Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective

Approach to Grid Stability and User Satisfaction

Aimen Khiar

1,2 a

, Mohamed-el-Amine Brahmia

1 b

, Ammar Oulamara

3 c

and Lhassane Idoumghar

2 d

CESI Lineact UR 7527, Strasbourg, France

IRIMAS UR 7499, University of Haute-Alsace, Mulhouse, France

LORIA UMR 7503, University of Lorraine, Nancy, France

Keywords:

Electric Vehicle, Charging Station Allocation, Multi-Objective Optimization, Scheduling, Metaheuristics,

NSGA-II, MOCS.

Abstract:

The transition to electric mobility offers substantial environmental beneﬁts but also introduces signiﬁcant chal-

lenges, particularly in managing the high demand for electric vehicle (EV) charging. This demand creates the

need for intelligent scheduling to optimize charging station resources and maintain grid stability. In order to

address this purpose, we propose a multi-objective scheduling model designed to both minimize peak energy

consumption and maximize user satisfaction by reducing waiting times at charging stations. Our model ac-

curately represents real-world scenarios, including sequential charger usage, vehicle-to-charger compatibility,

and limited availability of various charger types, each providing a constant power output. Given the complex-

ity of the problem, we adapt and evaluate two metaheuristic algorithms: the Non-Dominated Sorting Genetic

Algorithm-II (NSGA-II) and the Multi-Objective Cuckoo Search (MOCS), to approximate optimal solutions.

The results show that the proposed MOCS adaptation surpasses that of NSGA-II in terms of dominance and

achieving a well-distributed Pareto front approximation in a reasonable time frame. The proposed approach

thus provides a powerful framework for efﬁcient EV charging management, balancing user needs with grid

stability and highlighting its strong potential for adoption in large-scale charging infrastructures.

1 INTRODUCTION

As global environmental concerns intensify due to

factors like air pollution and climate change, Electric

vehicles (EVs) have emerged as a promising alterna-

tive to combustion engine vehicles, as they signiﬁ-

cantly reduce a major part of our environmental im-

pact (Electric Power Research Institute, 2023). This

shift has led to a substantial rise in the number of EVs

on the market. For instance, the International Energy

Agency (IEA) predicts that EV sales will reach ap-

proximately 17 million units by 2024 (International

Energy Agency (IEA), 2024).

However, while EVs show great promise, the main

obstacle to their widespread adoption is the long time

required to fully charge their battery. This delay re-

https://orcid.org/0009-0002-2724-223X

https://orcid.org/0000-0003-0114-210X

https://orcid.org/0000-0003-2357-0404

https://orcid.org/0000-0001-8853-3968

sults in several challenges, including electrical grid

overload, ﬂuctuations in electricity prices, and re-

duced customer satisfaction. To address these chal-

lenges, smart charging systems, also known as coordi-

nated charging, have become critically important. Co-

ordinated charging refers to ﬁnding optimal plans for

charging vehicles in a way that maximizes resource

efﬁciency, where schedules are generated by a control

system, also known as an aggregator. In contrast, un-

coordinated charging occurs when clients use charg-

ers freely without controlled energy distribution. This

is known as the Electric Vehicle Charging Schedul-

ing Problem (EVCSP), which involves minimizing

(or maximizing) one or more objectives while respect-

ing imposed constraints.

The literature on this topic is considerably rich,

with numerous studies conducted on the problem. For

example, (Khiar et al., 2025) proposed a multiobjec-

tive optimization approach for grid stability, by mini-

mizing the grid overload and maximizing the deliv-

ered energy to clients and proposed a MOCS vari-

146

Khiar, A., Brahmia, M.-E.-A., Oulamara, A. and Idoumghar, L.

Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective Approach to Grid Stability and User Satisfaction.

DOI: 10.5220/0013236400003893

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 14th International Conference on Operations Research and Enterprise Systems (ICORES 2025), pages 146-155

ISBN: 978-989-758-732-0; ISSN: 2184-4372

ant to approximate the optimal Pareto front. (Ren

et al., 2024) proposed an Adaptive Robust Optimiza-

tion model to address the uncertainty in EV charging

demands, focusing on minimizing grid overload. Inte-

ger programming techniques were employed by (Zhu

et al., 2014) and (An et al., 2023) to minimize the ﬁnal

charging time of vehicles. (Zaidi et al., 2024) devel-

oped a Mixed-Integer Linear Programming model to

minimize electric grid capacity and used a hybrid it-

erative local search metaheuristic to approximate the

optimal schedule. Additionally, (Mishra et al., 2023)

introduced a multi-objective optimization framework

for EV charge scheduling, aiming to maximize proﬁt

and customer satisfaction by utilizing a Satisﬁabil-

ity Modulo Theory solver for optimal solutions and

the NSGA-II Algorithm to approximate the Pareto

front. (Liu et al., 2019) improved a multi-objective

self-adaptive differential evolution algorithm and ap-

plied it to optimize the fueling of hybrid EVs, aim-

ing to minimize fuel consumption and emission load.

(Chen et al., 2023) developed a multi-objective opti-

mization scheduling model aimed at minimizing dis-

tribution network operating costs, reducing net load

variance, and maximizing the photovoltaic consump-

tion rate. They proposed an extension of the NSGA-

II Algorithm called NSGA-II-NDAX to approximate

the Pareto front.

This paper proposes a multi-objective scheduling

model for EV charging where interruptions are not al-

lowed during the charging process, aiming to mini-

mize grid capacity usage and client service times un-

der realistic scheduling conditions. The structure of

this paper is as follows: In section 2, we describe

the problem under study, while section 3 develops the

mathematical formulation of our model. Section 4 de-

scribes the metaheuristic techniques employed to ap-

proximate the Pareto front. In section 5, we provide

numerical experiments to compare the performance

of the proposed methods, and ﬁnally, section 6 con-

cludes the paper.

2 PROBLEM DESCRIPTION

In smart charging systems for EVs, aggregators or

control systems play an important role in optimizing

charging within the broader energy grid. These sys-

tems act as intermediaries between resources and EV

owners, gathering data such as energy requirements

(in kilowatt-hours, kWh) and expected arrival times.

Aggregators use this information to design optimal

charging schedules for each vehicle and to commu-

nicate charging or discharging instructions to the con-

nected chargers.

In this study, we address the EVCSP using a bi-

criteria optimization approach. Our aim is to schedule

EV charging requests in a way that balances two key

objectives:

1. Minimizing service times enhances customer

satisfaction, fosters customer loyalty, and unlocks

new business opportunities.

2. Preventing grid overload through efﬁcient re-

source utilization and energy distribution by min-

imizing instantaneous energy demand, commonly

referred to as grid capacity.

We consider a charging infrastructure consisting

of a limited number of chargers, each delivering a

constant power output and becoming available at pre-

deﬁned times. Charging durations are assumed to be

linear and deterministic. The goal is to determine a

feasible assignment of vehicles to chargers, while ac-

counting for compatibility factors such as port com-

patibility, charging speed, and power delivery proto-

cols.

Recall that in multi-objective optimization, a so-

lution is said to dominate another if it performs bet-

ter in at least one objective while being no worse in

all others. A solution is considered Pareto optimal

if no objective can be improved without degrading

at least one other objective. In other words, a solu-

tion is Pareto optimal if it is not dominated by any

other solution. The set of all such solutions forms the

Pareto front, representing the best possible trade-offs

between competing objectives. It is important to note

that the objectives at hand are conﬂicting, that is, min-

imizing one tends to maximize the other. Therefore,

the optimization model seeks to ﬁnd the Pareto front.

For illustration purposes, ﬁgure 1 shows a feasi-

ble schedule for charging 30 vehicles on 7 chargers.

The x-axis represents time, and the y-axis represents

chargers with the power they deliver. The blue lines

represent the chargers’ availability, and at the bottom

of the schedule, we indicate for each vehicle the ex-

pected arrival and the required energy expressed in

kWh.

Summarizing, each client provides the aggregator

with their expected arrival time and required energy.

Using this information, along with data on chargers,

the aggregator creates balanced charging schedules.

Each schedule speciﬁes the charging start time for

each vehicle, and energy transmission continues unin-

terrupted until the required energy is fully delivered.

Once a vehicle completes its charging session, its

charger becomes available for another use. The next

section presents our proposed mathematical model.

Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective Approach to Grid Stability and User Satisfaction

147

Figure 1: Example of a Schedule of 30 Vehicles on 7 Chargers.

3 MATHEMATICAL MODELING

The scheduling problem under study is deﬁned on

a discrete time horizon, subdivided into equal time

units of length τ (in hours). We shall model this

latter using the set of strictly positive integers N

∗

{

1,2,3,....

}

It is important to note that small values of τ make

the scheduling operation more ﬂexible since they of-

fer more options for the model in ordering the vehi-

cles, and as τ becomes small, we approach continuous

time scheduling.

An instance of the problem under study is charac-

terized by a set of n charging requests. The charging

operations of a vehicles are characterized by two main

parameters, namely the expected arrival time a

(v)

and

required energy amount e

, expressed in kWh. The

charging infrastructure comprises m chargers. The j

charger provides a constant power of w

and being

available at time a

(c)

. The assignability of a vehicle

i to charger j as described in the preceding section is

represented by binary constants δ

i, j

, where δ

i, j

= 1 if

the i

vehicle is assignable to the j

charger, and 0

otherwise. Without loss of generality, we suppose that

each vehicle is assignable to at least one charger, i.e

∀i ∈

{

1,2, ·· · ,n

}

∑

j=1

i, j

≥ 1

Given the discrete scheduling horizon and under

the linear deterministic charging time assumption, if

vehicle i is assigned to charger j, it must deliver

power for at least

hours to meet the required en-

ergy. Consequently, the number of time units re-

quired to serve vehicle i by charger j is given by

i, j

τw

, where

⌈

⌉

denotes the ceiling function.

These energy units are delivered consecutively. Re-

ferring back to ﬁgure 1, red dots represent these en-

ergy units.

We deﬁne the decision variables t

(s)

for all

i ∈

{

1,2, ·· · ,n

}

representing the charging beginning

time of vehicle i. We also deﬁne the binary de-

cision variables y

i, j

for all (i, j) ∈

{

1,2, ·· · ,n

}

{

1,2, ·· · ,m

}

that takes 1 if and only if vehicle i is

assigned to charger j. Each vehicle must be plugged

into a compatible charger, giving the constraints

∀i ∈

{

1,2, ·· · ,n

}

∑

j=1

i, j

= 1 (1)

and

∀(i, j) ∈

{

1,2, ·· · ,n

}

{

1,2, ·· · ,m

}

: y

i, j

≤ δ

i, j

(2)

The ﬁnal charging time of vehicle i denoted as t

(e)

is expressed by

(e)

= t

(s)

∑

j=1

i, j

− 1

Thus, the number of vehicles that use charger j at

time t is given by

∑

i=1

i, j

(t), where 1

represents

the indicator function of the set A. If two vehicles are

assigned to the same charger, then their usage periods

of the charger cannot overlap; this is explained by the

constraints

∀( j,t) ∈

{

1,2, ·· · ,m

}

× N

∗

∑

i=1

i, j

(t) ≤ 1 (3)

where T

(s)

+ 1,··· ,t

(e)

denotes the

charging period of vehicle i.

Additionally, the charging of vehicle i must be-

gin after the vehicle’s arrival date, which means t

(s)

≥

(v)

. Moreover, it cannot begin charging before the

ICORES 2025 - 14th International Conference on Operations Research and Enterprise Systems

148

assigned charger becomes available, that is, t

(s)

≥

∑

j=1

(c)

i, j

. This gives us the constraints

∀i ∈

{

1,2, ·· · ,n

}

: t

(s)

≥ max

(v)

∑

j=1

(c)

i, j

(4)

Denote by w

the maximum instantaneous en-

ergy consumption during the entire schedule, which

is the grid capacity that we aim to minimize and rep-

resents the ﬁrst objective function. The power con-

sumed at time slot t by all vehicles is expressed by

∑

j=1

∑

i=1

i, j

(t). Thus,

= max

t∈N

∗

∑

j=1

∑

i=1

i, j

(t)

(5)

The second objective is simply the sum of the

charging end times of the vehicles, which is given by

(e)

∑

i=1

(e)

(6)

The multi-objective optimization problem is to

minimize the objective functions (5) and (6) subject

to the constraints (1), (2), (3) and (4).

An important consideration is the time complex-

ity of the optimization process. By formulating a de-

cision version of the optimization problem, one can

show that identifying a feasible solution to this deci-

sion problem is strongly NP-Hard, even in the case of

identical chargers, via a reduction to the bin-packing

problem. Given this computational challenge, we are

motivated to explore approximation techniques, such

as nature-inspired metaheuristics, to approximate the

Pareto front within a reasonable time frame. The next

section will outline the speciﬁc adopted solving meth-

ods.

4 SOLVING METHODS

An adaptation of metaheuristics to combinatorial op-

timization problems, which are initially designed for

real-valued function optimization, involves deﬁning

the algorithmic structure of a feasible solution and the

operators needed to explore the feasibility space ac-

cording to the chosen algorithm. This section presents

the solving methods considered for our optimization

problem.

Given that we are dealing with a bi-objective con-

strained optimization problem, the NSGA-II algo-

rithm, proposed in (Deb et al., 2002), appears to be

a suitable candidate approach. We also consider an

adaptation of the MOCS algorithm proposed in (Yang

and Deb, 2013) and compare both metaheuristics in

the next section.

4.1 Non-Dominated Sorting Genetic

Algorithm II

Genetic algorithms (GA) are metaheuristics inspired

by the process of natural selection and are part of

the larger class of evolutionary algorithms, ﬁrst estab-

lished by Holland’s seminal work, (Holland, 1992).

These algorithms address optimization problems by

iteratively evolving a population of solutions using

three main operators: selection, crossover, and mu-

tation. The process starts with a random population

and iteratively:

1. Selects promising individuals

2. Creates offspring through crossover and mutation

3. Updates the population based on ﬁtness

This cycle continues until meeting speciﬁed stop-

ping criteria.

In the realm of multi-objective optimization, (Deb

et al., 2002) introduced the NSGA-II algorithm, a sig-

niﬁcant advancement in the ﬁeld of evolutionary op-

timization algorithms. NSGA-II has gained popular-

ity as one of the most widely applied nature-inspired

metaheuristics for solving multi-objective problems.

The core mechanism of NSGA-II revolves around

the principle of Pareto dominance, which serves as a

fundamental comparison criterion between different

solutions. Non-dominated sorting is a key process in

this algorithm, where solutions are classiﬁed based on

their dominance relationships. The objective is to cat-

egorize solutions into distinct ”fronts” according to

their level of dominance. The ﬁrst front is composed

of all non-dominated solutions, representing the opti-

mal trade-offs among the multiple objectives. Subse-

quent fronts are formed by identifying solutions that

are dominated only by those in the preceding fronts,

thus creating a hierarchy of solutions that reﬂects their

relative quality.

In addition to non-dominated sorting, NSGA-II

incorporates a mechanism known as crowding dis-

tance. This measure quantiﬁes the proximity of an in-

dividual solution to its neighbors within the objective

space. Solutions with higher crowding distance val-

ues are considered superior because they contribute

to a diverse set of solutions, which is important for

exploring the solution space effectively. By promot-

ing diversity, NSGA-II encourages the search pro-

cess to identify a well-distributed approximation of

the Pareto front.

The algorithm begins with an initial parent pop-

ulation consisting of pop

size

solutions. In each itera-

tion, an offspring population of the same size is gener-

ated from the parent population through the use of se-

lection, crossover, and mutation operators. After the

Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective Approach to Grid Stability and User Satisfaction

149

Figure 2: Flowchart of NSGA-II Algorithm.

crossover operation, mutation is applied to each off-

spring with a probability pm

∈ (0,1). Subsequently,

the parent and offspring populations are combined,

followed by the application of non-dominated sorting.

The top pop

size

solutions from this combined popula-

tion are then selected based on their dominance levels

to form the next parent population. The ﬂowchart il-

lustrating the algorithm’s process is presented in ﬁg-

ure 2.

For a more comprehensive overview of the algo-

rithm and the underlying concepts, we refer the reader

to (Deb et al., 2002).

4.2 Multi-Objective Cuckoo Search

Algorithm

The cuckoo search algorithm is a nature-inspired

metaheuristic, developed by (Yang and Deb, 2009)

for mono-objective optimization. It is inspired by the

breeding behavior of a type of bird called cuckoos,

which lay their eggs in the nests of other birds. These

cuckoos search for nests of host birds that have eggs

similar to cuckoo eggs, maximizing the chance that

their eggs are not discovered by the host bird. Each

egg in a nest represents a solution, and a cuckoo egg

represents a new solution. The aim is to use these

new and potentially better solutions (cuckoos) to re-

place suboptimal solutions in the nests, resulting in a

better population of eggs that can survive over more

generations. The main assumptions of the algorithm

are:

1. Each cuckoo lays one egg at a time and drops it in

a randomly chosen nest.

2. The best nests with high-quality eggs will carry

over to the next generations.

3. The number of available host nests is ﬁxed.

4. The egg laid by a cuckoo is discovered by the host

bird with a probability p

∈ (0, 1). In this case, the

host bird can either throw the egg away or aban-

don the nest and build a completely new nest.

Later, they proposed a generalization of the algo-

rithm to tackle multi-objective optimization problems

in (Yang and Deb, 2013), where the ﬁrst and last as-

sumptions are modiﬁed respectively as follows:

1. Each cuckoo lays K eggs at a time and drops its

eggs in randomly chosen nests.

2. Newly generated nests contain K eggs, represent-

ing the new solutions.

Here, K represents the number of objective func-

tions (in our case, K = 2). For simplicity, the last

assumption of the algorithm can be approximated by

replacing a fraction p

of the n nests with new nests

(i.e., new random solutions).

Additionally, various studies have shown that the

ﬂight behavior of many animals and insects exhibits

characteristics of L

evy ﬂights, which are random

walks governed by the L

evy distribution. Yang and

Deb incorporated these L

evy ﬂights to generate new

solutions (cuckoo eggs) in their continuous optimiza-

tion algorithm. For a more comprehensive overview

of these algorithms and the underlying concepts, we

refer the reader to (Yang and Deb, 2009) and (Yang

and Deb, 2013).

Since L

evy ﬂights are suitable only for continu-

ous domain optimization, we adapted the algorithm

for combinatorial optimization by deﬁning a special-

ized operator to ﬁnd new solutions. The algorithm’s

ﬂowchart is illustrated in ﬁgure 3.

4.3 Generating a Random Feasible

Schedule

Each feasible schedule for our optimization model is

represented by a n × 3 matrix, where each row i con-

tains respectively: the assigned charger for vehicle i,

ICORES 2025 - 14th International Conference on Operations Research and Enterprise Systems

150

Figure 3: Flowchart of MOCS Algorithm.

the charging start time t

(s)

, and the charging end time

(e)

. Although t

(e)

can be derived from the ﬁrst two

elements, it is included separately to optimize calcu-

lations.

Generating a random feasible schedule can be

achieved by repeatedly selecting a vehicle, a compat-

ible charger, and a possible charging period at ran-

dom until all vehicles are scheduled. Suppose that

we need to schedule vehicle i on charger j. Assume

that there is at least one vehicle already scheduled on

charger j, and let n

≥ 1 represent the number of ve-

hicles already scheduled to charge on that charger, or-

dered according to their charging order as i

,...,i

Then, there are at most n

+ 1 possible charging ses-

sions denoted S

for k ∈



1,2, ·· · ,n

+ 1



, for vehi-

cle i on that charger. A ”charging session” refers to a

time frame during which the charger is being free, and

charging start time for vehicle i can be chosen which

determines its charging period. The possible charging

sessions can be one of the three cases

1. Session S

: between t

= max



(c)

(v)



and the

charging start time of vehicle i

,i.e

+ 1,··· ,t

(s)

− 1

2. Session S

for k ∈



2,3, ·· · ,n



: between the

charging periods of vehicle i

k−1

and i

,i.e

(e)

k−1

+ 1,t

(e)

k−1

+ 2,··· ,t

(s)

− 1

3. Session S

: after the charging period of the last

vehicle, i.e

(e)

+ 1,t

(e)

+ 2,···

Now, if n

= 0 (i.e., no vehicle is scheduled to

charge on charger j), there is only one candidate

charging session, namely

{

+ 1,···

}

. With this

in mind, the scheduling of vehicle i on charger j is

performed using algorithm 1.

Data: A schedule, a vehicle i ∈ {1,2, ... ,n}, a

compatible charger j ∈ {1, 2,.. .,m}, and

a positive number σ

Result: Start charging time t

(s)

of vehicle i on

charger j

1. Calculate n

;

if n

> 0 then

a. Set the list of candidate charging sessions

as:

H := {n

+ 1} ∪ {k ∈ {1,2,.. .,n

} |

| ≥ p

i, j

};

b. Choose a random index k uniformly from

if k = 1 then

Choose t

(s)

uniformly from the range

+ 1,. ..,t

(s)

− p

i, j

};

end

else if k ∈ {2, 3,.. .,n

} then

Choose t

(s)

uniformly from the range

(e)

k−1

+ 1,t

(e)

k−1

+ 2,. ..,t

(s)

− p

i, j

};

end

else

a. Generate a random number λ from

the normal distribution N (0, σ

);

b. Set t

(s)

= t

(e)

+ ⌈|λ|⌉ + 1;

end

else

a. Generate a random number λ from the

normal distribution N (0, σ

);

b. Set t

(s)

= t

+ ⌈|λ|⌉;

end

return t

(s)

;

Algorithm 1: Schedule a Vehicle on a Charger.

Notice that if n

> 0 and the last session (i.e.,

) is chosen, which contains an inﬁnite number of

Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective Approach to Grid Stability and User Satisfaction

151

choices for t

(s)

, then we set t

(s)

:= t

(e)

⌈|

|⌉

+ 1. If

= 0, then the unique charging session is also theo-

retically inﬁnite, and we set t

(s)

:= t

⌈|

|⌉

, where λ

is drawn from N



0,σ



. Here, as the standard devia-

tion σ increases, the probability of t

(s)

being large also

increases, which encourages schedules that are less

favorable to the second objective function (6), thereby

improving the exploration of the search space.

4.4 Selection Operator

We deﬁne the selection operator which is the mecha-

nism that chooses individuals from the population for

reproduction phase based on their ranks and crowding

distances. Given a population where non-dominated

sorting algorithm is already applied, we calculate

crowding distances for each solution. We rank each

solution by the order of the front they belong to, so-

lutions with rank 1 are the non-dominated solutions,

hence the smaller the rank, the better the solution is.

Next, we select randomly without replacement

two schedules from 1 to N =



pop

size



with probabil-

ity p

2(N−k+1)

N(N+1)

for k ∈

{

1,2, ·· · ,N

}

, where pop

size

is the population size. We then retain the schedule

with smaller rank. If both individuals belong to the

same rank, the individual with the greater crowding

distance is preferred; if their crowding distances are

equal, one of the individuals is selected arbitrarily.

4.5 Crossover Operator

Given two selected parent solutions saying S

and S

the crossover operator is done as follows

1. Construct the set of vehicles in schedule S

where

their assigned charger is free for use in schedule

on the same charging period in S

, denote this

set as M .

2. Create a new schedule S

′

by choosing randomly

without replacement



/3 vehicles from the set

M and copy their charging plan from S

to S

3. Apply steps 1 and 2 where now you interchange

the order of S

and S

and derive a schedule S

′

Steps 1 and 2 ensure that when exchanging ve-

hicles between schedules S

and S

, we do not get

overlapping charging periods while combining the in-

formation contained in each schedules.

4.6 Mutation Operator

Notice that the crossover operator maintain the same

charger for a vehicle if it is exchanged between two

schedules, hence to be sure that any feasible sched-

ule could be found by the algorithm, given a sched-

ule, we deﬁned the mutation operator to select ran-

domly

⌈

∗ pop

size

⌉

vehicles and than change their

charger randomly using algorithm 1, where pm

∈

(0,1) .

4.7 Finding a Neighbor Solution

Operator (for MOCS)

For a feasible schedule, the neighbor solution oper-

ator used in the MOCS algorithm is deﬁned by ran-

domly selecting

⌈

∗ n

⌉

vehicles and a compatible

charger for each vehicle (which can be the current

one), and scheduling the vehicle to charge on it us-

ing algorithm 1, where p

∈ (0, 1). Large values of p

tend to perturb more the schedule at hand, which we

also observed through experiments; thus, one needs

to carefully choose this latter to enhance the quality

of the exploitation of the search space.

5 EMPIRICAL EXPERIMENTS

In this section, we present numerical experiments to

compare the proposed approaches. The experiments

were carried out on a computer featuring an Intel®

Core™ i5-8350U CPU running at 1.70 GHz (with a

turbo boost of up to 1.90 GHz) and equipped with

8.00 GB of RAM.

We considered instances of varying sizes, speciﬁ-

cally 50,100,150 and 200 charging requests. For each

instance size, ﬁve random instances were generated,

ordered from 1 to 20. The instances were created with

the following parameters:

• The time slots length τ was set to 10 minutes.

• Vehicle arrivals were selected randomly start-

ing from 00 : 00, and the required energy of

each vehicle was sampled randomly from the set

{

20,30, 40,...,300

}

• The number of available chargers was set to m =





, and the delivered energy was chosen ran-

domly from the set

{

10,20, 30,40, 50

}

. Availabil-

ity times were selected randomly starting from

00 : 00.

• For experimentation purposes, we assumed that

vehicles are assignable to all chargers, i.e: δ

i, j

1 for all (i, j) ∈

{

1,2, ·· · ,n

}

{

1,2, ·· · ,m

}

The parameters of NSGA-II and MOCS were cho-

sen based on preliminary experimentation. We com-

pared each algorithm with itself by running it several

times on different instances of varying sizes, and we

ICORES 2025 - 14th International Conference on Operations Research and Enterprise Systems

152

Figure 4: Mean Percentage of Dominance Comparison.

selected the parameters that seemed to yield the best

results in terms of balancing a highly dominant ap-

proximation of the Pareto front with a well-distributed

spread of the best solutions.

For both algorithms, we used 300 generations per

instance with a population size of 200 schedules,

which proved sufﬁcient to achieve signiﬁcant conver-

gence for the instance sizes considered. As previ-

ously mentioned, higher values of the parameter σ

tend to increase service times, a trend we observed

throughout our experiments. Setting σ to 1 yielded

satisfactory results for both algorithms, likely because

smaller steps improved exploitation quality. Thus,

we used σ = 1 in our experiments. For NSGA-II,

we set the mutation probability pm

= 0.2 and the

proportion pm

= 0.05 for vehicle charger changes,

as higher values for pm

tend to excessively pertur-

bate the schedule at hand, an effect also observed ex-

perimentally. For MOCS, we found a proportion of

abandoned nests p

= 0.25 to work well across dif-

ferent instance sizes, with the proportion p

= 0.05

for changes in vehicle charging sessions.

In order to compare between NSGA-II and

MOCS, we calculated the mean percentage of dom-

inance between both methods for each instance. The

dominance percentage of NSGA-II over MOCS, for

example, is deﬁned as the number of solutions on

the approximated Pareto front found by MOCS that

are dominated by NSGA-II, divided by the total num-

ber of non-dominated solutions found by MOCS, and

then multiplied by 100.

If we focus on the solutions within the section

of the Pareto front approximation found by the ﬁrst

method that lies close to the approximation from the

second method and vice versa the mean dominance

percentage can serve as an indicator of solution qual-

ity. Moreover, if we consider the opposite sense, an

important metric to consider is the percentage of non-

dominance. This percentage represents the portion

of solutions on the Pareto front found by the ﬁrst

method that remain non-dominated by any solution

from the second method. This metric can be inter-

preted as a measure of how well the ﬁrst method ex-

Figure 5: Mean Execution Time Comparison.

plores the true Pareto front: a higher non-dominated

percentage indicates better performance compared to

the second method, as it signiﬁes that the ﬁrst method

is ﬁnding unique trade-offs not matched by the sec-

ond method. The percentage of non-dominance of

Method 1 against Method 2 is calculated as 100 mi-

nus the percentage of dominance of Method 2 against

Method 1. A lower dominance percentage of Method

1 compared to Method 2 indicates better performance

of the ﬁrst method relative to the second.

Another important metric for comparing opti-

mization algorithms is execution time. We present in

table 1 the mean dominance percentage and the mean

execution time, calculated over the 50 runs, with the

standard deviation in parentheses. The results are il-

lustrated in ﬁgure 4 and ﬁgure 5, respectively, with

the shaded area representing conﬁdence intervals.

Table 1: Numerical Results for Mean Percentage of Domi-

nance and Execution Time.

Mean percentage of dominance Mean execution time

Instances NSGA-II |MOCS MOCS |NSGA-II NSGA-II MOCS

1 3.62 (5.85) 95.6 (6.62) 1.68 (0.08) 1.91 (0.11)

2 3.01 (4.96) 95.52 (6.68) 1.66 (0.08) 1.8 (0.01)

3 4.79 (6.34) 93.57 (9.13) 1.59 (0.06) 1.76 (0.02)

4 2.96 (5.31) 95.39 (7.03) 1.5 (0.05) 1.76 (0.04)

5 8.43 (11.41) 88.25 (16.48) 1.54 (0.07) 1.77 (0.01)

6 9.25 (7.52) 86.96 (10.51) 2.8 (0.14) 3.01 (0.03)

7 8.12 (7.22) 89.12 (10.53) 2.93 (0.12) 3.26 (0.04)

8 12.53 (7.93) 82.35 (11.32) 2.78 (0.12) 3.08 (0.02)

9 9.79 (7.96) 85.6 (12.01) 2.82 (0.12) 3.08 (0.03)

10 10.17 (7.05) 86.16 (9.4) 2.73 (0.14) 3.01 (0.04)

11 15.93 (9.82) 76.31 (14.37) 4.56 (0.25) 4.84 (0.03)

12 21.04 (10.79) 68.86 (16.47) 4.65 (0.24) 4.78 (0.06)

13 17.54 (8.49) 74.71 (12.45) 4.67 (0.21) 4.87 (0.03)

14 18.55 (10.36) 71.55 (16.45) 4.69 (0.21) 4.8 (0.03)

15 18.3 (9.89) 75.19 (12.46) 4.5 (0.2) 4.72 (0.03)

16 25.73 (10.42) 64.0 (16.8) 6.76 (0.32) 6.62 (0.04)

17 24.34 (13.53) 62.8 (21.68) 6.82 (0.32) 6.7 (0.06)

18 23.41 (8.87) 66.2 (12.49) 6.53 (0.3) 6.44 (0.09)

19 22.37 (7.73) 69.16 (12.43) 6.68 (0.27) 6.45 (0.03)

20 25.77 (9.77) 63.93 (12.95) 6.47 (0.29) 6.35 (0.06)

We also illustrated in ﬁgures 6,7,8 and 9 the Pareto

front found by both methods on instances 5, 10, 15,

and 20, which are respectively of size 50, 100, 150,

and 200 requests.

The ﬁndings indicate that MOCS outperforms

NSGA-II in dominance metrics. Speciﬁcally, the

mean dominance percentage of MOCS over NSGA-

II is markedly higher than that of NSGA-II over

Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective Approach to Grid Stability and User Satisfaction

153

Figure 6: Comparison of Pareto Fronts Generated by Both

Methods for Instance 5.

Figure 7: Comparison of Pareto Fronts Generated by Both

Methods for Instance 10.

MOCS. This suggests that MOCS consistently ﬁnds

more solutions that dominate those produced by

NSGA-II, with many MOCS solutions remaining

non-dominated by NSGA-II. Across all instances, the

total mean dominance percentage of NSGA-II over

MOCS is 14.28%, compared to 79.56% for MOCS

over NSGA-II, with notably lower standard devia-

tions, reﬂecting consistency in performance.

Regarding execution time, NSGA-II exhibits

slightly faster performance than MOCS; however, this

difference is marginal, remaining under 0.33 seconds

across all instances, including larger cases. The stan-

dard deviation remains similarly low, indicating sta-

bility in computational efﬁciency.

Additionally, the ﬁgures 6,7,8 and 9 clearly illus-

trate that the Pareto front approximations generated

by MOCS are more extensive than those produced

by NSGA-II. This trend was consistently observed

across all executions and instances, suggesting that

MOCS provides greater diversity in trade-off solu-

Figure 8: Comparison of Pareto Fronts Generated by Both

Methods for Instance 15.

Figure 9: Comparison of Pareto Fronts Generated by Both

Methods for Instance 20.

tions along the Pareto fronts. Consequently, MOCS

provides a broader range of options for decision-

makers.

The results clearly indicate that the proposed

adaptation of MOCS is more effective than NSGA-

II in identifying satisfactory solutions within a rea-

sonable time frame for this speciﬁc problem. There

is potential to enhance both methods further by ex-

ploring alternative operator deﬁnitions, employing re-

ﬁned versions of each algorithm, as suggested by var-

ious studies in the literature, or by considering ad-

ditional population-based metaheuristics within the

multi-objective optimization framework. These ap-

proaches may yield even more promising outcomes,

which could be a focus of future research. Nonethe-

less, the proposed MOCS demonstrates signiﬁcant

promise and appears well-suited to the requirements

of the proposed model.

To support reproducibility and further research,

ICORES 2025 - 14th International Conference on Operations Research and Enterprise Systems

154

a GitHub repository

provides the Python imple-

mentations of both algorithms, optimized with the

Numba library. This repository includes instance sim-

ulations and test cases in Jupyter Notebook format.

Additionally, it offers Pareto front approximations

for both methods across all instances and executions,

alongside numerical data on dominance and execution

times.

6 CONCLUSION

In summary, this study presents an innovative

multi-objective optimization model for EV charging

scheduling, aiming to minimize peak energy con-

sumption and reduce charging times. By incorpo-

rating real-world factors such as sequential charger

usage, compatibility, and operational constraints, the

model provides a robust framework for optimiza-

tion. It allows decision makers to select from various

schedules on the Pareto Front, balancing grid stability

with client service times based on actual grid capabil-

ities.

We have adapted the NSGA-II and MOCS al-

gorithms to our model, with comparative analysis

demonstrating that MOCS is the more effective so-

lution in this context. MOCS achieves broader Pareto

front coverage within a reasonable time frame of less

than 7 seconds, with a dominance percentage averag-

ing 79.56% for MOCS over NSGA-II, compared to

only 14.28% for NSGA-II over MOCS.

The proposed model and MOCS adaptation have

signiﬁcant implications for real-world EV infrastruc-

ture, providing a scalable and efﬁcient solution to

meet the growing demands of electric mobility. Fu-

ture work may include exploring other metaheuristics

and solving methods, as well as investigating variable

charging powers and preemptive charging modes to

enhance scheduling ﬂexibility.

REFERENCES

An, Y., Gao, Y., Wu, N., Zhu, J., Li, H., and Yang, J.

(2023). Optimal scheduling of electric vehicle charg-

ing operations considering real-time trafﬁc condition

and travel distance. Expert Systems with Applications,

213:118941.

Chen, J., Mao, L., Liu, Y., Wang, J., and Sun, X. (2023).

Multi-objective optimization scheduling of active dis-

tribution network considering large-scale electric ve-

hicles based on nsgaii-ndax algorithm. IEEE Access,

11:97259–97273.

https://github.com/aikhiar/Minimizing-grid-capacity-

and-service-times

Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002).

A fast and elitist multiobjective genetic algorithm:

Nsga-ii. IEEE Transactions on Evolutionary Compu-

tation, 6(2):182–197.

Electric Power Research Institute (2023). Environmen-

tal assessment of a full electric transportation port-

folio: Executive summary. Retrieved April 29,

2024, from https://www.epri.com/research/products/

3002006881.

Holland, J. H. (1992). Adaptation in Natural and Artiﬁcial

Systems: An Introductory Analysis with Applications

to Biology, Control, and Artiﬁcial Intelligence. The

MIT Press.

International Energy Agency (IEA) (2024). Global ev out-

look 2024. IEA, Paris. Retrieved from https://www.

iea.org/reports/global-ev-outlook-2024.

Khiar, A., Brahmia, M.-e.-A., Oulamara, A., and

Idoumghar, L. (2025). Multi-objective approach for

efﬁcient grid resources allocation in electric vehi-

cle charging schedules. In Congr

es de la Soci

Franc¸aise de Recherche Op

erationelle et d’Aide

a la

ecision (ROADEF’25), Paris.

Liu, M., Wang, X., Sheng, Y., and Wang, L. (2019). Im-

provement of multi-objective differential evolutionary

algorithm and its application for hybrid electric vehi-

cles. In 2019 Chinese Control And Decision Confer-

ence (CCDC), pages 553–558.

Mishra, S., Mondal, A., and Mondal, S. (2023). A

multi-objective optimization framework for electric

vehicle charge scheduling with adaptable charging

ports. IEEE Transactions on Vehicular Technology,

72(5):5702–5714.

Ren, Y., Tan, M., Su, Y., Wang, R., and Wang, L. (2024).

Two-stage adaptive robust charging scheduling of

electric vehicle station based on hybrid demand re-

sponse. IEEE Transactions on Transportation Elec-

triﬁcation, pages 1–1.

Yang, X.-S. and Deb, S. (2009). Cuckoo search via l

evy

ﬂights. In 2009 World Congress on Nature & Biolog-

ically Inspired Computing (NaBIC), pages 210–214.

Yang, X.-S. and Deb, S. (2013). Multiobjective cuckoo

search for design optimization. Computers & Op-

erations Research, 40(6):1616–1624. Emergent Na-

ture Inspired Algorithms for Multi-Objective Opti-

mization.

Zaidi, I., Oulamara, A., Idoumghar, L., and Basset, M.

(2024). Minimizing grid capacity in preemptive elec-

tric vehicle charging orchestration: Complexity, exact

and heuristic approaches. European Journal of Oper-

ational Research, 312(1):22–37.

Zhu, M., Liu, X.-Y., Kong, L., Shen, R., Shu, W., and

Wu, M.-Y. (2014). The charging-scheduling prob-

lem for electric vehicle networks. In 2014 IEEE

Wireless Communications and Networking Confer-

ence (WCNC), pages 3178–3183.

Optimized Scheduling for Electric Vehicle Charging: A Multi-Objective Approach to Grid Stability and User Satisfaction

155