# Control Strategy Optimization for Parallel Hybrid Electric Vehicles Using a Memetic Algorithm

^{1}

^{2}

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## Abstract

**:**

_{x}) of the vehicle engine. At the same time, driving performance requirements are also considered in the method. Four different driving cycles, the new European driving cycle (NEDC), Federal Test Procedure (FTP), Economic Commission for Europe + Extra-Urban driving cycle (ECE + EUDC), and urban dynamometer driving schedule (UDDS) are carried out using the proposed method to find their respectively optimal control parameters. The results show that the proposed method effectively helps to reduce fuel consumption and emissions, as well as guarantee vehicle performance.

## 1. Introduction

## 2. Configurations of HEVs

#### 2.1. Series HEV

#### 2.2. Parallel HEV

#### 2.3. Dual-Mode HEV

## 3. Control Strategy for Parallel HEV

- (1)
- When the battery state of charge (SOC) is more than SOC
_{L}, the engine will be shut down if the required speed is less than the ELS, which is also called the electric launch speed (as shown in Figure 3, Case 1). - (2)
- When the required torque is less than a minimum torque threshold (T
_{off}× T_{max}), the engine will also be shut down (as shown in Figure 3, Case 2). - (3)
- (4)
- When the battery SOC is less than its SOC
_{L}, an alternator-like torque (T_{ch}) is provided from the engine to charge the battery (as shown in Figure 4, Case 2). This alternator-like charging torque is proportional to the difference between the SOC and the average of the SOC_{L}and SOC_{H}. - (5)
- The engine charging torque is only applied when the engine is started up (as shown in Figure 4, Case 2).
- (6)
- To avoid the engine working at an inefficient low torque status, the engine torque must be maintained at the minimum torque threshold (T
_{min}× T_{max}) (as shown in Figure 4, Case 3).

## 4. Definition of Objective Function

_{x}) while meeting the charge sustaining requirement and driving performance. We thus define FC, HC, CO, and NO

_{x}as a single objective function that is a weighted aggregation as shown in Equation (1):

_{fc}, w

_{hc}, w

_{co}, and w

_{nox}are defined as weighting factors employed to respectively investigate the influences of the different objectives of FC, HC, CO, and NO

_{x}on the optimization results.

## 5. The Design of MA for Optimized Control Strategy of Parallel HEVs

Local Search Pseudo-Code for the Proposed Method |

1 Begin; |

2 Select an incremental value d = a × Rand (); |

3 For a given individual i∈Population: calculate fitness (i); |

4 For j = 1 to the number of variables in individual i; |

5 value (j) = value (j) + d; |

6 calculate fitness (i); |

7 If fitness of the individual is not improved then |

8 value (j) = value (j) − d; |

9 else if fitness of the individual is improved then |

10 retain value (j); |

11 Next j; |

12 End; |

- Acceleration time 1$${p}_{1}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}1\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}1\\ \mathrm{acceleration}\text{}\mathrm{time}\text{}1-\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}1,\text{}\mathrm{if}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}1\text{}\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}1\end{array}$$
- Acceleration time 2$${p}_{2}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}2\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}2\\ \mathrm{acceleration}\text{}\mathrm{time}\text{}2-\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}2,\text{}\mathrm{if}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}2\text{}\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}2\end{array}$$
- Acceleration time 3$${p}_{3}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}3\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}3\\ \mathrm{acceleration}\text{}\mathrm{time}\text{}3-\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}3,\text{}\mathrm{if}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}3\text{}\mathrm{PNGV}\text{}\mathrm{acceleration}\text{}\mathrm{time}\text{}3\end{array}$$
- Maximum speed$${p}_{4}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{max}\text{}\mathrm{speed}\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{PNGV}\text{}\mathrm{max}\text{}\mathrm{speed}\text{}\\ \mathrm{PNGV}\text{}\mathrm{max}\text{}\mathrm{speed}-\mathrm{max}\text{}\mathrm{speed},\text{}\mathrm{if}\text{}\mathrm{max}\text{}\mathrm{speed}\text{}\text{}\mathrm{PNGV}\text{}\mathrm{max}\text{}\mathrm{speed}\end{array}$$
- Maximum acceleration$${p}_{5}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{max}\text{}\mathrm{acceleration}\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{PNGV}\text{}\mathrm{max}\text{}\mathrm{acceleration}\\ \mathrm{PNGV}\text{}\mathrm{max}\text{}\mathrm{acceleration}-\mathrm{max}\text{}\mathrm{acceleration},\text{}\mathrm{if}\text{}\mathrm{max}\text{}\mathrm{acceleration}\text{}\text{}\mathrm{PNGV}\text{}\mathrm{max}\text{}\mathrm{acceleration}\end{array}$$
- Distance in 5 s$${p}_{6}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{distance}\text{}\mathrm{in}\text{}5\text{}\mathrm{s}\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{distance}\text{}\mathrm{in}\text{}5\text{}\mathrm{s}\\ \mathrm{PNGV}\text{}\mathrm{distance}\text{}\mathrm{in}\text{}5\text{}\mathrm{s}-\mathrm{distance}\text{}\mathrm{in}\text{}5\text{}\mathrm{s},\text{}\mathrm{if}\text{}\mathrm{distance}\text{}\mathrm{in}\text{}5\text{}\mathrm{s}\text{}\text{}\mathrm{PNGV}\text{}\mathrm{distance}\text{}\mathrm{in}\text{}5\text{}\mathrm{s}\end{array}$$
- Gradeability$${p}_{7}\left(x\right)=\{\begin{array}{c}0,\text{}\mathrm{if}\text{}\mathrm{grade}\text{}\mathrm{satisfied}\text{}\mathrm{the}\text{}\mathrm{PNGV}\text{}\mathrm{grrade}\\ \mathrm{PNGV}\text{}\mathrm{grade}-\mathrm{grade},\text{}\mathrm{if}\text{}\mathrm{grade}\text{}\text{}\mathrm{PNGV}\text{}\mathrm{grade}\end{array}$$

_{x}), and driving performance for the used control strategy in parallel HEVs, we have combined the ADVISOR with the proposed MA to evaluate the fitness in chromosomes. When the fitness function is called, the control strategy variables will be passed on to the ADVISOR to calculate the FC, emissions (HC, CO, and NO

_{x}), and driving performance and return their values. These values will then be used to evaluate the fitness of the control strategy.

## 6. Driving Cycles for Optimized Control Strategy of Parallel HEVs

## 7. Results

#### 7.1. Parameter Settings

#### 7.2. Results for the Used Driving Cycles

_{x}emissions. Furthermore, the dynamic performance not only simultaneously meets the PNGV constraints but also exceeds its requirements. From the above results, the ability of the proposed MA method to optimize the control parameters in parallel HEVs is confirmed. The results used in this study are freely accessible and provided online for those interested [50].

#### 7.3. Analysis of the Results

#### 7.3.1. Improvement in Overall Effectiveness

#### 7.3.2. Improvement in FC and Emissions

_{x}) as shown in Table 8 and Figure 8, we observe that the FC is improved for the driving cycles of the NEDC and FTP. The FC is improved by 0.72, 5.49, −0.36, and −0.05 mi/gal for the NEDC, FTP, ECE + EUDC, and UDDS, respectively.

_{x}emission is improved for the driving cycles of the NEDC and ECE + EUDC. The NO

_{x}emission is reduced by 0.16, −0.15, 0.15, and −0.03 g/mi for the NEDC, FTP, ECE + EUDC, and UDDS, respectively. The improvement results for the FC and emissions are shown in Figure 11. Although some values of the parameters are not greatly improved, their improved values are reflected in the other parameters or the following resultant dynamic performance.

#### 7.3.3. Improvement in Dynamic Performance

^{2}, the distance traveled in 5 s is increased by 0.005 mi, and the gradeability is maintained at 6.5%. For the FTP, the acceleration time is reduced by 3.12, 1.94, and 8.56 s for 0–60 mph, 40–60 mph, and 0–85 mph, respectively. The maximum speed is increased by 0.002 mi/s, the maximum acceleration is maintained at the original value of 0.003 mi/s

^{2}, the distance traveled in 5 s is increased by 0.003 mi, and the gradeability increased from 0% to 6.5%. For the ECE + EUDC, the acceleration time is reduced by 3.79, 2.35, and 10.31 s for 0–60 mph, 40–60 mph, and 0–85 mph, respectively. The maximum speed is increased by 0.003 mi/s, the maximum acceleration is maintained at its original value of 0.003 mi/s

^{2}, the distance traveled in 5 s is increased by 0.004 mi, and the gradeability is maintained at the original value of 6.5%. Finally, for the UDDS, the acceleration time is reduced by 5.61, 3.27, and 15.08 s for 0–60 mph, 40–60 mph, and 0–85 mph, respectively. The maximum speed is increased in 0.003 mi/s, the maximum acceleration is maintained at its original value of 0.003 mi/s

^{2}, the distance traveled in 5 s is increased by 0.006 mi, and the gradeability improves from 0% to 6.5%. There improvements in the dynamic performance are shown in Figure 12.

## 8. Conclusions

_{x}) of the vehicle engine based on the EACS. Furthermore, we consider that the driving performance requirements, which are referred to as the PNGV constraints, must be satisfied simultaneously. In order to verify the proposed method, we have employed four different driving cycles—NEDC, FTP, ECE + EUDC, and UDDS; the results for these driving cycles are verified. The fitness values of the optimal results are 0.011, 0.013, 0.008, and 0.012, which are better than those of the initial conditions in the driving cycles of the NEDC, FTP, ECE + EUDC, and UDDS, respectively. For the FC and emissions (HC, CO, and NO

_{x}), the FC is improved by 0.72 and 5.49 mi/gal for the NEDC and FTP, respectively. The HC emission is reduced by 0.10, 0.03, and 0.02 g/mi for the NEDC, FTP, and ECE + EUDC, respectively. The CO emission is substantially reduced by 5.12, 7.62, 0.16, and 1.92 g/mi for the NEDC, FTP, ECE + EUDC, and UDDS, respectively. The NO

_{x}emission is a reduced by 0.16 and 0.15 g/mi for the NEDC and ECE + EUDC, respectively. With regard to the dynamic performance, all the optimal values of the control strategy satisfy the seven PNGV dynamic performance constraints. The acceleration time is reduced by 4.98, 2.96, and 13.29 s for 0–60 mph, 40–60 mph, and 0–85 mph, respectively; the maximum speed is increased by 0.003 mi/s; and the distance traveled in 5 s is increased by 0.005 mi for the NEDC. The acceleration time is respectively reduced in 3.12, 1.94, and 8.56 s for 0–60 mph, 40–60 mph, and 0–85 mph; the maximum speed is increased in 0.002 mi/s; the distance traveled in 5 s is increased in 0.003 mi for the FTP. The acceleration time is reduced by 3.79, 2.35, and 10.31 s for 0–60 mph, 40–60 mph, and 0–85 mph, respectively; the maximum speed is increased by 0.003 mi/s; and the distance traveled in 5 s is increased by 0.004 mi for the ECE + EUDC. The acceleration time is reduced by 5.61, 3.27, and 15.08 s for 0–60 mph, 40–60 mph, and 0–85 mph, respectively; the maximum speed is increased by 0.003 mi/s; and the distance traveled in 5 s is increased by 0.006 mi for the UDDS. Furthermore, the maximum acceleration is maintained at 0.003 mi/s

^{2}and the gradeability reached a value of 6.5% in all the considered driving cycles. The results indicate that the proposed MA method is capable of determining the optimal parameters of the control strategy for parallel HEVs. It helps to improve the fuel consumption and reduce the emissions, as well as guarantee vehicle performance.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviation

Acronym | Term | Description |

ADVISOR | advanced vehicle simulator | A simulator for vehicles uses MATLAB/Simulink. |

BA | bees algorithm | An evolutionary computation method that based on bees foraging. |

BCS | baseline control strategy | A point of reference for control strategy in vehicles. |

CO | carbon monoxide | The exhaust gas from vehicles. |

DP | dynamic programming | An algorithmic method that applies solutions to larger and larger cases to inductively solve a computational problem for a given instance. |

EACS | electric assist control strategy | A rule-based strategy for power distribution between power sources. |

ECE + EUDC | Economic Commission for Europe + Extra-Urban Driving Cycle | A driving cycle. |

EM | electric motor | An electric motor is a machine that converts electrical energy into mechanical energy. |

FTP | Federal Test Procedure | A driving cycle is used for regulatory emission testing of heavy-duty on-road engines in the United States. |

GA | genetic algorithm | An evolutionary computation method inspired by the mechanisms of genetics. |

HC | hydrocarbons | The exhaust gas from vehicles. |

HEV | hybrid electric vehicle | HEVs have both a petrol- or diesel-powered combustion engine and an electric engine. |

ICE | internal combustion engine | An engine of one or more working cylinders in which the process of combustion takes place within the cylinders. |

MA | memetic algorithm | An evolutionary computation method inspired by Dawkins’ notion of a meme. MA is similar to GA yet superior to GA. The mechanism of local search is one of its main features. |

NEDC | new European driving cycle | A driving cycle eliminates the idling period that makes engine starts at 0s and the emission sampling begins at the same time as the entire cycle. |

NO_{x} | nitrogen oxides | The exhaust gas from vehicles. |

PMP | Pontryagin’s minimum principle | The principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. |

PNGV | Partnership for a New Generation of Vehicles | A cooperative research program between the U.S. government and major auto corporations, aimed at bringing extremely fuel-efficient (up to 80 mpg) vehicles to market by 2003. |

PSO | particle swarm optimization | An evolutionary computation method based on swarm behavior of animals, like bird flocking. |

SOC | state of charge | The equivalent of a fuel gauge for the battery pack in a battery electric vehicle (BEV), hybrid vehicle (HV), or plug-in hybrid electric vehicle (PHEV). |

UDDS | Urban Dynamometer Driving Schedule | A driving cycle used for light duty vehicle testing. It simulates an urban route of 7.5 mile with frequent stops. |

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**Figure 7.**The histogram of fitness values for initial and optimal values of the parameters of the control strategy.

**Figure 8.**The histogram for FC and emissions using initial and optimal values of the parameters of control strategy. (

**A**) FC and emissions based on NEDC cycle; (

**B**) FC and emissions based on FTP cycle; (

**C**) and emissions based on ECE + EUDC cycle, and (

**D**) FC and emissions based on UDDS cycle.

**Figure 9.**The histogram for dynamic performance using initial and optimal values of the parameters of control strategy. (

**A**) dynamic performance based on NEDC cycle; (

**B**) dynamic performance based on FTP cycle; (

**C**) dynamic performance based on ECE + EUDC cycle, and (

**D**) dynamic performance based on UDDS cycle.

**Figure 10.**The histogram of the improvement in overall effectiveness between the results using initial and optimal values of the parameters of the control strategy.

**Figure 11.**The histogram of the improvements in FC and emissions between the results using initial and optimal values of the parameters of control strategy.

**Figure 12.**The histogram of the improvements in the dynamic performance between the results using initial and optimal values of the parameters of the control strategy.

**Table 1.**Eight independent input parameters/variables for an electric assist control strategy (EACS).

Parameter | BCS Variable [8] | Description |
---|---|---|

SOC_{L} | cs_lo_soc | The lowest state of charge allowed. |

SOC_{H} | cs_hi_soc | The highest state of charge allowed. |

T_{ch} | cs_charge_trq | An alternator-like torque loading on the engine to recharge the battery pack. |

T_{min} | cs_min_trq_frac | When commanded at a lower torque, the engine will be manipulated at the threshold torque (minimum torque threshold =
T_{min} × T_{max}). Additionally, if SOC < SOC_{L}, the electric motor serves as a generator. |

T_{off} | cs_off_trq_frac | When commanded at a lower torque and if SOC > SOC_{L}, the engine will be shut down (minimum torque threshold = T_{off} × T_{max}). |

ELS_{L} | cs_electric_launch_spd_lo | The lowest vehicle speed threshold. |

ELS_{H} | cs_electric_launch_spd_hi | The highest vehicle speed threshold. |

D_{ch} | cs_charge_deplete_bool | To use charge deplete strategy or charge sustaining strategy. |

**Table 2.**The seven PNGV dynamic performance constraints considered [22]. PNGV: partnership for a new generation of vehicles.

Parameter | Description | y_{i} | c_{i}(x) |
---|---|---|---|

Acceleration time | Acceleration time 1 for 0–60 mph in 12 s | 1.2 | ${c}_{1}\left(x\right)$ |

Acceleration time 2 for 40–60 mph in 5.3 s | 1.5 | ${c}_{2}\left(x\right)$ | |

Acceleration time 3 for 0–85 mph in 23.4 s | 1.2 | ${c}_{3}\left(x\right)$ | |

Maximum speed | ≥0.017 mi/s | 1.2 | ${c}_{4}\left(x\right)$ |

Maximum acceleration | ≥0.0032 mi/s^{2} | 1.2 | ${c}_{5}\left(x\right)$ |

Distance in 5 s | ≥0.0265 mi | 1.2 | ${c}_{6}\left(x\right)$ |

Gradeability | 6.5% gradeability at 55 mph with 272 kg additional weight for 20 min | 2.0 | ${c}_{7}\left(x\right)$ |

Parameter (Unit) | Lower Bound | Upper Bound |
---|---|---|

SOC_{L} (-) | 0.1 | 0.5 |

SOC_{H} (-) | 0.55 | 1 |

T_{ch} (Nm) | 1 | 80.9 |

T_{min} (-) | 0.05 | 1 |

T_{off} (-) | 0.05 | 1 |

ELS_{L} (m/s) | 0 | 15 |

ELS_{H} (m/s) | 10 | 30 |

D_{ch} (-) | 0 | 1 |

**Table 4.**Parameters for NEDC, FTP, ECE + EUDC, and UDDS driving cycle. NEDC: new European driving cycle; FTP: Federal Test Procedure; ECE + EUDC: Economic Commission for Europe + Extra-Urban driving cycle; UDDS: urban dynamometer driving schedule.

Parameter | Value | |||
---|---|---|---|---|

NEDC | FTP | ECE + EUDC | UDDS | |

Time | 1184 s | 2477 s | 1225 s | 1369 s |

Distance | 6.79 miles | 11.04 miles | 6.79 miles | 7.45 miles |

Maximum speed | 74.56 mph | 56.70 mph | 74.56 mph | 56.70 mph |

Average speed | 20.64 mph | 16.04 mph | 19.95 mph | 19.58 mph |

Maximum acceleration | 0.00066 mi/s^{2} | 0.00092 mi/s^{2} | 0.00066 mi/s^{2} | 0.00092 mi/s^{2} |

Maximum deceleration | −0.00086 mi/s^{2} | −0.00092 mi/s^{2} | −0.00086 mi/s^{2} | −0.00092 mi/s^{2} |

Average acceleration | 0.00034 mi/s^{2} | 0.00034 mi/s^{2} | 0.00034 mi/s^{2} | 0.00031 mi/s^{2} |

Average deceleration | −0.00049 mi/s^{2} | −0.00036 mi/s^{2} | −0.00049 mi/s^{2} | −0.00036 mi/s^{2} |

Idle time | 298 s | 360 s | 339 s | 259 s |

Number of stops | 13 | 22 | 13 | 17 |

Maximum up grade | 0% | 0% | 0% | 0% |

Average up grade | 0% | 0% | 0% | 0% |

Maximum down grade | 0% | 0% | 0% | 0% |

Average down grade | 0% | 0% | 0% | 0% |

Component | Version | Type | Description |
---|---|---|---|

Vehicle | - | - | Hypothetical small car (VEH_SMCAR) |

Fuel Converter | ic | si | Spark Ignition; Geo 1.0 L (41 KW) SI engine (FC_SI41_emis) |

Exhaust Aftertreat | - | - | Standard catalyst for stoichiometric SI engine (EX_SI) |

Energy Storage | rint | pb | Lead-Acid; Hawker Genesis 12V26Ah10EP VRLA battery, tested by VA Tech. (ESS_PB25) |

Motor | - | - | Westinghouse 75-KW (continuous) AC induction motor/inverter (MC_AC75) |

Transmission | man | man | Manual transmission; manual 5-speed transmission (TX_5SPD) |

Torque Coupling | - | - | Lossless belt drive (TC_DUMMY) |

Wheel/Axle | Crr | Crr | Constant coefficient of rolling resistance model; wheel/axle assembly for small car (WH_SMCAR) |

Accessory | Const | Const | Constant power accessory load models; 700-W constant electric load (ACC_HYBRID) |

Powertrain Control | par | man | Parallel manual transmission; 5-speed parallel charge depleting hybrid (PTC_PAR_CD) |

Vehicle | - | - | Hypothetical small car (VEH_SMCAR) |

Fuel converter | ic | si | Spark Ignition; Geo 1.0 L (41 KW) SI engine (FC_SI41_emis) |

Parameter (Unit) | Variable | Value |
---|---|---|

Mass of the vehicle without components (kg) | veh_glider_mass | 592 |

Cargo mass (kg) | veh_cargo_mass | 136 |

Test mass, including fluids, passengers, and cargo (kg) | veh_mass | 1350 |

Vehicle frontal area (m^{2}) | veh_FA | 2 |

Coefficient of aerodynamic drag | veh_CD | 0.335 |

Coefficient of wheel rolling resistance | wh_1st_rrc | 0.009 |

Radius of the wheel (m) | wh_radius | 0.304 |

Parameter (Unit) | NEDC | FTP | ECE + EUDC | UDDS | ||||
---|---|---|---|---|---|---|---|---|

Initial | Optimal | Initial | Optimal | Initial | Optimal | Initial | Optimal | |

SOC_{L} (-) | 0.13 | 0.276 | 0.235 | 0.271 | 0.306 | 0.31 | 0.046 | 0.267 |

SOC_{H} (-) | 0.271 | 0.848 | 0.433 | 0.862 | 0.33 | 0.931 | 0.087 | 0.788 |

T_{ch} (Nm) | 61.144 | 66.879 | 74.815 | 14.61 | 7.186 | 14.33 | 1.41 | 6.64 |

T_{min} (-) | 0.29 | 0.211 | 0.703 | 0.355 | 0.83 | 0.09 | 0.87 | 0.798 |

T_{off} (-) | 0.047 | 0.431 | 0.891 | 0.236 | 0.957 | 0.084 | 0.077 | 0.342 |

ELS_{L} (m/s) | 12.583 | 1.998 | 5.137 | 2.496 | 10.974 | 13.932 | 4.207 | 0.23 |

ELS_{H} (m/s) | 27.902 | 18.566 | 25.473 | 14.75 | 28.098 | 25.214 | 26.695 | 17.776 |

D_{ch} (-) | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |

Fitness value | 0.017 | 0.028 | 0.015 | 0.028 | 0.021 | 0.029 | 0.017 | 0.029 |

**Table 8.**The result for fuel consumption (FC) and emissions using initial and optimal values of the parameters of the control strategy.

Parameter (Unit) | NEDC | FTP | ECE + EUDC | UDDS | ||||
---|---|---|---|---|---|---|---|---|

Initial | Optimal | Initial | Optimal | Initial | Optimal | Initial | Optimal | |

FC (mi/gal) | 31.08 | 31.80 | 26.69 | 32.18 | 32.08 | 31.72 | 29.56 | 29.51 |

HC (g/mi) | 0.71 | 0.61 | 0.50 | 0.47 | 0.69 | 0.67 | 0.63 | 0.67 |

CO (g/mi) | 8.05 | 2.93 | 10.83 | 3.22 | 3.73 | 3.56 | 5.73 | 3.81 |

NO_{x} (g/mi) | 0.68 | 0.52 | 0.30 | 0.45 | 0.73 | 0.58 | 0.65 | 0.68 |

**Table 9.**The result for the dynamic performance using initial and optimal values of the parameters of the control strategy.

Parameter (Unit) | NEDC | FTP | ECE + EUDC | UDDS | ||||
---|---|---|---|---|---|---|---|---|

Initial | Optimal | Initial | Optimal | Initial | Optimal | Initial | Optimal | |

0–60 mph (s) | 14.57 | 9.59 | 12.67 | 9.55 | 12.96 | 9.18 | 15.46 | 9.85 |

40–60 mph (s) | 7.84 | 4.89 | 6.81 | 4.86 | 6.96 | 4.61 | 8.31 | 5.05 |

0–85 mph (s) | 33.18 | 19.88 | 28.36 | 19.80 | 29.06 | 18.76 | 35.69 | 20.61 |

Maximum speed (mi/s) | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 |

Maximum acceleration (mi/s^{2}) | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 |

Distance in 5 s (mi) | 0.028 | 0.034 | 0.031 | 0.034 | 0.030 | 0.034 | 0.027 | 0.033 |

Gradeability (%) | 6.5 | 6.5 | - | 6.5 | 6.5 | 6.5 | - | 6.5 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cheng, Y.-H.; Lai, C.-M.
Control Strategy Optimization for Parallel Hybrid Electric Vehicles Using a Memetic Algorithm. *Energies* **2017**, *10*, 305.
https://doi.org/10.3390/en10030305

**AMA Style**

Cheng Y-H, Lai C-M.
Control Strategy Optimization for Parallel Hybrid Electric Vehicles Using a Memetic Algorithm. *Energies*. 2017; 10(3):305.
https://doi.org/10.3390/en10030305

**Chicago/Turabian Style**

Cheng, Yu-Huei, and Ching-Ming Lai.
2017. "Control Strategy Optimization for Parallel Hybrid Electric Vehicles Using a Memetic Algorithm" *Energies* 10, no. 3: 305.
https://doi.org/10.3390/en10030305