The principal context of this study was a combined heat and power plant (CHPP) system, with the aim of conducting the multi-objective optimization (MOO) of an energy, exergy, and economic (3E) analysis. To meet rising energy demands, optimal operational conditions for CHPPs are required. Enhancements to plant equipment and improvements in plant design are critical. CHPP design has its basis in the first law of thermodynamics; the losses from such systems are therefore most accurately determined via exergy analysis. Energy quality can also be assessed using exergy analysis. Consequently, it is possible for the designers of thermodynamic systems to apply the findings to achieve improved efficiencies. The economic aspect of CHPP optimization is also critical because the structure is highly complex. This study therefore makes use of a Henry gas solubility optimization (HGSO) algorithm in a CHPP base case situation to achieve MOO. In this particular CHPP system, the respective enthalpy and exergy efficiencies were increased in the case of the boiler (7.22% and 7.21%), the turbogenerator (4.52% and 6.84%), and the condenser (3.06% and 31.37%). In this study, four scenarios are proposed, whereby the design of a heat exchanger network (HEN) aims to optimize energy savings and economic performance through analysis of the profits generated through electricity and steam production. A payback period of around two to three years was reported, where the cost increase under optimal conditions was found to be 0.3824%. The results demonstrate clearly that the tested techniques may be appropriate in practical scenarios when enhancing CHPP performance in the context of the base case.