Computers and Chemical Engineering 33 (2009) 1451–1459 Contents lists available at ScienceDirect Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng Heat exchanger networks retrofit by coupling genetic algorithm with NLP and ILP methods Ebrahim Rezaei ∗ , Sirous Shafiei Faculty of Chemical Engineering, Sahand University of Technology, PO Box 51335/1996, Tabriz, Iran article info Article history: Received 6 March 2008 Received in revised form 26 August 2008 Accepted 30 March 2009 Available online 7 April 2009 Keywords: Heat exchanger networks (HENs) Retrofit Genetic algorithm (GA) Nonlinear programming (NLP) Integer linear programming (ILP) abstract This paper addresses the revamping of heat exchanger networks (HENs) using genetic algorithm (GA) coupled with nonlinear programming (NLP) and integer linear programming (ILP) methods. Structural modifications are carried out by the GA in which node representation is used for the addressing of exchanger locations. Continuous variables are handled using a modified NLP formulation for maximum energy recovery (MER). Simultaneous optimization of the NLP is replaced by a search loop to find the best minimum approach temperature and split ratios. In this way the NLP is converted to an LP procedure which is easier to solve. After each LP, an ILP problem is solved to determine the minimum investment cost of modifications. The ILP determines the elimination or reuse of current exchangers and/or introduc- ing new ones to the network. Results show that the proposed method usually finds better solutions than those reported in the literature. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction In recent years the revamping of existing heat exchanger net- works (HENs) has become more important as energy costs continue to increase. Retrofit projects have attracted significant research due to the large savings that can be achieved in utility costs especially after the 1990s. The major objectives of retrofit problems are the reduction of the utility consumption, the full utilization of the existing exchangers and identification of the required structural modifications. Retrofit methods can be grouped into three broad categories which are thermodynamic based approaches, mathematical pro- gramming methods and approaches combining both. The first approach was proposed by Tjoe and Linnhoff (1986, 1987) in which two steps were considered for HENs retrofit. Retrofit targeting is determined in the first step and modifications are carried out next. The drawback of this method is that there is no general rule for area distribution within a network in the design step. So applica- tion of pinch approaches depends on the designer experience and becomes difficult particularly in large networks. Mathematical programming methods were started with Ciric and Floudas (1990) and Yee and Grossmann (1991). Ciric and Floudas (1990) first, determined the energy target of the net- work and then proposed a mixed integer nonlinear programming (MINLP) model for the retrofit of HENs. This model incorporates ∗ Corresponding author. Tel.: +98 412 3444356; fax: +98 412 3444355. E-mail addresses: e rezaei24@yahoo.com (E. Rezaei), shafiei@sut.ac.ir (S. Shafiei). all possible process stream matches, network configurations and existing exchanger reassignment in a single mathematical formu- lation. It was also shown that how heat exchanger rating equations, repiping costs, pressure drop aspects and varying heat transfer coef- ficients could be included in the formulation. Predetermination of the utility consumption causes failure in area-utility tradeoff and solutions may be trapped at local optima. Yee and Grossmann (1991) developed a two-step approach in which the first step was a mixed integer linear programming (MILP) prescreening for determination of the economic feasibility of the retrofit project. In addition, the number of new units that might be required in the final network was decided in this step. An MINLP formulation was then applied to find the optimized network. Because the MINLP model is very detailed, different types of binary variables are needed in their formulation. This issue may restrict the application of the model to small scale problems. Ma, Hui, and Yee (2000) proposed a two-step approach where constant approach temperature model (CAT) was used in the first step to optimize the structure of the final HEN. The CAT model is an MILP problem since the same approach temperature is assumed for all heat exchangers. CAT model is solved first and an MINLP model is then used which takes into account the actual approach temperatures in the final HEN design. Asante and Zhu (1996, 1997) and Zhu and Asante (1999) combined pinch technology and mathematical programming to simplify the retrofit procedure by a thermodynamic concept called network pinch. In their method, sequential MILPs are solved until a desired energy recovery is obtained. After finding the final struc- ture, a nonlinear programming (NLP) model is solved to minimize 0098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2009.03.009