PreprintPDF Available

Towards an Optimal Hybrid Algorithm for EV Charging Stations Placement using Quantum Annealing and Genetic Algorithms

Authors:
  • Artificial Brain
Preprints and early-stage research may not have been peer reviewed yet.

Abstract

Quantum Annealing is a heuristic for solving optimization problems that have seen a recent surge in usage owing to the success of D-Wave Systems. This paper aims to find a good heuristic for solving the Electric Vehicle Charger Placement (EVCP) problem, a problem that stands to be very important given the costs of setting up an electric vehicle (EV) charger and the expected surge in electric vehicles across the world. The same problem statement can also be generalized to the optimal placement of any entity in a grid and can be explored for further uses. Finally, the authors introduce a novel heuristic combining Quantum Annealing and Genetic Algorithms to solve the problem. The proposed hybrid approach entails seeding the genetic algorithm with the results of quantum annealing. Experimental results show that this method decreases the minimum distance from Points of Interest (POI) by 42.89% compared to vanilla quantum annealing over the sample EVCP datasets.
1
Towards an Optimal Hybrid Algorithm for EV
Charging Stations Placement using Quantum
Annealing and Genetic Algorithms
Aman Chandra2, Jitesh Lalwani1,2, and Babita Jajodia3
1Artificial Brain Tech Inc, 2055 Limestone RD, STE 200-C, Wilmington, Delaware, USA 19808
2Artificial Brain Technology (OPC) Private Limited, Pune, India 411057
3Department of Electronics and Communication Engineering,
Indian Institute of Information Technology Guwahati, India
Email: {aman.chandra@artificialbrain.in, jitesh.lalwani@artificialbrain.us, babita@iiitg.ac.in}
Abstract—Quantum Annealing is a heuristic for solving op-
timization problems that have seen a recent surge in usage
owing to the success of D-Wave Systems. This paper aims to
find a good heuristic for solving the Electric Vehicle Charger
Placement (EVCP) problem, a problem that stands to be very
important given the costs of setting up an electric vehicle (EV)
charger and the expected surge in electric vehicles across the
world. The same problem statement can also be generalized
to the optimal placement of any entity in a grid and can be
explored for further uses. Finally, the authors introduce a novel
heuristic combining Quantum Annealing and Genetic Algorithms
to solve the problem. The proposed hybrid approach entails
seeding the genetic algorithms with the results of quantum
annealing. Experimental results show that this method decreases
the minimum distance from Points of Interest (POI) by 42.89%
compared to vanilla quantum annealing over the sample EVCP
datasets.
Index Terms—Electric Vehicle, Optimization, D-Wave Sys-
tems, Quantum Annealing, Genetic Algorithm, Quadratic Un-
constrained Binary Optimization (QUBO)
I. INTRODUCTION
Electric Vehicle Charger Placement (EVCP) is an optimiza-
tion problem that is sure to become of great interest in the
upcoming years, given the increase in electric vehicles, and the
costs associated with setting up an electric charger. However,
this problem is non-deterministic polynomial time (NP) hard,
and becomes intractable with an increase in the number of
charging stations to be placed.
Optimal EVCP is a problem that the authors suspect will
be of great interest in the near future, owing to the fact that
electric vehicles are just starting to catch up in popularity,
meanwhile the infrastructure to support them is just starting
to be built. Few research works are available till date on EVCP
problem [1], [2], and to the best of the authors’ knowledge,
there is no existing literature or work done yet on using
the newly available strategy of quantum annealing [3]. To
explore this area further, the authors referred the work done
in [1] and [2] and decided to model a basic version of the
problem on quantum annealing of D-Wave computers. The
only reference available is a GitHub repository [4] outlining a
very basic and non-performant example. the authors took the
same and made few developments to improve the performance
greatly, and incorporated a few novel techniques in doing so.
The reason the authors we believe it important to have a
workable quantum solution is that annealing is a method that
shows promise to greatly outperform classical heuristics when
it comes to optimization problems [3]. Quantum computing
hardware is still in an intermediate stage, but the authors
believe it necessary to accelerate the adoption process by
working towards useful solutions feasible on the currently
available D-Wave hybrid solvers [5].
The motivation behind this paper was to improve on the
method for solving the EVCP problem proposed by Pagany
et al. [6]. The focus of this paper is threefold. First, to make
any changes to the only quantum solution so as to improve
the result. Then to find a good machine learning algorithm
for solving the problem when seeded randomly, and finally
to integrate the two heuristics together to see if there are any
advantages in computation time, robustness and optimality of
solution.
Given the limitations of current quantum hardware, an entirely
quantum approach to solving a problem is not practical.
However, this work stands to show that quantum computing
can be utilised despite this hardware limitation to improve
results of the classical heuristics that are currently being used
to solve similar problems. The authors suggest that this is
the best way to utilise quantum computing in the current era,
and we wish to explore more use cases where this approach
improves performance in future research.
The paper is organised as follows: Section II gives a brief
overview of quantum annealing using D-Wave computers
and evolutionary Genetic Algorithms. Section III gives a
detailed description of the proposed hybrid algorithm using
quantum annealing and genetic algorithm towards an optimal
electric vehicle charging stations placement problem. Section
IV discusses about the performance metric that establish
the proposed algorithm along with experimental results and
discussions in Section V. Section VI concludes the paper with
future works.
2
II. BACKGROU ND O N D-WAVE QUA NT UM ANNEALING
AN D GEN ET IC ALGORITHMS
A. Quantum Annealing on D-Wave Computers
Quantum annealing is a meta-heuristic for finding the global
minima of an objective function. The quantum advantage
stems from the ability to explore multiple candidate solutions
in parallel, as well as the ability to quantum tunnel, over-
coming energy walls between two local minima, allowing for
easier traversal of the energy landscape [7].
Using the D-Wave methodology, the problem is encoded
as a Quadratic Unconstrained Binary Optimization (QUBO)
problem, and quantum annealing is used to find the solution
to this QUBO formulation. The objective function f(x)in a
QUBO problem is written in the form of
f(x) =
N
X
i=1
i
X
j=1
qij xixj(1)
where, Xis a vector of binary variables x, and qij are the
weights of the N×NQUBO matrix. The weights can be
written in the form of either a symmetric matrix or an upper
triangular matrix that we call the N×NQUBO matrix.
The result of the quantum annealing is the value of Xthat
minimizes the objective function f(x). The challenge with
Quantum annealing lies in finding the correct values of QUBO
matrix to efficiently represent the problem that the authors are
aiming to solve.
B. Genetic Algorithms
Genetic algorithms are a well known heuristic for solving
optimization problems that are difficult to solve precisely [8].
The general outline of a genetic algorithm can be described
as follows:
1) Define an individual that carries the necessary informa-
tion in it’s genes to be a solution to the optimization
problem
2) Create a population of these individuals
3) Define a method for breeding these individuals
4) Define a method for mutation in the population
5) Define a fitness function that describes how good the
solution represented by the genes are
6) Carry out an evolutionary simulation that mimics the
concept of natural selection, where the population is
updated every generation following the mutation and
breeding methods mentioned above.
Then, the population of the final generation is used as a
solution to the problem.
III. PROP OS ED HYBRID ALGORITHM FOR EVCP USING
QUAN TU M ANNEALING AND GEN ET IC ALGORITHMS
A. The EVCP Problem
The EVCP can be defined by setting up a grid on which the
Points of Interest (POI) and already existing electric chargers
are set up on the nodes. The proposed algorithm then places
down new charging points in an optimal manner. For the
sake of this research work, optimality has been defined as
Fig. 1. Picture showing an example of EVCP, where buildings are Points of
Interest (POI), blue cars are old chargers and red cars are new chargers
minimizing travel distance to a charger for all points of interest
on the grid. As shown in Fig. 1, the algorithm will decide
where to place the red cars (new charging points), to optimize
the scoring metric that will be explained in Section IV-A.
B. Proposed Quantum Annealing Approach
This proposed quantum annealing approach is inspired by
the QUBO formulation presented in [6] that aims to optimize
three objectives:
1) Minimize distance from Points of Interest (POI)
2) Maximize distance from previous existing charger loca-
tions
3) Maximize distance between the new charger locations
Based on these objectives, the three constraints are chosen to
try to place the chargers close to the POI, without placing them
trivially close to each other or previously present chargers.
The reason for including all three is to distribute the points to
maximize coverage of POI for the given number of chargers
to be placed. It must be noted that in the QUBO formulation,
the centroid of all POI are considered for minimization, and
similarly for previously existing chargers as well as new
chargers.
Mathematically, the three constraints (H1,H2and H3)
referring to the three objective functions can be represented
as follows:
H1= +
N
X
i=1
xidp
i(2)
H2=
N
X
i=1
xidc
i(3)
H3=
N
X
i=1
xidl
i(4)
with the values of dp
i,dc
iand dl
igiven as
dp
i=
nP OI
X
k=1
dist(P OIkxi)2(5)
dc
i=
ncharger
X
k=1
dist(chargerkxi)2(6)
3
dl
i=
nlocations
X
k=1
dist(xkxi)2(7)
Here, Nis the no. of points, P OI are the Points of Interest,
charger refers to the chargers that are already present, thus
ncharger is the number of chargers, nlocations refers to the
number of available locations to place a new charger, mis
the no. of new chargers we want to place and dist refers to
euclidean distance between the two points.
The last constraint where the number of chargers must be
equal to a value mcan be given as
H4= (
N
X
i=1
xi)m(8)
The final QUBO formulation can be given by
Hfinal =
N
X
i=1
λiHi(9)
Please note that the parameters λconstitute the trade-off
between different optimization functions. A careful balance of
all the constraints (H1,H2,H3and H4) is required to achieve
the aim of the scoring metric described in Section IV-A.
C. Inclusion of Entropy
An error observed with the initial QUBO formulation is that
it rewarded extreme minimization to a few POI at the expense
of other POI. This has been combated by changing the distance
minimization in H1to a distance entropy minimization. The
motivation for this idea stems from information entropy given
by
H(X) = XP(xi) log P(xi)(10)
where Xis a discrete distribution, H(X)is the entropy of the
distribution and P(X)is the probability distribution of the
variable X.
For the proposed hybrid algorithm, we replaced (5) with
H(dp), by taking our distribution to be a softmax distribu-
tion, and used this new equation to calculate (2). The chosen
probability distribution can be thought of as a softmax over
the distances of the POI from each possible charger location,
and minimizing the value of this entropy instead of just the
distances from the POI has led to significantly improved
results as compared to before this change on the datasets. For
the rest of this paper, Quantum Annealing has been used with
this entropic version of (5) and all results have been calculated
using this, as they were too poor to be considered otherwise.
D. Integration of Evolutionary Genetic Algorithm with Quan-
tum Annealing
The output from the Quantum annealing, although signif-
icantly improved after introducing an entropic loss function,
and optimization of hyper-parameters, still has much room
for improvements. The authors introduce a method of using
evolutionary genetic algorithms to optimize the output received
from the quantum annealing. Research findings show that
Fig. 2. Sample Output using only quantum annealing. The blue, red and green
colours in the graph indicates POI, old charging stations and new charging
stations respectively, with the score of 64.0
Fig. 3. Sample Output where a GA was seeded with quantum annealing. The
colours- blue, red and green indicates POI, old charging stations and new
charging stations respectively with the score of 17.74
seeding a genetic algorithm with the results of quantum
annealing improves on the result of either on its own to solve
the problem.
The authors first explored the uses of genetic algorithms in
solving the problem of EVCP directly, and found out that the
use of genetic algorithms brings two advantages as compared
to quantum annealing as follows:
1) Reduced time to solution - it completes a basic search
much quicker
2) Easy transformation into a continuous problem - The
quantum annealing solves this as a discrete problem,
using evolutionary algorithms however, it is possible to
turn the same into a continuous problem.
However, the problem becomes very chaotic to solve using
a randomly seeded genetic algorithm when the number of
new chargers increases. The authors theorize that this is due
to the energy landscape being scattered with local minima,
especially if the search space is assumed to be continuous.
Since the heuristic used involves a random mutation and
crossover approach, it is quite difficult for it to traverse
this landscape. The proposed solution is to use a quantum
annealing to search the space discretely and traverse over the
4
local minima in the energy landscape of the problem. Then, the
genetic algorithm can take outputs of the quantum annealing
as a seed and optimize it further. This optimization is doubly
useful as it turns the problem discrete, which allows better
solutions than possible in a discrete space. This also allows
the genetic algorithm to search the local area highlighted by
the annealing to improve on it if possible.
Fig. 2 shows the output from just quantum annealing, while
Fig. 3 shows the output from the proposed quantum annealing
+ genetic algorithm. These graphs are plotted using the sample
EVCP (5,3,3) dataset. As it can be seen from Fig. 3, the score
is lower with respect to Fig. 2. The lower the score is, the better
the placement of charger is. The placement of the chargers also
looks to be better intuitively.
This strategy does have some drawbacks that the authors
would like to point out. The algorithm will fail entirely if the
genetic algorithm used is not capable of solving the problem
independently, due to either a poor crossover and mutation
strategy, or a bad choice of hyper-parameters. It might be
advisable to perform some kind of search to find the best
parameters possible, and extensive experimentation needs to
be done to find the right crossover and mutation strategies,
depending on the specific problem.
IV. PERFORMANCE METRIC
A. Scoring Metric
The proposed hybrid algorithm aims to solve the charger
placement problem by minimizing the sum of minimum dis-
tance to a charger from each POI by Pmin(Di
k), where Di
k
is the array of distances of all kcharger locations from the ith
point of interest. This hopes to place new chargers such that
they are not redundant due to other chargers existing close
by, but are still close to POI, reducing travel time and cost
for reaching a charger. This scoring metric however, did not
account for robustness and thus the score used finally was
the sum of the mean and variance of the above the proposed
scoring metric over the no. of runs.
B. Disparity of QUBO formulation with Scoring Metric
It is reasonable to question why the authors did not create
a QUBO that directly minimized what the scoring metric
described above measures. The problem was the involvement
of a min() function in the scoring metric. This cannot be
easily translated into a binary quadratic problem, and the
increased computation during the QUBO generation due to
the added computational complexity would make the process
extremely inefficient. Therefore, the objective functions were
chosen such that (i)they were simple and efficient to code
in and (ii)could be used to give a result that minimized our
scoring metric when the right lambda parameters were chosen.
Hence, there was no testing done using that formulation,
however if an efficient method to encode the scoring metric
into a QUBO can be found, the authors suspect the results
would be better than what we have achieved.
TABLE I
COMPARISON TAB LE OF T HE PRO POS ED HYBRID ALGORITHM
INTEGRATING QUANTU M ANNEALING AND GEN ETI C ALGORITHM OVER
EXISTING ONLY QA AND G A ON OUR SAMPLE EVCP DATASET S
Sample EVCP Dataset Score
Only QAOnly GAProposed‡‡
EVCP (5,2,3) 40 91.40 23.70
EVCP (5,3,3) 63 43.77 34.80
EVCP (6,3,3) 105 105 48.81
EVCP (9,3,3) 172 185.43 60.44
EVCP (10,3,3) 400 945.02 339.16
EVCP (15,1,3) 781 1267.95 467.37
EVCP (20,4,3) 1071.66 1872.87 624.77
EVCP (20,4,4) 5014 6488.56 2922.91
EVCP (20,3,3) 1402 1868.76 1115.66
QA: Quantum Annealing, GA: Genetic Algorithm
‡‡ Proposed: Integration of QA and GA
C. Parameter Search
The Lagrange parameters for the QUBO were optimized us-
ing a Bayesian search which aimed to minimize the score form
the scoring metric described in Section IV-A and IV-B. This
parameter search is a necessary step since the performance of
the algorithm is very dependent on these parameters. However,
this is a very computationally expensive step, and thus it is
not scalable to carry out this search every time the algorithm
is run. Optimal parameters change based on the problem size
and number of points quite drastically, hence the same values
can not be used except for specifically chosen problem sets.
V. EX PE RI ME NTAL RE SU LTS A ND DISCUSSIONS
Experimental evaluations were performed using D-Wave
Quantum Annealing along with the two other techniques as
follows:
1) Only Quantum Annealing
2) Only Genetic Algorithm
3) Integration of Quantum Annealing and Genetic Algorithm
The first evaluation is based on the score described in Section
IV-A of the aforementioned techniques over a few differently
sized datasets. The authors have named the sample datasets as
EV C P (nP OI , nch old, nch new), where nP OI ,nch old and
nch new are the no. of POI, no. of existing charging stations
and no. of new charging stations to be placed respectively.
Experiments were performed over a few sample data sets with
grid size of 15×20, 30×30 and 100×100 are as follows:
1) 15×20 grid: EVCP (5,2,3), EVCP (5,3,3), EVCP (6,3,3),
EVCP(9,3,3)
2) 30×30 grid: EVCP (10,3,3),EVCP (15,1,3),EVCP (20,4,3),
EVCP (20,3,3)
3) 100×100 grid: EVCP (20,4,4)
Table I illustrates the score of the proposed hybrid algorithm
(integration of quantum annealing and genetic algorithm) over
only quantum annealing and only genetic algorithm on the
sample EVCP datasets. It is also clear from Fig. 4 and Fig. 5
that the advantage provided by the genetic approach is greater
when the grid size is larger. The authors suspect this isn’t
due to the GA performing better on larger datasets, but rather
due to the limited size of the Bayesian search in finding the
5
EVCP(5,2,3) EVCP(5,3,3) EVCP(6,3,3) EVCP(9,3,3)
EVCP Sample Datasets
0
50
100
150
200
Score
Only QA
Only GA
Proposed QA+GA
Fig. 4. Comparison Results of Only QA, Only GA and Proposed QA+GA
for EVCP sample datasets: EVCP (5,2,3), EVCP (5,3,3), EVCP (6,3,3),
EVCP (9,3,3). The lower the score, the better the performance
EVCP(10,3,3) EVCP(15,1,3) EVCP(20,4,3) EVCP(20,4,4) EVCP(20,3,3)
EVCP Sample Datasets
0
1000
2000
3000
4000
5000
6000
7000
Score
Only QA
Only GA
Proposed QA+GA
Fig. 5. Comparison Results of Only QA, Only GA and Proposed QA+GA
for EVCP sample datasets: EVCP (10,3,3), EVCP (15,1,3), EVCP (20,4,3),
EVCP (20,3,3), EVCP (20,4,4). The lower the score, the better the perfor-
mance
Lagrange parameters for the quantum annealing. This is mostly
a temporal constraint, as the run time for the search was very
high for the 100×100 grid EVCP (20,4,4) sample dataset, and
it might have even been possible to find an exact solution in
that time. With our proposed quantum annealing + genetic
algorithm approach, however, it is possible to get good results
without an extensive parameter search, and that saves on a lot
of time. It should also be mentioned that the search for the
right parameters was run on QBSolv [9], a simulator provided
by D-Wave Systems. This is due to the limited compute time
available on the Leap hybrid solvers [5].
After confirming the increase in performance (Fig. 4 and
Fig. 5), the best score per epoch were also calculated and
plotted for the randomly seeded and Quantum annealing
seeded algorithms as shown in Fig. 4 and Fig. 5. The largest
dataset taken by us for the experimental evaluations contains
a100 ×100 grid and 20 POI.
It can be clearly illustrated from Fig. 6 that the training
process is much more stable and the convergence is much
quicker for the Quantum annealing seeded process. The dis-
advantage of this proposed hybrid method however is that the
total time is the sum of both quantum annealing and the genetic
0 100 200 300 400 500 600 700 800 900 1000
Generations
0
0.5
1
1.5
2
2.5
3
3.5
4
Fitness
Only GA
Proposed QA+GA
Fig. 6. Plot of fitness vs generation using (a) Only Genetic Algorithm and
(b) Integration of Quantum Annealing and Genetic Algorithm
algorithm, so in situations which are extremely time sensitive,
this approach is not the best. However, in larger data sets, the
time taken for the genetic algorithm is trivial compared to the
quantum annealing part of the hybrid algorithm.
It should be noted that the genetic algorithm was run for
100 generations when seeded by the quantum annealing, while
for 1000 generations when randomly seeded for these results
(Table I). All other parameters were kept constant.
The authors tested the performance of these proposed
strategies on the EVCP sample datasets, and saw that the
scores were significantly improved as compared to a vanilla
quantum annealing, with an average improvement in score of
42.89% across all the data sets tested on, based on minimum
distance to POI. For each dataset, the score for each computing
method was the average over five runs. This is quite a great
result when looked at face value, however it has to be noted
that the Bayesian search could not be performed extensively
on larger datasets, which led to a decrease in performance
of Quantum Annealing. This is because it is not possible
to run the Bayesian search effectively for larger grid sizes,
due to extremely high computation times. The other factor to
note here is the lack of research done in Quantum annealing
with regards to the EVCP, which points to the fact that
improvements on the purely quantum end are sure to be made
there.
VI. CONCLUSION AND FUTURE WO RK S
This work started with the aim of improving the perfor-
mance of quantum annealing in solving the EVCP problem.
In trying to do so, the authors have come up with strategies that
might be usable beyond just this problem and can be applicable
to multiple NP hard problems. Based on experimental results,
the authors mentioned findings that seeding a evolutionary
genetic algorithm with the results of a quantum annealing
provides a decrease in minimum distance from POI of 42.89%
compared with QA and 57.54% compared to a randomly
seed GA. The algorithm outlined above shows great promise
in terms of making quantum annealing usable in the near
term. The authors therefore think that both the inclusion of
an entropic optimization function in the QUBO formulation,
as well as the seeding of genetic algorithm using quantum
6
annealing needs to be tested on other problems that can be
solved using quantum annealing.
VII. ACKN OWLEDGEMENTS
The authors would like to thank D-Wave Systems for
continuous support and providing our team the platform to
perform experiments using D-Wave Quantum Computers. Also
a big thanks to Naman Jain from Artificial Brain Team for
helping review the paper and bringing up great points during
the process.
REFERENCES
[1] Henrik Fredriksson and Mattias Dahl and Johan Holmgren, “Optimal
placement of Charging Stations for Electric Vehicles in large-scale
Transportation Networks, journal = Procedia Computer Science,” vol. 160,
pp. 77–84, 2019, the 10th Int. Conf. on Emerging Ubiquitous Systems
and Pervasive Networks (EUSPN-2019) / The 9th Int. Conf. on Current
and Future Trends of Information and Communication Technologies in
Healthcare (ICTH-2019) / Affiliated Workshops. [Online]. Available:
https://www.sciencedirect.com/science/article/pii/S1877050919316618
[2] J. He, H. Yang, T.-Q. Tang, and H.-J. Huang, “An optimal
charging station location model with the consideration of electric
vehicle’s driving range,” Transportation Research Part C: Emerging
Technologies, vol. 86, pp. 641–654, 2018. [Online]. Available:
https://www.sciencedirect.com/science/article/pii/S0968090X17303558
[3] J¨
org, Thomas and Krzakala, Florent and Kurchan, Jorge and Maggs,
Andrew Colin, “Quantum Annealing of Hard Problems,” Progress of
Theoretical Physics Supplement, vol. 184, p. 290–303, 2010. [Online].
Available: http://dx.doi.org/10.1143/PTPS.184.290
[4] “Placement of Charging Stations,” https://github.com/dwave-examples/
ev-charger-placement, Accessed on October 20, 2021.
[5] “D-Wave Leap Solver,” https://cloud.dwavesys.com/leap/login/?next=
/leap/, Accessed on October 20, 2021.
[6] Pagany, Raphaela and Marquardt, Anna and Zink, Roland, “Electric
Charging Demand Location Model—A User- and Destination-Based
Locating Approach for Electric Vehicle Charging Stations,” Sustainability,
vol. 11, no. 8, 2019. [Online]. Available: https://www.mdpi.com/
2071-1050/11/8/2301
[7] “D-Wave Systems,” https://docs.dwavesys.com/docs/c gs 2.html,
AccessedonOctober20,2021.
[8] S. M. Elsayed, R. A. Sarker, and D. L. Essam, “A new genetic
algorithm for solving optimization problems,” Engineering Applications
of Artificial Intelligence, vol. 27, pp. 57–69, 2014. [Online]. Available:
https://www.sciencedirect.com/science/article/pii/S0952197613001875
[9] “QBSolv,” https://docs.ocean.dwavesys.com/projects/qbsolv/en/latest/
,AccessedonOctober22, 2021.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
In recent years, with the increased focus on climate protection, electric vehicles (EVs) have become a relevant alternative to conventional motorized vehicles. Even though the market share of EVs is still comparatively low, there are ongoing considerations for integrating EVs in transportation systems. Along with pushing EV sales numbers, the installation of charging infrastructure is necessary. This paper presents a user- and destination-based approach for locating charging stations (CSs) for EVs—the electric charging demand location (ECDL) model. With regard to the daily activities of potential EV users, potential positions for CSs are derived on a micro-location level in public and semipublic spaces using geographic information systems (GIS). Depending on the vehicle users’ dwell times and visiting frequencies at potential points of interest (POIs), the charging demand at such locations is calculated. The model is mainly based on a survey analyzing the average time spent per daily activity, regional data about driver and vehicle ownership numbers, and the georeferenced localization of regularly visited POIs. Optimal sites for parking and charging EVs within the POIs neighborhood are selected based on walking distance calculations, including spatial neighborhood effects, such as the density of POIs. In a case study in southeastern Germany, the model identifies concrete places with the highest overall demand for CSs, resulting in an extensive coverage of the electric energy demand while considering as many destinations within the acceptable walking distance threshold as possible.
Article
Full-text available
Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems for which the efficiency can be studied analytically using techniques based on the statistical mechanics of spin glasses.
Article
Reasonable charging station positions are critical to prompt the widespread use of electric vehicles (EVs). This paper proposes a bi-level programming model with the consideration of EV's driving range, for finding the optimal locations of charging stations. In this model, the upper level is to optimize the position of charging stations so as to maximize the path flows that use the charging stations, while the user equilibrium of route choice with the EV's driving range constraint is formulated in the lower level. In order to find the optimal solution of the model efficiently, we reformulate the proposed model as a single-level mathematical program and further linearize it in designing the heuristic algorithm. The model validity is demonstrated with numerical examples on two test networks. It is shown that the vehicle's driving range has a great influence on the optimal charging station locations.
Article
Over the last two decades, many different genetic algorithms (GAs) have been introduced for solving optimization problems. Due to the variability of the characteristics in different optimization problems, none of these algorithms has shown consistent performance over a range of real world problems. The success of any GA depends on the design of its search operators, as well as their appropriate integration. In this paper, we propose a GA with a new multi-parent crossover. In addition, we propose a diversity operator to be used instead of mutation and also maintain an archive of good solutions. Although the purpose of the proposed algorithm is to cover a wider range of problems, it may not be the best algorithm for all types of problems. To judge the performance of the algorithm, we have solved aset of constrained optimization benchmark problems, as well as 14 well-known engineering optimization problems. The experimental analysis showed that the algorithm converges quickly to the optimal solution and thus exhibits a superior performance in comparison to other algorithms that also solved those problems.
Optimal placement of Charging Stations for Electric Vehicles in large-scale Transportation Networks, journal = Procedia Computer Science
  • Henrik Fredriksson
  • Mattias Dahl
  • Johan Holmgren
Henrik Fredriksson and Mattias Dahl and Johan Holmgren, "Optimal placement of Charging Stations for Electric Vehicles in large-scale Transportation Networks, journal = Procedia Computer Science," vol. 160, pp. 77-84, 2019, the 10th Int. Conf. on Emerging Ubiquitous Systems and Pervasive Networks (EUSPN-2019) / The 9th Int. Conf. on Current and Future Trends of Information and Communication Technologies in Healthcare (ICTH-2019) / Affiliated Workshops. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1877050919316618