## 4 Energy Management Strategies
### Incorporation of the Optimization Algorithm to the Model  
In this study, the decisive control parameters of the EMS cases, \(\mu\) for the LPF, and \(\tau\) for the ECMS, were introduced into a genetic algorithm (GA) scripted in MATLAB, which is incorporated into the Simulink-based vehicle model. The widely used GA works are based on the evolutionary process concept of natural selection in [PERSON]'s theory. This theory proposes that only the fittest populations can produce offspring through natural selection and survival, while unsuitable populations will be eliminated. The same concept can be conducted into mathematical optimizations where during processes like crossover, mutation, and natural selection, the good design points can be selected while neglecting worse answers toward finding optimization solutions for objective functions (survival of the fittest) [59]. The desired constraints can be defined separately or be integrated into the objective functions as penalties [16]. In the present study, the optimization algorithm and the vehicle model worked iteratively in tandem to update each other for the optimization procedure. The GA considers the decision variables as input chromosomes aside from the defined minimum and maximum values of the constraints to minimize the fuel consumption and satisfy the EMS constraints as follows.  
\[\min(Fuel)=\min J=\min\int\limits_{0}^{t}\frac{\frac{\mu}{f}}{\rho_{f}}dt \tag{22}\]  
\[\big{|}SoC_{f}-SoC_{i}\big{|}<\varepsilon_{0} \tag{23}\]  
\[SoC_{\text{min}}-\varepsilon<SoC(t)<SoC_{\text{max}}+\varepsilon \tag{24}\]  
\[C\_Rate(t)\geq\beta \tag{25}\]  
Two sets of \(SoC\) constraints were considered here where the first one, based on Equation (23), represents the charge-maintenance requirement in HEVs. The second SoC constraint, based on Equation (24), expresses the allowable minimum and maximum limits of the SoC considered for the optimization through the driving cycle. Regarding the first mentioned inequality, the typical charge-maintaining equality \(SoC_{f}=SoC_{i}\) was used to define the inequality constraint (23). Hence, \(\Delta SoC\), as the difference between the initial and final \(SoC\) values would need to stay within a small enough feasible bound \(\varepsilon_{0}\) in the optimization process. It is remarkable that this constraint can be hardened/softened via altering \(\varepsilon_{0}\). Furthermore, to avoid sudden charges and to prevent fast aging of the battery pack, the EMS must consider the \(C\_Rate(t)\) limitation of the battery. In this regard,  
Figure 7: Simplified diagram of input and output states for ECMS.  
the \(C\_Rate(t)\) constraint, based on Equation (25), of the provided features of the battery chemistry was considered where \(\beta=-3\).  
For the explained constraints, they were incorporated into the optimization process as penalties penalizing the objective function by adding a big enough penalty value when a desired constraint is violated. This method is a practical method to consider the constraints that cannot directly be included in the optimization formulations. The interrelations of the described modeling and optimization process are illustrated in Figure 8.