mechanical Design,1990,112:223-229.
[121]Deb K. GeneAS:a robust optimal design technique for mechanical component design, In Dasgupta D, Michalewicz Z. (Eds) [J]. Evolutionary algorithms in engineering applications, Springer, Berlin 1997, pp.497-514.
[122]Belegundu A D. A study of mathematical programming methods for structural optimization[D]. University of Iowa, Iowa,1982.
[123]Arora J S. Introduction to optimum design [M]. McGraw-Hill, New York,1989.
[124]Cerda J, Henning P, Grossmann I E. A mixed integer linear programming model for short-term scheduling of single-stage multi-product batch plants with parallel lines [J]. Industrial and Engineering Chemistry Research,1997,36:1695-1707.
[125]陈昌领,袁德成,邵惠鹤.多产品批处理过程调度的MILP建模[J].上海交通大学学报,2002,36(8)：1132-1137.
[126]陈昌领,刘长龄,袁德成,邵惠鹤.单阶段多产品批处理过程的短期调度1-基本模型的建立[J].控制与决策,2002,31(2)：106-111.
[127]陈昌领,宗学军,孙鹏,等.单阶段多产品批处理过程的短期调度2-模型的简化[J].控制与决策,2002,3 1(3)：202-210.
[128]Castro P M, Grossmann I E. An efficient MILP model for the short-term scheduling of single stage batch plants [J]. Computers and Chemical Engineering,2006,30:1003-1018.
[129]He Y, Hui C W. Rule-evolutionary approach for single-stage multi-product scheduling with parallel units [J]. Industrial and Engineering Chemistry Research,2006,45:4679-4692.
[130]Castro P M, Grossmann I E, Novais A Q. Two new continuous-time models for the scheduling of multistage batch plants with sequence dependent changeovers [J]. Industrial and Engineering Chemistry Research,2006,45:6210-6226.
[131]2009年中国涂料行业现状分析.中华市场调研报告网.[EB／OL].[2010-03-13].http://www.cmrr.com.cn/freereport/freereports/201003/13/36554.html
[132]王晓梅.我国涂料行业的现状与发展对策[J].河北化工,2006,29(6)：40-41.
[133]岳望坤.对涂料行业发展几个问题的思考[J].中国涂料,2005,20(4)：1-3.
[134]刘栋,张玉龙.功能涂料配方设计与制造技术[M].北京：中国石化出版社,2009.
[135]洪啸吟,冯汉保.涂料化学[M].北京：科学出版社,2005.
[2]Kallrath J. Planning and scheduling in the process industry [J]. OR Spectrum,2002, 24(3):219-250.
[3]徐俊刚.流程企业生产调度方法与应用研究[D].中国科学院研究生院,2003.
[4]杨勇.化工批处理过程调度的建模与优化[D].浙江大学,2003.
[5]丁然.不确定条件下鲁棒性生产调度的研究[D].山东大学,2006.
[6]Rippin D W T. Batch process systems engineering:a retrospective and prospective review [J]. Computers and Chemical Engineering,1993,17(S1):1-13.
[7]Zimmermann H J. An application-oriented view of modeling uncertainty [J]. European Journal of Operational Research,2000,122(2):190-198.
[8]Garey M R, Johnson D S. A guide to the theory of NP-Completeness [J]. Computers and Intractability:Freeman, New York,1979.
[9]Voudouris V T, Grossmann I E. MILP model for scheduling and design of a special class of multipurpose batch plants [J]. Computers and Chemical Engineering,1996,20:1335-1360.
[10]Floudas C A, Lin X. Continuous-time versus discrete-time approaches for scheduling of chemical processes:a review [J]. Computers and Chemical Engineering,2004,28(11): 2109-2129.
[11]Carlos A. Mendez C A, Cerda J, Grossmann IE, et al. State-of-the-art review of optimization methods for short-term scheduling of batch processes [J]. Computers and Chemical Engineering,2006,30:913-946.
[12]Kondili E, Pantelides C C, Sargent R W H. A general algorithm for scheduling batch operations [J]. In:Proceeding of 3rd International Symposium on Process Systems Engineering. Sydney, Australia,1988,62-75.
[13]Pantelides C C. Unified frameworks for optimal process planning and scheduling [J]. In: Rippin, D. W.T. and Hale, J., Editors, Proc. Second Conf. on Foundations of Computer Aided Operations. CACHE Publications,1994.253-274.
[14]Crooks C. Synthesis of operating procedures for chemical plants [D].University of London. 1992.
[15]Majozi T, Zhu X X. A novel continuous-time MILP formulation for multipurpose batch plants 1-short-term scheduling [J]. Industrial and Engineering Chemistry Research,2001,40 (25):5935-5949.
[16]陈昌领.批处理过程计划调度的研究和应用[D].上海交通大学,2002.
[17]Bowman EH. The schedule-sequencing problem [J]. Operations Research,1959, 7(5):621-624.
[18]Kondili E, Pantelides C C, Sargent R W H. General algorithm for short-term scheduling of batch operations-I. MILP formulation [J]. Computers and Chemical Engineering,1993,17(2): 211-227.
[19]Shah N, Pantelides C C, Sargent R W H.A general algorithm for short-term scheduling of batch operations-II.Computational issues [J]. Computers and Chemical Engineering,1993, 17(2):229-244.
[20]Dedopoulos I T, Shah N. Optimal short-term scheduling of maintenance and production for multipurpose plants [J]. Industrial and Engineering Chemistry Research,1995,34:192-201.
[21]潘明.重要化工过程生产调度的数学建模与研究[D].华南理工大学,2008.
[22]Pinto J M, Grossmann I E. A continuous time mixed integer linear programming model for short term scheduling of multistage batch plants [J]. Industrial and Engineering Chemistry Research,1995,34(9):3037-3051.
[23]Pinto J M, Grossmann I E. An alternate MILP model for short-term scheduling of batch plants with preordering constraints [J]. Industrial and Engineering Chemistry Research,1996, 35(1):338-342.
[24]Moon S, Hrymak A N. Mixed-integer linear programming model for short-term scheduling of a special class of multipurpose batch plants [J]. Industrial and Engineering Chemistry Research,1999,38:2144-2150.
[25]Chen C, Liu C, Feng X and Shao H. Optimal short-term scheduling of multiproduct single-stage batch plants with parallel lines [J]. Industrial and Engineering Chemistry Research,2002,41(5):1249-1260.
[26]Sundaramoorthy A, Karimi I A. A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants [J]. Chemical Engineering Science,2005, 60:2679-2702.
[27]Dogan M E, Grossmann I E. Slot-based formulation for the short-term scheduling of multistage multiproduct batch plants with sequence-dependent changeovers [J]. Industrial and Engineering Chemistry Research,2008,47(4):1159-1183.
[28]Zhang X, Sargent R W H. The optimal operation of mixed production facilities. Part A. General formulation and some solution approaches for the solution [J]. Computers and Chemical Engineering,1996,20:897-904.
[29]Zhang X, Sargent R W H. The optimal operation of mixed production facilities-extensions and improvements [J]. Computers and Chemical Engineering,1998,22:1287-1295.
[30]Mockus L, Reklaitis G .V. Mathematical programming formulation for scheduling of batch operations based on nonuniform time discrimination [J]. Computers and Chemical Engineering,1997,21(10):1147-1156.
[31]Mockus L, Reklaitis G. V. Continuous time representation approach to batch and continuous process scheduling. Part 1.MINLP formulation [J]. Industrial and Engineering Chemistry Research,1999,38:197-203.
[32]Mockus L, Reklaitis G. V. Continuous time representation approach to batch and continuous process scheduling. Part 2.Computational issues [J]. Industrial and Engineering Chemistry Research,1999,38:204-210.
[33]Schilling G, Pantelides C C.A simple continuous-time process scheduling formulation and a novel solution algorithm [J]. Computers and Chemical Engineering,1996,20(S2): 1221-1226.
[34]Castro P, Barbosa-Povoa A, Matos H. An improved RTN continuous-time formulation for the short-term scheduling of multipurpose batch plants[J]. Industrial and Engineering Chemistry Research,2001,40 (9):2059-2068.
[35]Lee K H, Park H I, Lee I B. A novel nonuniform discrete time formulation for short-term scheduling of batch and continuous processes [J]. Industrial and Engineering Chemistry Research,2001,40 (22):4902-4911.
[36]Giannelos N F, Georgjadis M C.A simple new continuous-time formulation for short-term scheduling of multipurpose batch processes [J]. Industrial and Engineering Chemistry Research,2002,41:2178-2184.
[37]Maravelias C T, Grossmann I E. New general continuous-time state-task network formulation for short-term scheduling of multipurpose batch plants [J]. Industrial and Engineering Chemistry Research,2003,42 (13):3056-3074.
[38]Ierapetritou M G, Floudas C A. Effective continuous-time formulation for short-term scheduling.1. Multipurpose batch processes [J]. Industrial and Engineering Chemistry Research,1998,37 (11):4341-4359.
[39]Ierapetritou M G, Floudas C A. Effective continuous-time for short-term scheduling.2. Continuous and semicontinuous processes [J]. Industrial and Engineering Chemistry Research,1998,37:4360-4374.
[40]Ierapetritou M G, Floudas C A. Effective continuous-time for short-term scheduling.3. Multiple intermediate due dates [J]. Industrial and Engineering Chemistry Research,1999, 37:3446-3461.
[41]Lin X, Floudas C A. Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation [J]. Computers and Chemical Engineering, 2001,25(4-6):665-674.
[42]Janak S L, Lin X, Floudas C A. Enhanced continuous-time unit-specific event-based formulation for short-term scheduling of multipurpose batch processes:resource constraints and mixed storage policies [J]. Industrial and Engineering Chemistry Research,2004,43 (10):2516-2533.
[43]Shaik M A, Janak S L, Floudas C A. Continuous-time models for short-term scheduling of multipurpose batch plants:a comparative study [J]. Industrial and Engineering Chemistry Research,2006,45:6190-6209.
[44]Janak S L, Lin X, Floudas C A. A new robust optimization approach for scheduling under uncertainty:Ⅱ. Uncertainty with known probability distribution [J]. Computers and Chemical Engineering,2007,31(3):171-195.
[45]Mendez C A, Cerda J. Optimal scheduling of a resource-constrained multiproduct batch plant supplying intermediates to nearby end-product facilities [J]. Computers and Chemical Engineering,2000,2A:369-376.
[46]Mendez C A, Henning G P, Cerda J. Optimal scheduling of batch plants satisfying multiple product orders with different due-dates [J]. Computers and Chemical ngineering,2000,24: 2223-2245.
[47]Mendez C A, Henning G P, Cerda J. An MILP continuous time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities [J]. Computers and Chemical Engineering,2001,25:701-711.
[48]Hui C W, Gupta A, Harke A J van der Meulen. A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints [J]. Computers and Chemical Engineering,2000,24(12):2705-2717.
[49]Hui C W, Gupta A. A novel MILP formulation for short-term scheduling of multistage multi-product batch plants [J]. Computers and Chemical Engineering,2000,24(2-7): 1611-1617.
[50]Hui C W, Gupta A. A bi-index continuous-time mixed-integer linear programming model for single-stage batch scheduling with parallel unit [J]. Industrial and Engineering Chemistry Research,2001,40(25):5960-5967.
[51]Gupta S, Karimi I A. An improved MILP formulation for scheduling multiproduct multistage batch plants [J]. Industrial and Engineering Chemistry Research,2003,42:2365-2380.
[52]Castro P M, Grossmann I E. New continuous-time MILP model for the short-term scheduling of multistage batch plants [J]. Industrial and Engineering Chemistry Research, 2005,44,9175-9190.
[53]Liu Y, Karimi IA. Novel continuous-time formulations for scheduling multi-stage batch plants with identical parallel units [J]. Computers and Chemical Engineering,2007,31: 1671-1693.
[54]Xue Y F, Yuan J Q. Scheduling model for a multi-product batch plant using a pre-ordering approach [J]. Chemical Engineering and Technology,2008,31(3),433-439.
[55]Pan M, Qian Y, Li X X. A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants [J]. Chemical Engineering Science,2008,63:4313-4332.
[56]Wu D, Ierapetritou M G. Decomposition approaches for the efficient solution of short-term scheduling problems [J]. Computers and Chemical Engineering,2003,27,1261-1276.
[57]Wu D, Ierapetritou M G Lagrangean decomosition using an improved Nelder-Mead approach for langrangean multiplier update [J]. Computers and Chemical Engineering,2006, 30:778-789.
[58]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.
[59]Maravelias C T, Grossmann I E. Using MILP and CP for the scheduling of batch chemical processes [J]. Lecture Notes in Computer Science,2004,3011:1-20.
[60]Maravelias C T, Grossmann I E. A decomposition framework for the scheduling of single-and multi-stage processes [J]. Computers and Chemical Engineering,2006,30:407-420.
[61]Roe B, Papageorgiou L G, Shah N. A hybrid MILP/CLP slgorithm for multipurpose batch process scheduling [J]. Computers and Chemical Engineering,2005,29:1277-1291.
[62]Ku H M, Karrimi I A. An evaluation of simulated annealing for batch process scheduling [J]. Industrial and Engineering Chemistry Research,1991,30:163-169.
[63]Gelatt Jr C D, Kirkpatrick S, Vecchi M P. Optimization by simulation annealing[J]. Science, 1983,220:671-680.
[64]Holland J H. A daptation in national and artificial systems, Ann Arbor, The University of Michigen Press,1975.
[65]Do Jong K A. Analysis of the behavior of a class of genetic adaptive system [D]. University of Michigen, No.76-9381,1975.
[66]鄢烈祥.过程系统全局优化搜索新算法-列队竞争算法[D].北京化工大学,1998.
[67]Das H, Cummings P T, Levan M D. Scheduling of serial multiproduct batch processes via simulated annealing [J]. Computers and Chemical Engineering,1990,14:1351-1362.
[68]王举,袁希钢,陈中州.用于多产品间歇化工过程排序的模拟退火算法[J].化工学报,2000,51(6)：751-755.
[69]He Y, Hui C W. Genetic algorithm for large-size multi-stage batch plant scheduling [J]. Chemical Engineering Science,2007,62(5):1504-1523.
[70]He Y, Hui C W. Genetic algorithm based on heuristic rules for high-constrained large-size single-stage multi-product scheduling with parallel units [J]. Chemical Engineering and Processing:Process Intensification,2007,46(11):1175-1191.
[71]He Y, Hui C W. A rule-based genetic algorithm for the scheduling of single-stage multi-product batch plants with parallel units [J]. Computers and Chemical Engineering, 2008,32(12):3067-3083.
[72]孔令启,李玉刚,岳金彩,等.列队竞争算法求解多目的厂间歇过程调度问题.青岛科技大学学报(自然科学版),2006,27(5)：419-422.
[73]孔令启,岳金彩,李玉钢,等.列队竞争算法求解多产品间歇生产过程排序问题[J].计算机与应用化学,2007,24(7)：915-918.
[74]赵均,曹润生.发酵过程调度问题的约束指导模拟退火算法[J].浙江大学学报(工学版),2001,35(5)：487-491.
[75]Catherine A P, Leonardo B H, Philippe B, et al. A two-stage methodology for short-term batch plant scheduling:discrete-event simulation and genetic algorithm [J]. Computers and Chemical Engineering,1998,22(10):1461-1481.
[76]Wang K, Lohl T, Stobbe M, et al. A genetic algorithm for online-scheduling of a multiproduct polymer batch plant [J]. Computers and Chemical Engineering,2000,24(2-7): 393-400.
[77]Wu L Y, Hu Y D, Xu D M, et al. Solving batch production scheduling using genetic algorithm[J]. Computer Aided Chemical Engineering,2003,15(1):648-653.
[78]王健,陈丙珍,何小荣.并行计算在化工系统模拟与优化中的应用[J].化工学报,2002,53(5)：441-446.
[79]陈国良等编著.并行算法实践[M].北京：高等教育出版社,2004.1.
[80]Ananth Grama(美).并行计算导论[M].北京：机械工业出版社,2005.1.
[81]Cantu-Paz E. A survey of parallel genetic algorithm [J]. Caclulateurs Paralleles,1998, 10(2):141-171.
[82]Cantu-Paz E, Goldberg D E. Efficient parallel genetic algorithms:theory and practice [J]. Computer Methods in Applied. Mechanics and Engineering,2001,186:221-238.
[83]戴晓明,许超,龚向阳,等人.并行遗传算法收敛性分析及优化运算[J].计算机工程.2002,28(6)：92-95.
[84]Alba E., Luna F., Nebro A.J., et al, Parallel heterogeneous genetic algorithms for continuous optimization [J]. Parallel. Computer,2004,30:699-719.
[85]康立山,陈毓屏.解货担郎问题的异步并行模拟退火算法[J].自然科学进展,1991,3：246-252.
[86]Ram D J, Sreenivas T H, Subramaniam K G Parallel simulated annealing algorithms [J]. Journal of parallel and distributed computing,1996,37(2):207-212.
[87]Onbasoglu E., Ozdamar, L. Parallel simulated annealing algorithms in global optimization[J]. Journal of Global Optimization,2001,19:27-50.
[88]Schutte J F, Reinbolt J A, Fregly B J, et al, Parallel global optimization with particle swarm algorithm [J]. International Journal for Numerical Methods in Engineering,2004,61: 2296-2315.
[89]Koh B I, George A D, Haftka R T, et al. Parallel asynchronous particle swarm optimization [J]. International Journal for Numerical Methods in Engineering,2006,67:578-595.
[90]Chen H, Flann N. Parallel simulated annealing and genetic algorithms:a space of hybrid methods [J]. In:Y Davidor, H.P. Schwefel, R. Manner (Eds.), Proceedings of International Conference on Evolutionary Computation-PPSN III, Lecture Notes in Computer Science, Springer-Verlag, Berlin,1994,428-438.
[91]吴浩扬,常炳国,朱长纯,等人.基于模拟退火机制的多种群并行遗传算法[J].软件学报,2000,11(3)：416-420.
[92]Wang Z G, Wong Y S, Rahman M. Development of a parallel optimization method based on genetic simulated annealing algorithm [J]. Parallel Computing,2005,31:839-857.
[93]Lee C Y, Kim S J. Parallel genetic algorithms for the earliness-tardiness job scheduling problem with general penalty weights [J]. Computers and Industrial Engineering,1995,28(2): 231-243.
[94]Mayer M K. A network parallel genetic algorithm for the one machine sequencing problem[J]. Computers and Mathematics with Applications,1999,37(3):71-78.
[95]路飞,田国会,姜健.用基于模拟退火机制的多种群并行遗传算法解Job-Shop调度问题[J].山东工业大学学报,2001,31(4)：361-364.
[96]魏英姿,赵明扬.资源受限单机动态调度的并行GA算法研究[J].系统仿真学报,2005,17(4)：827-830.
[97]Gu J, Gu X, Gu M. A novel parallel quantum genetic algorithm for stochastic job shop scheduling [J]. Journal of Mathematical Analysis and Applications,2009,355(1):63-81.
[98]Yan L X, Ma DX. Global optimization of nonconvex nonlinear programs using line-up competition algorithm [J]. Computers and Chemical Engineering,2001,25:1601-1610.
[99]Sun D Y, Huang TC. Integrating controlled random search into the line-up competition algorithm to solve unsteady operation problems [J]. Industrial and Engineering Chemistry Research,2008,47:8869-8887.
[100]Sun D Y, Huang T C. The solutions of time-delayed optimal control problems by the use of modified line-up competition algorithm [J]. Journal of the Taiwan Institute of Chemical Engineers,2010,41(1):54-64.
[101]Yan L X. Solving combinatorial optimization problems with line-up competition algorithm [J]. Computers and Chemical Engineering,2003,27:251-258.
[102]鄢烈祥.用列队竞争算法解旅行商问题[J].运筹与管理,1999,8(3)：24-30.
[103]Yan L X, Shen K, Hu S H. Solving mixed integer nonlinear programming problems with line-up competition algorithm [J]. Computers and Chemical Engineering,2004, 28:2647-2657.
[104]鄢烈祥,麻德贤.全局优化搜索新算法—列队竞争算法(1)：解非线性和混合整数非线性规划问题[J].化工学报,1999,50(5)：663-670.
[105]鄢烈祥,胡晟华,麻德贤.锅炉蒸汽系统多操作周期的优化调度[J].化工学报,2003,(12).
[106]Adamidis P. Parallel evolutionary algorithms:a review, HERCMA'98,4th Hellenic-European Conference on Computer Mathematics and Its Applications, Athens, Greece,1998.
[107]Muhlenbein H, Schomisch M, Born J. The parallel genetic algorithm as function optimizer [J]. Parallel Computing,1991,17:619-632.
[108]Cohoon J P, Martin W N, Richards D S. Genetic algorithms and punctuated equilibria in VLSI [J]. In Schwefel H P, Manner R(Eds.), Proceedings of Parallel Problem Solving from Nature (PPSN 1),1st Workshop, Springer-Verlag, Berlin, Germany,1991, pp.134-144.
[109]Gordon V S, Whitney D. Serial and parallel genetic algorithms as function optimizers [J]. In Forrest S. (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA,1993, pp.177-183.
[110]Yao X, Liu Y, Lin G. Evolutionary programming made faster [J]. IEEE Transactions on Evolutionary Computation,1999,3:82-102.
[111]Lee C Y, Yao X. Evolutionary programming using mutations based on the Levy probability distribution [J]. IEEE Transactions on Evolutionary Computation,2004,8:1-13.
[112]Alba E. Parallel evolutionary algorithms can achieve super-linear performance [J]. Information Processing Letters,2002,82:7-13.
[113]Kumar V, Grama A, Gupta A, et al. Introduction to parallel computing-design and analysis of algorithms [M]. The Benjamin/Cummings Publishing Company, Inc., Redwood City, CA, 1994.
[114]Rao S S. Engineering optimization third ed. [M]. Wiley, New York,1996.
[115]Deb K. Optimal design of a welded beam via genetic algorithms [J], AIAA. J.1991, 29:2013-2015.
[116]Coello Coello C A. Use of a self-adaptive penalty approach for engineering optimization problems [J]. Computers and industrial engineering,2004,41:113-127.
[117]Coello Coello C A, Montes E M. Constraint-handling in genetic algorithms through the use of dominance-based tournament selection [J]. Advanced Engineering Materials,2003, 16:193-203.
[118]He Q, Wang L. An effective co-evolutionary particle swarm optimization for constrained engineering design problems [J]. Engineering Applications of Artificial Intelligence,2007, 20:89-99.
[119]Kannan B K, Kramer S N. An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design [J]. Journal of Mechanical Design, Transactions of the ASME,1994,116:318-20.
[120]Sandgren E. Nonlinear integer and discrete programming in mechanical design [J]. Journal of Mechanical Design,1990,112:223-229.
[121]Deb K. GeneAS:a robust optimal design technique for mechanical component design, In Dasgupta D, Michalewicz Z. (Eds) [J]. Evolutionary algorithms in engineering applications, Springer, Berlin 1997, pp.497-514.
[122]Belegundu A D. A study of mathematical programming methods for structural optimization[D]. University of Iowa, Iowa,1982.
[123]Arora J S. Introduction to optimum design [M]. McGraw-Hill, New York,1989.
[124]Cerda J, Henning P, Grossmann I E. A mixed integer linear programming model for short-term scheduling of single-stage multi-product batch plants with parallel lines [J]. Industrial and Engineering Chemistry Research,1997,36:1695-1707.
[125]陈昌领,袁德成,邵惠鹤.多产品批处理过程调度的MILP建模[J].上海交通大学学报,2002,36(8)：1132-1137.
[126]陈昌领,刘长龄,袁德成,邵惠鹤.单阶段多产品批处理过程的短期调度1-基本模型的建立[J].控制与决策,2002,31(2)：106-111.
[127]陈昌领,宗学军,孙鹏,等.单阶段多产品批处理过程的短期调度2-模型的简化[J].控制与决策,2002,3 1(3)：202-210.
[128]Castro P M, Grossmann I E. An efficient MILP model for the short-term scheduling of single stage batch plants [J]. Computers and Chemical Engineering,2006,30:1003-1018.
[129]He Y, Hui C W. Rule-evolutionary approach for single-stage multi-product scheduling with parallel units [J]. Industrial and Engineering Chemistry Research,2006,45:4679-4692.
[130]Castro P M, Grossmann I E, Novais A Q. Two new continuous-time models for the scheduling of multistage batch plants with sequence dependent changeovers [J]. Industrial and Engineering Chemistry Research,2006,45:6210-6226.
[131]2009年中国涂料行业现状分析.中华市场调研报告网.[EB／OL].[2010-03-13].http://www.cmrr.com.cn/freereport/freereports/201003/13/36554.html
[132]王晓梅.我国涂料行业的现状与发展对策[J].河北化工,2006,29(6)：40-41.
[133]岳望坤.对涂料行业发展几个问题的思考[J].中国涂料,2005,20(4)：1-3.
[134]刘栋,张玉龙.功能涂料配方设计与制造技术[M].北京：中国石化出版社,2009.
[135]洪啸吟,冯汉保.涂料化学[M].北京：科学出版社,2005.