Comprehensive Analysis of MultiObjective Optimization Algorithms for Sustainable Hybrid Electric Vehicle Charging Systems
Abstract
:1. Introduction
Contribution
 Development of a biobjective optimization model that balances TNPC and LPSP objectives.
 Evaluation of four multiobjective algorithms based on criteria, such as convergence, diversity, efficiency, scalability, and robustness, to determine the most suitable algorithm for attaining the Pareto optimal solution for the PVWB/EVCS system.
 Utilization of the Pareto method for selecting the Pareto optimal solution.
 Investigation of sensitivity analysis by considering various factors, such as cost of LithiumIon batteries, PV system, and WT.
2. Literature Review
2.1. Review of Hybrid EVCS System
2.2. Review the Optimization Methods
3. Mathematical Modeling of RE System Components
3.1. EV Charging Station Load Model
3.2. PV Model
3.3. Wind Turbine Model
3.4. Battery Storage System Model
4. The Optimization Framework
4.1. Total Net Present Cost
4.2. Loss of Power Supply Probability
4.3. The Proposed System’s Energy Management Technique
5. Optimization Algorithms
5.1. MultiObjective Particle Swarm Optimization
Algorithm 1: Multiobjective Particle Swarm Optimization (MOPSO) 
1. Initialize population of particles 
2. Evaluate objective functions for each particle and calculate their fitness values 
3. Identify nondominated solutions among the particles and store them in a reference set. 
4. Repeat steps 4.1 to 4.4 until a stopping criterion is met or for a predefined number of iterations. 
4.1. Update velocity of each particle based on optimal positions of other particles and nondominated solutions in reference set. 
4.2. Update position of each particle based on updated velocity. 
4.3. Evaluate new objective functions for each updated particle and calculate their fitness values. 
4.4. Update reference set with newly evaluated solutions. 
5. Select best solution from reference set based on criteria specified in optimization problem. 
6. Return the best solution as the result of the optimization process. 
5.2. NonDominated Sorting Genetic Algorithm II
Algorithm 2: Nondominated Sorting Genetic Algorithm (NSGAII) 
1. Problem Definition 
a. Define the objective function to be optimized. 
b. Define the constraints that must be satisfied. 
2. Initialization 
a. Generate a set of initial solutions. 
b. Evaluate the solutions using the objective function and constraints. 
c. Create an initial nondominated set using the evaluated solutions. 
3. Fast Nondominated Sorting 
a. Sort the solutions into nondomination levels to create a front of nondominated 
solutions. 
b. Assign a crowding distance to each solution in each front. 
4. Create the Offspring Population 
a. Select solutions from the current front to generate offspring solutions through 
genetic operators (crossover and mutation). 
b. Evaluate the offspring solutions using the objective function and constraints. 
5. Merge the Parent and Offspring Populations 
a. Combine the parent and offspring solutions into a single set. 
6. Environmental Selection 
a. Select the next generation of solutions from the combined set, based on non 
domination level and crowding distance. 
b. Solutions with the lowest nondomination level and highest crowding distance are 
preferred. 
7. Repeat from Step 3 
a. Repeat the process from Step 3 until a stopping criterion is met (maximum 
number of generations). 
8. Return the best solution 
a. Return the solution with the best fitness as the result of the optimization. 
5.3. NonDominated Sorting Genetic Algorithm III
Algorithm 3: Nondominated Sorting Genetic Algorithm (NSGAIII) 
1. Initialization: Generate an initial population of solutions, where each solution represents a candidate design for the (PVWB/EVCS) system. 2. Nondominated Sorting: Sort the solutions in the initial population based on their nondomination levels. A solution is considered nondominated if it is not dominated by any other solution in the population. 3. Crowding Distance Calculation: Calculate the crowding distance of each solution. The crowding distance measures the degree of separation between solutions in the population and helps to prevent premature convergence. 4. Selection: Select a set of solutions to form the mating pool for the next generation. The selection process is based on the nondominated levels and crowding distances of the solutions. 5. Mating: Use genetic operators such as crossover and mutation to generate offspring solutions from the mating pool. 6. Evaluation: Evaluate the fitness of the offspring solutions by calculating their objectives. 7. Nondominated Sorting and Crowding Distance Calculation: Repeat steps 2 to 3 for the offspring solutions. 8. Replacement: Replace the solutions in the current population with the offspring solutions to form the next generation. 9. Termination: Repeat steps 4 to 8 until a termination criterion is met, such as a maximum number of generations. 10. Result: Return the final set of nondominated solutions as the result of the optimization process. These solutions represent the best tradeoff designs for the (PVWB/EVCS) system based on the objectives used in the optimization process. 
5.4. MultiObjective Evolutionary Algorithm Based on Decomposition
Algorithm 4: MultiObjective Evolutionary Algorithm based on Decomposition (MOEA/D) 
Step 1: Initialization

5.5. Performance Evaluation of MultiObjective Optimization Algorithms
Algorithm 5: Performance Evaluation of MultiObjective Optimization Algorithms 
INPUT: Set of multiobjective optimization algorithms, problem to be optimized (sizing of the PVWB/EVCS system) 
OUTPUT: Best algorithm for sizing the PVWB/EVCS system 
1. SELECT a set of multiobjective optimization algorithms to be evaluated, including algorithms such as MOPSO, NSGAII, NSGAIII, MOEA/D. 
2. DEFINE the problem to be optimized, in this case the sizing of the PVWB/EVCS system. 
3. FOR each algorithm, 
a. RUN it several times to find a set of solutions. 
b. CALCULATE the performance metrics for each set of solutions (Convergence, Diversity, Efficiency, and Robustness). 
4. DISPLAY the performance metrics for each algorithm in a table. 
5. Compute the performance score for each algorithm by summing up the performance metrics for each algorithm. 
6. COMPARE the algorithms based on the performance metrics and determine the bestperforming algorithm. 
5.5.1. Convergence Metric
5.5.2. Diversity Metric
5.5.3. Efficiency Metric
5.5.4. Robustness Metric
6. Results and Discussion
6.1. Case Study
6.2. Results
6.3. Sensitivity Analysis
6.3.1. Sensitivity Analysis of LithiumIon Cost and Its Implications
6.3.2. Sensitivity Analysis of PV System Cost and Its Effects
6.3.3. Sensitivity Analysis of Wind Turbine Cost and Its Effects
7. Conclusions
 ➣
 The optimum system consisted of a 223 kW PV system, an 80kW wind turbine, and seven LithiumIon battery banks, with an TNPC of USD 564,846, an LCOE of 0.2521 USD/kWh, and an LPSP of 1.21%.
 ➣
 The Pareto front plots of TNPC vs. LPSP for the four suggested optimization algorithms showed a clear tradeoff between the two objectives.
 ➣
 NSGAII achieved the highest overall performance among the four algorithms, with the best scores for convergence and diversity.
 ➣
 NSGAIII had the highest efficiency score, while MOPSO attained the highest diversity score.
 ➣
 MOEA/D was observed to have the highest robustness score, indicating its suitability for diverse problem conditions.
 ➣
 The proposed system can adjust to different energy requirements in different seasons, showcasing its ability to function effectively under diverse weather conditions.
 ➣
 The study concludes that the development of a hybrid renewable energy system can provide a reliable source of sustainable electricity for institutions and neighboring communities.
 ➣
 The findings have implications for designing and implementing sustainable renewable energy systems that consider seasonal variations in energy production and consumption.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
${P}_{pv}$  PV Output Power  ABC  Artificial Bee Colony 
${P}_{PVr}$  PV Rated Power  CRF  Capital Recovery Factor. 
G  Global Irradiance Incident on Titled Plane  DOD  Depth of Discharge. 
$D{F}_{pv}$  PV Derating Factor  DRP  Demand Response Participation 
$DEG{F}_{pv}$  PV Degradation Factor  EVCS  Electric Vehicle Charging Stations 
$S{F}_{pv}$  Shading Factor  EVs  Electric Vehicles 
${N}_{pv}$  The number of PV system.  GHG  Greenhouse Gas 
${T}_{amb}$  Ambient Temperature  HOMER  Hybrid Optimization of Multiple Energy Resources 
${T}_{base}$  Base Temperature  HPS  Hybrid Power Systems 
${N}_{WT}$  The number of wind turbines  LCOE  levelized Cost of Energy 
${\eta}_{w}$  The wind turbine efficiency  LPSP  Loss of Power Supply Probability 
${P}_{WTr}$  The rated power of the wind turbine (kW).  LSA  Lightning Search Algorithm 
V(t)  The upgraded wind speed in (m/s)  MOEA/D  MultiObjective Evolutionary Algorithm Based on Decomposition 
V_{ci}  The cutin wind speed in (m/s)  MOPSO  MultiObjective Particle Swarm Optimization 
V_{co}  The cutout wind speed in (m/s)  NOCT  Normal Operating Cell Temperature 
V_{r}  The rated wind speed (m/s)  NSGAII  Nondominated Sorting Genetic Algorithm 
${C}_{Bat}$  Battery bank nominal capacity (kWh).  NSGAIII  Nondominated Sorting Genetic Algorithm III 
${C}_{Bat,min}$  Minimum allowable storage battery capacity.  POWER  NASA Prediction of Worldwide Energy Resource database 
${C}_{Bat,max}$  Maximum allowable storage battery capacity.  PSO  Particle Swarm Optimization 
N_{bat}  The number of battery banks.  PV  Photovoltaic 
${C}_{I}$  The initial capital cost.  PVBESS  PhotovoltaicBattery Energy Storage Systems 
${C}_{R}$  The replacement costs of the components  PVWB/EVCS  PhotovoltaicWind TurbineBattery/Electric Vehicle Charging Station 
${C}_{O\&M}$  Operating and Maintenance Costs  RES  Renewable Energy Sources 
I_{r}  Interest rate.  RF  Renewable Fraction 
I_{f}  Inflation rate.  SDGs  Sustainable Development Goals 
${E}_{served}$  The primary load served (kWh/year).  TNPC  Total Net Present Cost 
$\sigma $  The Battery SelfDischarge  TNPC  Total Net Present Cost 
${\eta}_{b}$  The Battery efficiency  V2G  VehicletoGrid 
${P}_{EVCS}$  The EVCS load  VCS  Virus Colony Search Optimization 
S  Salvage value  WT  Wind Turbines 
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Model  Battery Capacity (kWh)  Charging Time (min)  Proportion of EV Population (%)  Type of Charging  Battery Technology 

Volkswagen eGolf  36  40  30  Fast Charge  Lithiumion 
Mercedes EQA 250  67  30  30  
Fiat 500e Hatchback  24  25  10  
BMW i3  43  40  30 
1. MOPSO  

population size  100 
Stopping criteria (Max. iteration)  200 
Inertia Weight  0.85 
Inertia Weight Damping Rate  0.90 
Personal Learning Coefficient  1.8 
Global Learning Coefficient  2 
Leader Selection Pressure  2 
Deletion Selection Pressure  2 
Mutation Rate  0.10 
2. NSGAII  3. NSGAIII 
population size  100 
Stopping criteria (Max. iteration)  200 
Crossover Percentage  0.70 
Number of Parents (Off springs)  70 
Mutation Percentage  0.40 
Number of Mutants  40 
Mutation Rate  0.02 
4. MOEA/D  
population size  100 
Stopping criteria (Max. iteration)  200 
Number of Neighbors  30 
Crossover Percentage  0.50 
Item  Parameter  Value  Unit 

Generic flat plate PV [73]  capacity  1  kW 
IC  1187  USD  
RC  1187  USD  
O&M  5  USD/year  
lifetime  25  years  
Wind turbine (WES 18) [97]  capacity  80  kW 
IC  84,000  USD  
RC  52,080  USD  
O&M  400  USD/year  
lifetime  20  years  
Lithium Ion (Blue Ion 2.0) [73]  Nominal capacity  16.8  kW 
IC  15,000  USD  
RC  13,800  USD  
O&M  1.0  USD/year  
lifetime  25  years  
Discount rate  3  (%)  
Inflation rate  2.15  (%)  
Project lifetime  25  years 
PV (Kw)  WT (units)  Battery (units)  LPSP (%)  LCOE (USD/kWh)  TNPC (USD)  

MOEAD  223  1  7  1.21  0.2521  564,846 
MOPSO  224  1  9  0.87  0.2654  596,662 
NSGAIII  208  1  11  0.76  0.2673  601,519 
NSGAII  171  2  9  0.83  0.2861  643,510 
HOMER  222  1  22  0.00  0.319  724,004 
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Alshammari, N.F.; Samy, M.M.; Barakat, S. Comprehensive Analysis of MultiObjective Optimization Algorithms for Sustainable Hybrid Electric Vehicle Charging Systems. Mathematics 2023, 11, 1741. https://doi.org/10.3390/math11071741
Alshammari NF, Samy MM, Barakat S. Comprehensive Analysis of MultiObjective Optimization Algorithms for Sustainable Hybrid Electric Vehicle Charging Systems. Mathematics. 2023; 11(7):1741. https://doi.org/10.3390/math11071741
Chicago/Turabian StyleAlshammari, Nahar F., Mohamed Mahmoud Samy, and Shimaa Barakat. 2023. "Comprehensive Analysis of MultiObjective Optimization Algorithms for Sustainable Hybrid Electric Vehicle Charging Systems" Mathematics 11, no. 7: 1741. https://doi.org/10.3390/math11071741