The aim of this paper is to conduct retrofit analysis of large, complex industrial Heat Exchanger Networks using an automated Bridge Analysis. Large, complex networks have many different possible retrofit designs, or Retrofit Bridges, which requires both computational effort and user effort to evaluate. In this paper, constraints relating to the thermodynamic and economic performance of a retrofit design are proposed and applied to significantly reduce Retrofit Bridge options to a smaller, manageable number of design options. These constraints relate to capital costs, payback period, piping, and plant layout. The method is demonstrated with a Kraft pulp mill case study. The Kraft pulp mill currently has 54 heat exchangers and 73 hot and cold streams. Without constraints, the number of possible Retrofit Bridges is 1 x 1020. After applying the constraints, this number is reduced to 15. The remaining Retrofit Bridges are considered to provide high thermodynamic and economic benefit and can be more easily assessed for the best projects. The use of constraints has allowed the complex case study to be solved quickly, and a single design can be selected for further development. The suggested design reduces the utility consumption by 9.2 MW and has an annual Total Retrofit Profit of NZD 2,140,000, requiring a single new exchanger.