换热网络全局最优化研究

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摘要

随着工业化的推进，能源日益短缺。换热网络作为过程工业的一个重要组成

部分，对整个系统能量的合理利用具有决定性的作用，对降低生产能耗及降低生

产成本具有重要的意义。目前换热网络优化问题的研究工作绝大部分仍然采用局

部最优化方法和随机性优化方法。随机性优化方法虽然对优化目标函数要求很低，

容易得到优化结果，但该方法基于概率统计学原理和模拟某些自然现象或过程而

形成的，得到的换热网络优化结果不能证明是最优解。局部最优化方法虽然发展

的比较成熟，形成了一系列经典理论，对于单峰问题的求解，能够搜索到最优解，

但应用于换热网络综合时，该方法对初始值的依赖性很强，由于其优化方法本身

的局限，也不可能得到全局最优解。鉴于此，本文进行换热网络全局优化确定性

方法的研究，使其在换热网络变量寻优的过程中，跳出局部最优解，寻找更优的

换热网络结构和解，直至全局最优解。

首先，本文以综合费用为目标函数，建立了换热网络优化数学模型，通过典

型算例的优化结果揭示了换热网络优化的目标函数具有多峰值的特点，并对优化

变量中整型变量和连续型变量造成的非线性特点进行了分析。

然后，本文应用确定性方法优化换热网络，提出了填充打洞函数优化换热网

络，并构造了适当的填充打洞函数跳出局部极小点，对换热网络进行优化，通过

实例验证了该方法的可行性；并首次提出峰谷轮换法优化换热网络，建立了峰谷

轮换算法跳出换热网络局部极小点陷阱。

继之，基于全局优化方法不断跳出局部极小点的思想，本文提出外推内插法

跳出换热网络局部极小点的思想，并建立单变量一维向量搜索、多变量多维向量

搜索和多维空间多面体搜索算法对换热网络进行优化，通过实例验证并比较了各

种算法优化结果的质量。

最后，针对大规模换热网络综合问题的特点，提出了大规模换热网络的优化

策略，结合了随机性方法和确定性方法的优点，应用随机性方法缩小换热网络结

构规模，在此基础上，应用确定性方法优化各换热器面积，提出了换热网络混合

优化算法。

总之，本文立足于全局优化确定性方法思想，对换热网络确定性方法进行了

深入研究，提出了多种跳出换热网络局部极小点的优化方法，对换热网络的全局

优化与综合有着重要的理论和现实意义。

关键词：换热网络综合全局优化确定性方法随机性方法

数学规划法

ABSTRACT

With the advance of industrialization, energy reserves are growing short. Heat

exchanger networks, as an important part of process industries, have a positive impact

on the rational use of energy throughout the system, and are significant for reducing

energy consumption, and reducing product cost in the course of production. At present

the local optimization methods and stochastic optimization methods are widely used for

heat exchanger network optimization problem. Although it is easy to get optimal results

by stochastic optimization methods which don’t rely on the objective function, the

methods are established based on statistical probability theory and simulation of some

natural phenomena or processes so that the heat exchanger network structure cannot be

proved to be the best solution. Local optimization methods develop relatively mature,

have formed a series of classical theory, and solve the problem for a single peak

function to get the optimal solution, but the methods are very dependent on the initial

value strong when used in optimization of heat exchanger networks, and cannot obtain

the global optimal solution with the limitations of the optimization method itself. So, the

deterministic methods of global optimization are studied for the heat exchanger network

to jump out of local optimal solution in the process of searching variables, looking for

better heat exchanger network structure and result until the global optimal solution is

found in this paper.

Firstly, with the comprehensive cost as the objective function, a mathematical

model of heat exchanger network optimization was established. The optimization results

of benchmark example were used to reveal the objective function of heat exchanger

network optimization had multi-peak characteristics, and the nonlinear characteristics

caused by the integer variables and continuous variable were analyzed.

Secondly, deterministic optimization methods were applied to optimization of heat

exchanger networks. Filling and tunneling function algorithm of heat exchanger

networks optimization was proposed, with the appropriate filling and tunneling function

constructed, to jump out of local minimum of objective function of heat exchanger

networks optimization and its feasibility was checked by an example. Peak-Valley

Superseding Approach was first proposed for heat exchanger networks optimization, the

algorithm was established to jump out of the trap of local optimum of heat exchanger

networks.

Then, based on idea of jumping out of local minimum of global optimization

method, the interpolation and extrapolation approach was proposed to jump out of the

local minimum point of heat exchanger networks. The single variable one-dimensional

vector searching, multi-variable one-dimensional vector searching and

multi-dimensional polyhedron searching algorithm were established for heat exchanger

network optimization, and their optimization results were verified and compared by a

case.

Furthermore, the strategy of large-scale heat exchanger networks optimization was

proposed as to its feature. Hybrid optimization algorithms of heat exchanger networks

were presented combined with advantages of random methods and deterministic

methods. The size of heat exchanger networks’ structure was reduced with application

of stochastic methods, and then, the areas of heat exchangers were optimized by

deterministic method.

In a word, the heat exchanger network deterministic methods were deeply studied

based on the idea of global optimization deterministic method. Several optimization

methods jumping out of local minimum of heat exchanger networks were presented, and

they have an important theoretical and practical significance at global optimization of

heat exchanger networks.

Key Word: Synthesis of Heat Exchanger Networks, Global

Optimization, Deterministic Method, Stochastic Method,

Mathematical Programming Method

摘要

ABSTRACT

第一章绪论 ···················································································1

§1.1 课题研究背景及意义 ··································································1

§1.2 国内外研究现状 ········································································2

§1.2.1 换热网络优化模型的研究现状 ··············································2

§1.2.2 换热网络优化方法的研究现状 ··············································3

§1.3 本文主要研究内容 ·····································································7

第二章换热网络优化存在的问题及难点 ················································· 8

§2.1 换热网络优化模型 ·····································································8

§2.1.1 换热器热力计算 ································································ 8

§2.1.2 换热网络优化数学模型 ····················································· 10

§2.2 换热网络优化存在的问题及难点 ·················································12

§2.2.1 换热网络优化问题存在多个极值 ········································· 12

§2.2.2 连续变量优化的非线性特性分析 ········································· 14

§2.2.3 整型变量引起的问题非线性分析 ········································· 17

§2.3 本章小结 ··············································································· 18

第三章换热网络确定性优化方法研究 ···················································19

§3.1 全局优化确定性方法介绍 ·························································· 19

§3.2 填充打洞函数算法优化换热网络 ·················································20

§3.2.1 换热网络填充打洞算法 ····················································· 20

§3.2.2 优化算例 ········································································23

§3.3 峰谷轮换法优化换热网络 ·························································· 24

§3.3.1 换热网络峰谷轮换法 ························································ 24

§3.3.2 优化算例 ········································································27

§3.4 本章小结 ··············································································· 29

第四章换热网络优化的外推内插算法 ···················································31

§4.1 多维向量跳出局部极小值点 ······················································· 31

§4.1.1 单变量一维向量搜索 ························································ 31

§4.1.2 多变量多维向量搜索 ························································ 33

§4.2 多维空间多面体跳出局部极小值点 ··············································36

§4.3 优化算例 ··············································································· 39

§4.4 本章小结 ··············································································· 42

第五章随机方法和确定方法混合优化换热网络 ·······································43

§5.1 全局优化随机性方法介绍 ·························································· 43

§5.2 大规模换热网络优化策略 ·························································· 44

§5.3 换热网络综合的混合峰谷轮换法 ·················································45

§5.3.1 Monte Carlo 方法 ······························································ 45

§5.3.2 混合峰谷轮换法优化换热网络 ············································ 45

§5.3.3 混合峰谷轮换法算例 ························································ 47

§5.4 换热网络综合的混合外推内插法 ·················································48

§5.4.1 遗传算法 ········································································48

§5.4.2 混合外推内插法优化换热网络 ············································ 50

§5.4.3 混合外推内插法算例 ························································ 52

§5.5 本章小结 ··············································································· 54

第六章结论 ················································································· 55

§6.1 主要结论 ··············································································· 55

§6.2 展望 ····················································································· 56

附录 ······························································································ 57

主要符号表 ························································································ 59

参考文献 ··························································································· 61

在读期间公开发表的论文、专利及承担科研项目 ········································67

致谢 ······························································································ 69

第一章绪论

§1.1 课题研究背景及意义

能源是国民经济持续稳定健康发展的命脉。能源问题直接决定着国家经济安

全，决定着国家民生，决定着经济社会能否进行可持续发展。近二三十年来，科

技创新日新月异，全球经济快速发展，工业化进程推进迅猛，能源消耗量急剧上

升，全球化石燃料资源储备日益减少，能源供需矛盾日趋突出。在十九世纪以前

的长久历史时期中，人类主要依靠可再生能源(生物质能、太阳能、水能、风能)

作为一次能源。自十九世纪中期以来，煤的开发利用逐步取代了木柴，经历约半

个世纪后成为全球的主要一次能源，使整个二十世纪成为化石能源世纪。

据国际能源署数据，2004 年全世界一次能源供应中，煤炭所占比例为 25.1%、

石油所占比例为 34.3%、天然气所占比例为 20.9%、核电所占比例为 6.5%、水电

所占比例为 2.2%、可燃可再生能源所占比例为 10.6%、地热能、太阳能、风能及

热能等所占比例为 0.4%[1]。尽管目前许多国家都在大力开发风能和生物燃料等替

代能源，但在未来 20 年里，全球仍不可能摆脱对化石能源的依赖[2]。按照 2008 年

的开采速度计算，全球石油剩余探明储量可供开采 42 年，天然气和煤炭分别可供

应60 年和 122 年[3]。在中国，截至 2008 年底煤炭探明储量 1145 亿吨，占全球探

明储量的 13.9%，仅次于美国和俄罗斯，而我国的石油和天然气储量分别仅占世界

总储量的 1.2%和1.3%[2]。2008 年我国煤炭储采比约为 41 年，天然气和石油储采

比分别约为 32 年和 11 年。

目前，我国总体上仍处于工业化初、中期阶段，工业部门的能耗占整个能源

消耗总量的 70%。热能是国民经济和人民生活中应用最广泛的能量形式，其在民

用方面，主要用于家用炊事和供暖；在工业方面，主要用于工业生产中。而在工

业生产中，工艺过程的加热和冷却尤为普遍，特别是能量密集型工业，石油、化

工、冶金、电力、轻工等行业，工艺流体种类较多，工艺过程复杂，工艺流体加

热和冷却环节众多，工艺过程中加热和冷却环节的实现主要依赖于换热器—能量

传递的重要设备,众多换热器构成换热器网络。热能来源于化石燃料燃烧后释放的

能量，为了提高热能的利用率，节约化石燃料的用量，可以从两个方面进行改进：

一是单体换热器强化换热技术；二是换热网络整体优化。通过涂层表面、粗糙表

面扩展表面、增加扰流元件、涡流发生器、螺旋管、添加物、冲击射流、对流换

热介质的机械搅拌、换热表面振动、换热流体振动等技术强化换热提高热能的利

用率[4,5]；合理匹配工艺流体的换热组合，充分利用工艺流体自身携带的能量（包

换热网络全局最优化研究

括热量和冷量），最大限度地减少能量的投入，节约能源。

能源成本也是产品成本的主要组成部分，能量利用方式的改进、节能措施的

执行是降低单位产品成本、提高市场竞争能力的关键。换热网络作为过程系统的

一个重要组成部分，对整个系统能量的合理利用具有决定性的作用，对降低生产

能耗，降低产品成本具有重要的意义[6]。因此，对换热网络进行综合优化，得到最

佳网络结构布置显得尤为重要。

§1.2 国内外研究现状

§1.2.1 换热网络优化模型的研究现状

在石油化工及炼钢生产等行业中，常常会碰到某些过程工艺流体需要加热，

另一些过程工艺流体需要冷却，为了利用过程流体自身的能量，节省外部能量的

投入，通常将需要加热的过程流体和需要冷却的过程流体进行换热，为了保证过

程流体达到指定的目标温度，往往需要增加外部热量（如高温蒸汽等）和冷量（如

冷却水等）分别对需要加热的流体及需要冷却的流体加热和冷却。这样一来，就

提出了一个换热网络综合优化的问题。如何配置过程流体之间的换热，使整个过

程系统最节约能源，经济性最好？自二十世纪六十年代起，越来越多的科研工作

者关心能源利用问题，在过程系统综合优化方面做了很多工作。换热网络综合优

化模型主要分为以最大热量回收及最小热量投入为目标和以最小经济费用投入为

目标两类。

1969 年，Kesler 和Parker[7]建立了换热网络问题数学模型，将参与换热的每一

股过程流体划分成若干个相同热负荷区间，然后将冷、热流体的这些热负荷区间

进行匹配形成网络结构。后来 Kobayashi、

Umeda[8]等人将该匹配问题进行了改进，

并将其扩展到分流结构和循环匹配过程中。

1983 年，Linnhoff 等提出了将热力学方法应用于换热网络优化中，并广泛应

用于工业生产中，依次以最小的公用工程费用、最少的换热器数目和最小经济费

用为目标，设定窄点温度，将换热网络综合问题按照温度区间不同，分解成为一

系列子问题，然后依次求解，多目标分步优化，属于序贯优化[9]。

1983 年，

Cerda 和Westerberg[10]等将每股过程流体划分成若干个温度区间，然

后以最小公用工程和最小换热器单元数目为目标，将温度区间进行匹配，将换热

网络优化问题描述为混合整数线性规划问题。

1986 年，

Floudas 等[11]利用线性模型求出最小公用工程量，在公用工程量已知

的情况下，利用混合线性模型求解过程流体最小匹配数，即换热器的个数，然后

在已求得的热负荷和换热器数目的条件下，进行非线性优化得到最终网络结构。

第一章绪论

1989 年，Yuan[12]等在网络热回收温差(HRAT)给定时，对无分流换热网络进行

优化，不进行子问题的分解，进行同步优化，形成混合整数非线性规划问题

(MINLP)。

1990 年，Yee 和Grossmann[13]将投资费用和运行费用结合在一起同时优化，并

提出级的概念建立换热网络 Grossmann 分级超结构模型，采用同步优化方法优化

换热网络问题(MINLP)时，不依赖于网络热回收温差，并将同步优化方法推广到有

分流换热网络优化问题中。

1995 年，Zhu 等[14]提出以面积最小为目标优化换热网络，与 Grossmann 提出

的级的概念相似，提出了块的概念。

2000 年，Shethnaa 等[15]在建立换热网络优化目标函数时，将换热器费用、换

热面积费用和公用工程费用结合在一起，将换热网络优化问题转化为计算该三项

费用的折中点。

2001 年，Furman 和Sahinidis[16]证明换热网络优化问题是 NP 难问题。

§1.2.2 换热网络优化方法的研究现状

换热网络优化问题的求解方法经过几十年的发展，形成了一系列的方法。虽

然文献中的优化方法很多，但可以将这些优化方法分成两大类：热力学方法和数

学规划法。数学规划法包括确定性方法和随机性方法。确定性方法以优化函数的

性质为基础，一步一步逐渐收敛于全局最优解，得到的结果可以从理论上证明为

全局最优解，但受到计算问题规模的限制，对于大规模的问题很难求解。随机性

方法基于概率统计理论，不依赖于所研究的问题函数的性质，对于大规模优化问

题的计算，较确定性方法的优势更为明显，该方法总能得到一个解，但该优化结

果不能证明是全局最优解，只是接近于最优解的解。

热力学方法是由 Linnhoff[9]等人首次建立，设定最小传热温差，在温焓图上将

冷、热流体分别表示成组合曲线，或通过问题表格法来确定窄点位置和最小公用

工程消耗量。窄点处无热量传递，将换热网络分成两个子系统。窄点的上方尽量

避免加入冷公用工程；窄点的下方尽量避免加入热公用工程。该方法以最大热量

回收为目的，没有考虑换热器投资费用及换热面积费用的投入得到的优化结果必

然是次优结果。虽然后来一些学者 Trividid[17]、Fraser 等[18]对热力学方法进行了发

展并做了一些改进，但始终没有解决热力学方法无法得到全局最优解的难题。在

国内，姚平经教授对窄点法也进行了发展，建立了三温差法设计、优化换热网络。

自1983 年Cerda[19]建立换热网络综合问题的数学模型，用优化目标函数及约

束条件来描述并求解换热网络综合问题以来，数学规划法在换热网络优化问题中

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摘要：

摘要随着工业化的推进，能源日益短缺。换热网络作为过程工业的一个重要组成部分，对整个系统能量的合理利用具有决定性的作用，对降低生产能耗及降低生产成本具有重要的意义。目前换热网络优化问题的研究工作绝大部分仍然采用局部最优化方法和随机性优化方法。随机性优化方法虽然对优化目标函数要求很低，容易得到优化结果，但该方法基于概率统计学原理和模拟某些自然现象或过程而形成的，得到的换热网络优化结果不能证明是最优解。局部最优化方法虽然发展的比较成熟，形成了一系列经典理论，对于单峰问题的求解，能够搜索到最优解，但应用于换热网络综合时，该方法对初始值的依赖性很强，由于其优化方法本身的局限，也不可能得到全局最优解。鉴于...

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