Heat exchanger network synthesis (HENS) is still a challenging task for minimizing the Total Annual Cost (TAC). In this work, a Cuckoo Search Algorithm (CSA) is introduced to solve the NonLinear Programming (NLP) problem of the fixed heat exchanger network design to determine the optimal heat load distribution, which can help improve the heat load configurations of previously found optimum configurations. The improved CSA (ICSA) is used to solve the Mixed Integer NonLinear Programming (MINLP) problem for optimal HENS, which can simultaneously optimize continuous and integer variables, and the proposed stream arrangement strategy aims to optimize the stream match search space by lowering the stage demands, i.e. reducing the number of independent variables, which is a promising means for an easier solution of large and medium sized HENS problems. Four large and medium sized benchmark cases have been investigated, obtaining no-splits results with lower TAC in a shorter computational time. In addition, a special feature from case 3 and 4 is analyzed, which is useful in order to achieve a lower TAC by using modified Stage-Wise Superstructure (SWS) models with flexible utility placement. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.