The optimization of multi-energy systems (MESs) in which multiple energy carriers interact with each other is a complex problem. Their optimal operation and design can be determined through mathematical programming. A classical technology used in MESs is the combined heat and power units (CHP) whose efficiency is modeled through non-linear equations. These non-linear functions are approximated through piecewise linear ones by introducing binary decision variables, which generates a mixed-integer linear program (MILP). Consequently, optimizing such systems over a long time period with a high temporal resolution becomes infeasible in a reasonable amount of time. In this work, we propose a fast heuristic algorithm to optimize the design and operation of such an MES. Our case study is an MES at the scale of a district with five types of generation units, including a CHP, over a time period of one year with a temporal resolution of one hour. Comparison of the proposed heuristic and a state-of-the-art MILP solver over smaller time periods shows that the heuristic is up to 99.9 % faster, with a mean error of 2.3e-4 % compared to the optimal solution. The heuristic can also solve the optimal design and operation problem over a year in about 10 minutes.