## 6 Results and Discussion
### Multi-Objective Optimization Results  
In order to optimize the performance of the combined cycle systems shown in Figures 1-3, the following parameters are selected as design parameters: compressor pressure ratio, gas turbine inlet temperature, compressor isentropic efficiency, gas turbine isentropic efficiency, regenerator efficiency, steam generator pinch point temperature difference and condenser pressure. In addition, exergy efficiency, overall cost rate and exergy unit cost of generated electricity are considered as objective functions:  
\[Maximize\ \eta_{ex}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{38}\]  
\[Minimize\ \dot{C}_{tot}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{39}\]  
\[Minimize\ \dot{c}_{el,tot}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{40}\]  
Furthermore, due to the existing temperature limitations, the design parameters investigated vary within the following ranges:  
\[10<P_{r,comp}<19 \tag{41}\]  
\[1180(^{\circ}\mathrm{C})<GTTT(Config.1)<1250(^{\circ}\mathrm{C}) \tag{42}\]  
\[1100(^{\circ}\mathrm{C})<GTTT(Config.2,3)<1250(^{\circ}\mathrm{C}) \tag{43}\]  
\[0.8<\eta_{gt}<0.88 \tag{44}\]  
\[0.78<\eta_{comp}<0.88 \tag{45}\]  
\[0.55<\epsilon_{reg}(Config.2)<0.88 \tag{46}\]  
\[0.55<\epsilon_{reg}(Config.3)<0.7 \tag{47}\]  
\[Minimize\ \dot{C}_{tot}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{39}\]0  
\[Minimize\ \dot{C}_{tot}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{39}\]1  
The Pareto approach to multi-objective optimization is the key concept to establish optimal set of design variables, since the concepts of Pareto dominance and optimality are straightforward tools for determining the best trade-off solutions among conflicting objectives [32; 33; 34]. Pareto optimum solutions using a multi-objective genetic algorithm [30; 32] for the combined simple Brayton and Rankine cycle (config. 1), combined regenerative Brayton and Rankine cycle (config. 2) and new combined regenerative Brayton and Rankine cycle (config. 3) presented in Figures 14-16, respectively. In the multi-objective optimization, a process of decision making for the selection of the final optimal results from the available solutions is required. In selection of the final optimum point, it is desired to achieve the better magnitude for each objective than its initial value of the problem. The related values of design variables in the optimum case are given in \[Minimize\ \dot{C}_{tot}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{39}\]2 The output values and objective functions of three configurations shown in Figures 1-3 including the exergy unit cost of electricity, the total cost rate and exergy efficiency in the optimum cases are listed in \[Minimize\ \dot{C}_{tot}\big{(}P_{r,comp},GTT,\ \eta_{gt},\eta_{comp},\ \epsilon_{rg},\ \Delta T_{PP,gg},\ P_{cond}\big{)} \tag{39}\]3 As can be seen from this table, the trend of the overall values is in accordance with the base case such as the largest amount of total output power and exergy efficiency belongs to the first configuration which results in the highest overall cost rate for this configuration. On the other hand, the lowest overall amount of power, exergy efficiency and overall cost rate belongs to the third configuration. Further, the lowest exergy unit cost of electricity produced is obtained by the second configuration. On the other hand, in all three configurations studied, the overall exergoeconomic factor is below 20%, indicating that the rate of exergy destruction cost dominates over the initial cost rate.