换热网络非线性特性及其全局最优化研究
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摘要
换热网络是能源、石化等工业领域中的一个重要环节，良好的换热网络综合性能对于节省能源、增加经济效益有着至关重要的作用。因此，寻找性能优良的换热网络结构成为相关工作者的共同目标，换热网络的优化设计受到国内外学者越来越多的重视。换热网络优化设计本质上属于混合整数非线性规划问题，随着换热网络规模的不断扩大，其非线性特性表现得越来越严重，局部最优解以阶乘级别增长，在这种情况下如何有效地跳出局部最优解，实现换热网络的全局最优化就成了各国学者的工作焦点。鉴于此，本文通过对换热网络非线性特性的分析，提出和改进了多种换热网络优化方法，对换热网络的全局最优化进行了深入的探讨。
论文首先对换热网络优化问题的非线性特性进行了深入分析，阐述了包括换热网络优化过程在内的混合整数非线性规划（MINLP）问题在求解过程中的难度。以换热网络的具体实例论证了换热网络MINLP问题中的非线性特性，通过某一特例的非线性的性能图谱来阐述二维变量，三维变量以及整型变量对换热网络非线性特性的影响，指出了顺序优化方法应用在这种优化问题上存在着陷入局部最优解的弊端。同时由于不同的优化顺序会导致最终优化结果的差异，本文通过对传统换热网络优化顺序改变，避免了换热网络优化过程中过早陷入局部最优解的问题，使优化质量得到一定程度的提高。
在此基础上，从如何跳出局部最优解及如何改进换热网络优化质量的角度出发，提出了三种改进的换热网络优化方法——回路面积断开/合并的优化方法、改进的多起点方法以及次级超结构的换热网络模型，这些方法都在一定程度上能够避免换热网络优化过程陷入局部最优解，可以有效地打破热平衡，使其跳出局部最优解而继续优化进程。
随后，首次将填充函数算法应用到换热网络的全局优化中，应用填充函数克服局部最优解的陷阱，使得在换热网络优化过程中，能够依靠填充函数和局部优化方法的交替操作跳出局部最优解，从而找到区域内的全局最优解。
继之，首次提出了一种函数逼近割平面全局最优化方法，并将其应用到换热网络全局优化中。通过在一维和二维非线性问题上给出的求解步骤示例，阐述了该方法应用于全局最优化的总体策略。针对切割平面的区域界定这一困难问题的反问题，运用一维搜索的方法确定区域边界的上、下界，并采用函数逼近的方法，通过反复地等平面切割，使得换热网络总年费用的性能函数所对应的可行域不断缩小，直到找到全局最优解。
最后将确定性方法和启发式方法有效地结合起来，应用到换热网络的全局优化上。由随机性方法产生初始结构，由确定性方法对初始结构的连续变量进行优化得到最优解，这样不但提高了搜索效率，同时也能相对地提高求解精度。
总之，论文针对换热网络全局优化过程中的容易陷入局部最优解的难点，对其进行了深入的研究，并提出了多种方法来克服这些困难，为换热网络的全局优化研究提供了解决的思路和方法。
The perfect overall performances of heat exchanger networks (HENs) have crucialimpact on energy conservation and economic benefit in the energy, petroleum andchemical field. Therefore, desiging a HEN with excellent performance is the commongoals for all of the workers in this studing field, more and more attention is paid tooptimization design of HENs. The global optimization of HENs is a Mixed-IntegerNonlinear Programming problem(MINLP) in nature, With the development of networksscale, the nonlinear characteristics become more and more serious for HENsoptimization and the local optimal solutions will increase in the form of factorial. Forachieving global optimization, it should be important to escape from the local optimalsolution effectively. By analysing the nonlinear characteristics of HENs, this articalproposed and improved several HENs optimization methods for further investigatingthe global optimization problems.
Firstly, the nonlinear characteristics of HENs was in-depth analysis, and explainingthe difficuly in the sloving process of mixed-integer nonlinear programming (MINLP),including the global optimization of HENs. Base on a specific HEN example, thenonlinear characteristics and the influence of continous variable and integar variable onHENs performance were investigated with performance atlas., it shows that it would beeasily prone to fall into a local optimal solution with sequence optimizing methods. Fordifferent optimizing sequence generates different results, this paper avoided theproblems of local optimal solutions by changing the optimizing sequence and thenimproved the optimization quality.
Furthermore, for escaping from a local optimal solution and improving theoptimization quality, this paper proposed three improved optimizing methods: heat loadloop breaking and merging method, improved multi-start method and secondarysuperstructure model. These methods could avoid the problems of optimal solutions andcontinue further optimization by breaking thermal equilibrium effectively.
Subsquently, for overcoming trapping in the local optimal solutions, filled functionalgorithm was then introduced into HENs global optimization. With filled function andlocal optimizing methods alternately, the global optimal solution in solving domaincould be obtained by escaping from the local optimal solutions.
Afterwards, the function approximation and cutting plane method for the global optimizing of HENs was presented. The typical example of the solving steps based onone-dimensional and two-dimensional nonlinear problems shows the general strategyapplying to the global optimization of HENs. To the inverse problem of confirming thesolving area boundary using cutting plane method, one-dimensional searching methodwas applied to determine the upper and lower bound of solving area boundary. Bycutting the plane repeatedly, the feasible region of performance function would shrinkcontinuously until the global optimal solution was obtained.
Finally, the effectively combination of deterministic methods and randomizationmethods was applied to the global optimization of HENs. The initial structure generatedby randomization methods would be further optimized by deterministic methods, whichcould both improve the search efficiency and the solving precision relatively.
In a word, for achieving HENs global optimization, the difficulty of easily trappingin optimal solutions in optimizing process was studied and sevel methods wereproposed corresponding to the existing problems
论文首先对换热网络优化问题的非线性特性进行了深入分析，阐述了包括换热网络优化过程在内的混合整数非线性规划（MINLP）问题在求解过程中的难度。以换热网络的具体实例论证了换热网络MINLP问题中的非线性特性，通过某一特例的非线性的性能图谱来阐述二维变量，三维变量以及整型变量对换热网络非线性特性的影响，指出了顺序优化方法应用在这种优化问题上存在着陷入局部最优解的弊端。同时由于不同的优化顺序会导致最终优化结果的差异，本文通过对传统换热网络优化顺序改变，避免了换热网络优化过程中过早陷入局部最优解的问题，使优化质量得到一定程度的提高。
在此基础上，从如何跳出局部最优解及如何改进换热网络优化质量的角度出发，提出了三种改进的换热网络优化方法——回路面积断开/合并的优化方法、改进的多起点方法以及次级超结构的换热网络模型，这些方法都在一定程度上能够避免换热网络优化过程陷入局部最优解，可以有效地打破热平衡，使其跳出局部最优解而继续优化进程。
随后，首次将填充函数算法应用到换热网络的全局优化中，应用填充函数克服局部最优解的陷阱，使得在换热网络优化过程中，能够依靠填充函数和局部优化方法的交替操作跳出局部最优解，从而找到区域内的全局最优解。
继之，首次提出了一种函数逼近割平面全局最优化方法，并将其应用到换热网络全局优化中。通过在一维和二维非线性问题上给出的求解步骤示例，阐述了该方法应用于全局最优化的总体策略。针对切割平面的区域界定这一困难问题的反问题，运用一维搜索的方法确定区域边界的上、下界，并采用函数逼近的方法，通过反复地等平面切割，使得换热网络总年费用的性能函数所对应的可行域不断缩小，直到找到全局最优解。
最后将确定性方法和启发式方法有效地结合起来，应用到换热网络的全局优化上。由随机性方法产生初始结构，由确定性方法对初始结构的连续变量进行优化得到最优解，这样不但提高了搜索效率，同时也能相对地提高求解精度。
总之，论文针对换热网络全局优化过程中的容易陷入局部最优解的难点，对其进行了深入的研究，并提出了多种方法来克服这些困难，为换热网络的全局优化研究提供了解决的思路和方法。
The perfect overall performances of heat exchanger networks (HENs) have crucialimpact on energy conservation and economic benefit in the energy, petroleum andchemical field. Therefore, desiging a HEN with excellent performance is the commongoals for all of the workers in this studing field, more and more attention is paid tooptimization design of HENs. The global optimization of HENs is a Mixed-IntegerNonlinear Programming problem(MINLP) in nature, With the development of networksscale, the nonlinear characteristics become more and more serious for HENsoptimization and the local optimal solutions will increase in the form of factorial. Forachieving global optimization, it should be important to escape from the local optimalsolution effectively. By analysing the nonlinear characteristics of HENs, this articalproposed and improved several HENs optimization methods for further investigatingthe global optimization problems.
Firstly, the nonlinear characteristics of HENs was in-depth analysis, and explainingthe difficuly in the sloving process of mixed-integer nonlinear programming (MINLP),including the global optimization of HENs. Base on a specific HEN example, thenonlinear characteristics and the influence of continous variable and integar variable onHENs performance were investigated with performance atlas., it shows that it would beeasily prone to fall into a local optimal solution with sequence optimizing methods. Fordifferent optimizing sequence generates different results, this paper avoided theproblems of local optimal solutions by changing the optimizing sequence and thenimproved the optimization quality.
Furthermore, for escaping from a local optimal solution and improving theoptimization quality, this paper proposed three improved optimizing methods: heat loadloop breaking and merging method, improved multi-start method and secondarysuperstructure model. These methods could avoid the problems of optimal solutions andcontinue further optimization by breaking thermal equilibrium effectively.
Subsquently, for overcoming trapping in the local optimal solutions, filled functionalgorithm was then introduced into HENs global optimization. With filled function andlocal optimizing methods alternately, the global optimal solution in solving domaincould be obtained by escaping from the local optimal solutions.
Afterwards, the function approximation and cutting plane method for the global optimizing of HENs was presented. The typical example of the solving steps based onone-dimensional and two-dimensional nonlinear problems shows the general strategyapplying to the global optimization of HENs. To the inverse problem of confirming thesolving area boundary using cutting plane method, one-dimensional searching methodwas applied to determine the upper and lower bound of solving area boundary. Bycutting the plane repeatedly, the feasible region of performance function would shrinkcontinuously until the global optimal solution was obtained.
Finally, the effectively combination of deterministic methods and randomizationmethods was applied to the global optimization of HENs. The initial structure generatedby randomization methods would be further optimized by deterministic methods, whichcould both improve the search efficiency and the solving precision relatively.
In a word, for achieving HENs global optimization, the difficulty of easily trappingin optimal solutions in optimizing process was studied and sevel methods wereproposed corresponding to the existing problems
引文
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