针对炼油厂系统性运营优化问题的混合分布递归及分支定界算法

doi:10.15960/j.cnki.issn.1007-6093.2025.04.012

摘要/Abstract

摘要：

炼油厂运营优化问题是原油产业链中非常重要的问题, 在学术界和工业界都有非常多的研究和应用。一般而言, 炼油厂优化问题会被建模为混合非线性整数规划问题(MINLP)。由于原油品种和相关产品繁多并且加工装置复杂多样, 所以变量维度较大。并且在具体的加工过程中涉及物料物性变化和加工规则, 从而产生非凸非线性和整数约束, 使得问题求解难度变大。目前学术界研究主要针对小规模问题或者运营流程的子系统进行建模求解, 并且求解方法集中在使用商用求解器, 如GAMS环境中的BARON、DICOPT等。本文针对炼厂优化的MINLP提出了一种混合分布递归和分支定界算法(Hybrid-DRBB), 分别对非线性约束和整数约束进行松弛和求解, 从而得到原问题的近似最优解。在实际的工业场景大规模数据中, 本文的算法速度被证实优于直接调用求解器的建模求解方式。

关键词: 炼厂运营优化, 混合非线性整数规划, 分布递归算法, 分支定界算法

Abstract:

The optimization of refinery operations is a critical issue within the crude oil supply chain, garnering extensive research and application interest across both academic and industrial sectors. Typically, refinery optimization problems are modeled as Mixed Integer Non-Linear Programming (MINLP) problems. The complexity of these problems arises from the vast diversity of crude oil types and their derivative products, coupled with intricate processing procedures. Moreover, specific processing steps involve changes in material properties and rules, introducing non-convex, nonlinear, and integer constraints, which increase the solution-finding difficulty. Currently, academic research primarily focuses on modeling and solving small-scale issues or subsystems of operational processes. Commercial solvers like BARON and DICOPT in GAMS are commonly employed for such tasks. This paper introduces a Hybrid Distribution Recursion and Branch and Bound algorithm (Hybrid-DRBB) for solving MINLP in refinery optimization. This method relaxes and solves nonlinear and integer constraints separately, thereby obtaining near-optimal solutions for the original problem. Through numerical experiments utilizing real-world, large-scale data scenarios, we demonstrate the efficiency of our method in comparison to traditional commercial solvers, highlighting its reduced computational cost and improved solving approach.

Key words: refinery optimization, MINLP, distribution recursion algorithm, branch and bound algorithm

中图分类号:

O221.2

孙鑫, 葛冬冬, 付德生, 魏志伟, 董丰莲, 潘师畅. 针对炼油厂系统性运营优化问题的混合分布递归及分支定界算法[J]. 运筹学学报（中英文）, 2025, 29(4): 141-158.

Xin SUN, Dongdong GE, Desheng FU, Zhiwei WEI, Fenglian DONG, Shichang PAN. A hybrid distribution recursion and branch and bound algorithm for Petroluem refinery optimization problem[J]. Operations Research Transactions, 2025, 29(4): 141-158.

图/表 7

图1

表1

表2

表3

图2

表4

表5

参考文献 29

1	DarbyM L,NikolaouM.MPC: Current practice and challenges[J].Control Engineering Practice,2012,20(4):328-342. doi: 10.1016/j.conengprac.2011.12.004
2	BodingtonC E,BakerT E.A history of mathematical programming in the petroleum industry[J].Interfaces,2019,20(4):117-127.
3	LasdonL S,JoffeB.The Relationship Between Distributive Recursion and Successive Linear Programming in Refining Production Planning Models[M].Washington:National Petroleum Refiners Association,1990.
4	HaverlyC A.Studies of the behavior of recursion for the pooling problem[J].ACM Sigmap Bulletin,1978,25,19-28.
5	Ben-TalA,EigerG,GershovitzV.Global minimization by reducing the duality gap[J].Athematical Programming,1994,63(1-3):193-212. doi: 10.1007/BF01582066
6	QuesadaI,GrossmannI E.Global optimization of bilinear process networks with multicomponent flows[J].Computers & Chemical Engineering,1995,19(12):1219-1242.
7	PintoJ M,MoroL F L.A planning model for petroleum refineries[J].Brazilian Journal of Chemical Engineering,2000,17,575-586. doi: 10.1590/S0104-66322000000400022
8	PittyS S,LiW K,AdhityaA,et al.Decision support for integrated refinery supply chains: Part 1. Dynamic simulation[J].Computers & Chemical Engineering,2008,32(11):2767-2786.
9	KooL Y,AdhityaA,SrinivasanR,et al.Decision support for integrated refinery supply chains: Part 2. Design and operation[J].Computers & Chemical Engineering,2008,32(11):2787-2800.
10	RochaR,GrossmannI E,Poggi de AragãoM,et al.Petroleum allocation at PETROBRAS: Mathematical model and a solution algorithm[J].Computers & Chemical Engineering,2009,33(12):2123-2133.
11	NeiroS M,PintoJ.Multiperiod optimization for production planning of petroleum refineries[J].Chemical Engineering Communications,2005,192(1):62-88. doi: 10.1080/00986440590473155
12	MouretS,GrossmannI E,PestiauxP.A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling[J].Computers & Chemical Engineering,2005,35(12):2750-2766.
13	AlattasA M,GrossmannI E,Palou-RiveraI.Refinery production planning: Multiperiod MINLP with nonlinear CDU model[J].Industrial & Engineering Chemistry Research,2012,51(39):12852-12861.
14	CastilloC P,CastroP M,MahalecV.Global optimization algorithm for large-scale refinery planning models with bilinear terms[J].Industrial & Engineering Chemistry Research,2017,56(2):530-548.
15	LoteroI,TrespalaciosF,GrossmannI E,et al.An MILP-MINLP decomposition method for the global optimization of a source based model of the multiperiod blending problem[J].Computers & Chemical Engineering,2016,87,13-35.
16	DemirhanC D,BoukouvalaF,KimK W,et al.An integrated data-driven modeling & global optimization approach for multi-period nonlinear production planning problems[J].Computers & Chemical Engineering,2020,141,107007.
17	BoucheikhchoukhA,BergerV,SwartzC L E,et al.Multiperiod refinery optimization for mitigating the impact of process unit shutdowns[J].Computers & Chemical Engineering,2022,164,107873.
18	DechterR,PearlJ.Generalized best-first search strategies and the optimality of A^*[J].Journal of the ACM,1985,32(3):505-536. doi: 10.1145/3828.3830
19	MorrisonD R,SauppeJ J,ZhangW D,et al.Cyclic best first search: Using contours to guide branch-and-bound algorithms[J].Naval Research Logistics,2017,64(1):64-82. doi: 10.1002/nav.21732
20	NaddefD.Polyhedral theory and branch-and-cut algorithms for the symmetric TSP[J].The Traveling Salesman Problem and Its Variations,2007,29-116.
21	AchterbergT,KochT,MartinA,et al.Branching rules revisited[J].Operations Research Letters,2005,33(1):42-54. doi: 10.1016/j.orl.2004.04.002
22	BénichouM,GauthierJ M,GirodetP,et al.Experiments in mixed-integer linear programming[J].Mathematical Programming,1971,1,76-94. doi: 10.1007/BF01584074
23	Achterberg T. Constraint integer programming[D]. Berlin: Technische Universität, 2007.
24	PryorJ,ChinneckJ W.Faster integer-feasibility in mixed-integer linear programs by branching to force change[J].Computers & Operations Research,2011,38(8):1143-1152.
25	GendronB,KhuongP V,SemetF.A Lagrangian-based branch-and-bound algorithm for the two-level uncapacitated facility location problem with single-assignment constraints[J].Transportation Science,2016,50(4):1286-1299. doi: 10.1287/trsc.2016.0692
26	BertaccoL,FischettiM,LodiA.A feasibility pump heuristic for general mixed-integer problems[J].Discrete Optimization,2007,4(1):63-76. doi: 10.1016/j.disopt.2006.10.001
27	BüdenbenderK,GrünertT,SebastianH.A hybrid tabu search/branch-and-bound algorithm for the direct flight network design problem[J].Transportation Science,2000,34(4):364-380. doi: 10.1287/trsc.34.4.364.12319
28	郭锦标,杨明诗.化工生产计划与调度的优化[M].北京:化学工业出版社,2006.
29	郭锦标.线性规划技术在石油化工行业的应用——生产计划优化的历史、现状[J].计算机与应用科学,2004,21(1):1-5.

集合	注释
$ m $	物料, $ m=\{mi, mb, mq, mrc, mr, ms, mv, my\} $
$ mi $	原油切割馏分, $ mi=\{ma, mrc, mv\} $
$ e $	装置, $ e=\{bu, c, v, u, b, sa\} $
$ p $	二次装置加工方案
$ q $	物性
$ tj $	二次装置中条件操作变量
$ d $	delta-base结构
$ cap $	加工能力, $ cap=\{capc, capv, capu\} $
$ ul $	公用工程, $ ul=\{ulp, uls\} $
$ I_{e, m} $	物料$ m $以进料的方式进入装置$ e $的集合, $ \{e, m\} \in I_{e, m} $
$ O_{e, m} $	物料$ m $以出料的方式进入装置$ e $的集合, $ \{e, m\} \in O_{e, m} $

连续变量	注释
$ WM_{e, m} $	装置$ e $中物料$ m $的量
$ WUL_{e, ulp} $	装置$ e $中公用工程$ ulp $的量
$ XB_{b, mb, m} $	调和池$ b $中调和物料$ mb $使用的物料$ m $的用量
$ WUP_{e, p} $	二次装置$ e $中使用方案$ p $的加工量
$ WPM_{e, p, m} $	二次装置$ e $中方案$ p $使用的物料$ m $加工量
$ Con_{e, tj, p} $	二次装置$ e $中方案$ p $的操作条件变量$ tj $
$ MatQua_{m, q} $	物料$ m $的物性$ q $的原形式
$ IndexMatQua_{m, q} $	物性$ m $的物性$ q $的指数形式
$ MatQuaP_{u, p, mq, q} $	二次装置$ u $中方案$ p $传递的某子物料$ mq $的物性$ q $原形式
$ IndexMatQuaP_{u, p, mq, q} $	二次装置$ u $中方案$ p $传递的某子物料$ mq $的物性$ q $指数形式

整数变量	注释
$ CapBi_{e} $	装置$ e $的启停, $ CapBi_{e}\in \{0, 1\} $
$ WemBi_{m} $	是否购买或销售物料$ m $, $ WemBi_{m}\in \{0, 1\} $
$ WemBatch_{m} $	物料$ m $批次量的倍数, $ WemBatch_{m}\in \{0, 1, 2, \cdots\} $
$ BldWgtBi_{b, mb, m} $	调和池$ b $中物料$ m $是否参与调和了$ mb $, $ BldWgtBi_{b, mb, m}\in \{0, 1\} $
$ BldWgtBatch_{b, mb, m} $	调和池中调和$ mb $使用物料$ m $的批次数目, $ BldWgtBatch_{b, mb, m}\in \{0, 1, 2, \cdots\} $
$ UntBasBi_{u, p} $	二次装置$ u $中是否采用方案$ p $生产, $ UntBasBi_{u, p}\in \{0, 1\} $

常数参数	注释
$ CCUT $	原油切割收率
$ WCAP $	装置加工能力
$ UDB $	原料性质影响的delta-base定义
$ UDR\_P $	二次装置中对原料性质影响的delta-base结构的幂次项收率
$ UTR $	温度压强影响下的二次装置收率
$ UTB\_\theta $	常温
$ UPR $	二次装置某方案收率
$ UPC $	常压公用工程单耗
$ UPU $	二次装置公用工程单耗
$ Price $	物料销售单价
$ Cost $	物料成本单价
$ UCost $	公用工程成本单价
$ Batch $	单位批次量
$ WemBatchBND $	采购和销售时批次量数目上下限
$ WemBND $	采购和销售时物料量上下限
$ BldWgtBiBND $	调和过程中物料使用上下限
$ BldWgtBatchBND $	调和过程中物料批次量使用上下限
$ BlendNum $	调和过程中需要的物料数目
$ M1, M2 $	生产中物料缺损量和冗余量
$ UL1, UL2 $	生产中公用工程缺损量和冗余量
$ Penalty $	关于缺损和冗余的惩罚项

算例规模	算例名称
算例规模	算例1	算例2	算例3	算例4
装置数量	67	87	115	71
物性数量	22	36	69	54
原油数量	19	12	19	18
产品数量	39	45	98	41
连续变量数目	2 068	3 215	4 640	1 885
整数变量数目	7	12	8	16
约束数目	2 218	3 583	5 269	2 045

		算例名称
		算例1	算例2	算例3	算例4
Hybrid-DRBB	求解时间	24	42	124	297
	是否有可行解	是(已收敛)	是(已收敛)	是(已收敛)	是(已收敛)
	目标函数值	40 224	1 408 388	145 016	35 648
	GAP/%	0.01	—	—	0.9
BARON	求解时间	33	1 800	1 800	1 800
	是否有可行解	是(且最优)	否	否	是
	目标函数值	40 220	—	—	41 124
	GAP/%	0	—	—	16.4
ANTIGONE	求解时间	27	1 800	1 800	1 608
	是否有可行解	是(且最优)	否	否	是(且最优)
	目标函数值	40 220	—	—	35 320
	GAP/%	0	—	—	0