In this work, the enumeration algorithms presented in Parts I and II for the globally optimal synthesis of minimal and non-minimal heat exchanger networks are extended to consider non-isothermal mixing. New mathematical models, including non-isothermal mixing constraints, are proposed to target the bounds of energy consumption and the binding exchanger minimum approximation temperature. These models are solved using the algorithms, which involve solving systems of equations instead of mathematical programming. Three global optimization strategies are proposed to optimize each enumerated structure, involving the use of a global solver directly, or the use of a Golden Search based on energy consumption and a flowrate optimization model considering non-isothermal mixing. The flowrate optimization model is reformulated as a convex problem, which is solved by using nonlinear programming or a mathematical programming-free methodology, that is, solving Karush–Kuhn–Tucker equations. A new Global Optimum Search Algorithm is developed and examples are tested comparing different optimization strategies.

中文翻译：

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换热器网络的全局优化合成。第三部分：最小和非最小网络中的非等温混合

在这项工作中，第 I 部分和第 II 部分中介绍的用于最小和非最小换热器网络全局优化合成的枚举算法被扩展到考虑非等温混合。提出了新的数学模型，包括非等温混合约束，以针对能量消耗的界限和结合交换器的最小近似温度。这些模型是使用算法求解的，这些算法涉及求解方程组而不是数学规划。提出了三种全局优化策略来优化每个枚举结构，包括直接使用全局求解器，或使用基于能量消耗的黄金搜索和考虑非等温混合的流量优化模型。流量优化模型被重新表述为一个凸问题，这是通过使用非线性规划或无数学规划的方法来求解的，即求解 Karush-Kuhn-Tucker 方程。开发了一种新的全局最优搜索算法，并测试了比较不同优化策略的示例。