**1. Introduction**

The application of heat integration strategies can have a significant impact on reducing the amount of utility used by a process and thus improve its economic performance. Against the background of increasing global competition, environmental specifications, climate change and assumedly increasing energy costs heat integration using heat exchanger networks (HENs) have a significant importance [1].

Heat integration strategies have been developed to reduce both, capital and operating costs since decades by now. Pinch technology [2] and mathematical programming [3] have been the two main approaches and have been improved numerous times by many researchers [4]. Not only single processes but also total site heat integration has been considered. Initial works have been carried out by Dhole and Linnhoff [5]. Due to new challenges, in recent years publications have covered relevant practical issues in a higher degree of detail. As a consequence the problem complexity increased. The main issues influencing practical implementation of total site integration have been formulated by Chew et al. [6]. The consideration of further impact factors like safety related issues has been a major topic in heat integration during the last years [1]. The identification of critical risk equipment and respective streams for total site heat integration was developed by Liu et al. [7]. Nemet et al. [8,9] developed approaches for including risk assessment already during the HEN synthesis. Multiperiod HEN synthesis as well as controllability and disturbance propagation have been studied [10–12]. Due to operational issues and safety concerns direct heat integration is not always practical to realize [13,14]. Therefore, Wang et al. [14] developed a graphical methodology to investigate different connection patterns for total site heat integration. This methodology was developed further by applying mathematical models to determine the optimal solution for multi-plant heat integration [15]. Multi-plant heat integration has been further considered by Chang et al. [13,16]. The consideration of plant layout issues is an important factor during optimization. Liew et al. [17] introduced an improved heat cascade algorithm considering pressure drop and heat loss for utility targeting in total site heat integration. Pouransari and Maréchal [18] took into account individual priority levels for different possible connections and Souza et al. [19] included pressure drops in piping as well as in heat exchangers.

The review given above shows that the various demands on HEN optimization in the literature are manifold and a huge variety of optimization models are used. In this work our aim is to incorporate a flexible consideration of cost functions into the cost-optimal HEN synthesis to account for various fields of application. The most important part is the definition of individual factors for each possible connection of heat source and sink. Therefore it is possible to represent a multitude of practical implementation requirements with the same mixed integer nonlinear programming (MINLP) model. For example, it is possible to consider individual cost functions for different types of heat exchangers required for different operation conditions and properties of the involved process streams. Depending on the properties of the process streams the material and thus the costs of the installed heat exchanger can vary significantly. Peripheral equipment, layout constraints as well as cost of premises can be taken into account. These cost functions can be directly incorporated without changing the model or the solution algorithm itself. Concerning the algorithm performance it is the clear aim to be able to generate valid network structures that are competitive to the best solutions published in literature by now. Therefore, different approaches are combined. This model was primarily developed for direct heat integration [1], but is also shown to be applicable for the cost optimization of indirect heat integration problems.
