Timetable Generator Using Genetic Algorithm

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Timetable Generator Using Genetic Algorithm
Sahil Sarnaik1, Tanmay More2, Sanket Shinde3, Dipesh Shah4
1Student, Dept. Of Computer Engineering, AISSMS College Of Engineering, Pune, Maharashtra, India
------------------------------------------------------------***----------------------------------------------------------
Abstract- Timetable planning is a critical aspect of
efficient resource management in organizations and
businesses. While manual planning suffices for smaller-
scale operations, larger-scale endeavors require
computer-assisted planning to accurately accommodate
various constraints. However, human error can still affect
the overall efficiency of the organization. To overcome this
challenge, recent trends have seen the use of software
developed using genetic algorithms. The rapid
advancement of computing technologies that has fueled
the progress of artificial intelligence provides answers for
the notoriously difficult organizational conundrums
known as NP-hard problems, which arise frequently. As a
sophisticated category of algorithms modeled after
evolutionary mechanisms in nature that hone in on
optimal solutions, genetic algorithms emulate the process
of natural selection in a particularly ingenious fashion.
Existing software applications typically utilize a one-hour
timeframe and have several dependencies, such as XAMPP
server or an internet connection, to run the program
successfully. In contrast, our proposed software aims to
introduce a novel approach by utilizing a more optimized
half-hour timeframe. This enhancement addresses a
significant limitation of existing solutions and enables
finer-grained scheduling precision. By employing this
improved temporal resolution, our software endeavors to
provide more efficient and effective timetable generation.
In this regard, this research seeks to leverage evolutionary
algorithms, specifically genetic algorithms, combined with
adaptive and elite traits to create an artificial intelligence
system that can generate a university timetable. The aim
is to create the correct and best solution, considering a set
of rules, while minimizing human error and enhancing
efficiency.
Keywords- Artificial Intelligence, Genetic
Algorithm, Timetable Generation, Evolutionary
Algorithm, Optimization
I. INTRODUCTION
The process of scheduling involves creating a
plan that meets specific constraints based on the given
scenario. In the recent times, the scheduling of
timetables has been the subject of extensive research in
fields such as Operations Research and AI. Various
enhancement methods employed address these
problems, with the aim of generating solutions that are
either optimal or near-optimal rather than exact. It is
widely used in various industries such as transportation
planning and complex scheduling for automated
factories. While smaller jobs are typically scheduled
manually, larger projects require computerized planning.
The increasing computing power has led to the
rapid growth of Artificial Intelligence, which is becoming
increasingly popular. It is capable of addressing a wide
range of problems, including optimizing existing
solutions and devising innovative ones that were
previously impossible due to several limitations.
Artificial Intelligence can offer valuable solutions to
organizations and businesses by solving indeterminate
polynomial time problems.
GA emulates natural selection as an effective
method for optimization improvement. Although there
are various types of genetic algorithms, they all follow
the same basic principle. The primary aim of this
research is developing an Artificial Intelligence system
that leverages evolutionary algorithms, specifically a
genetic algorithm to generate a university timetable that
satisfies specific constraints while being both feasible
and optimal. Genetic algorithms have found applications
in various areas, including optimized searching and
scheduling processes. This algorithm is typically used
when optimization is the primary objective. In the case
of a timetable problem, the challenge involves
determining the precise timing allocation of a collection
of activities (like academic sessions and lectures) within
a limited time frame and assigning them to specific
resources (like instructors, learners and rooms)
adhering to certain guidelines.
This research paper employs a genetic algorithm
to generate the timetable for Engineering Faculty. The
algorithm features a dynamic chromosome size that can
be easily adjusted to account for the course numbers in
each department.
II. REVIEW OF LITERATURE
As per the findings of Asif Ansari [4], there are
multiple approaches available for solving scheduling
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 10 Issue: 11 | Nov 2023 www.irjet.net p-ISSN: 2395-0072

problems in the field of operational research. These
include techniques such as graph coloring and
mathematical programming, local search methods,
constraint satisfaction manipulation through taboo
searches and simulated cooling, as well as backtracking.
Genetic algorithm, a type of optimization algorithm, is an
evolutionary algorithm that builds upon traditional
methods.
According to Immanuel and Chakraborty
(2019), the genetic algorithm functions on the concept of
"survival of the fittest," where successive generations
produce enhanced solutions until an optimal solution is
achieved [7].
To efficiently create a timetable for an
engineering college, a genetic algorithm proves to be a
valuable tool. In their study, G. Alnowaini and A. A.
Aljoma [1] introduced a technique that incorporates
dynamic chromosome size, specifically designed for this
type of scheduling problem. The authors developed a
system that allows for the input of various elements,
including lecture halls, buildings, lecturers, levels and
departments. Additionally, they implemented
restrictions to govern the timetable creation process.
The main objective of the authors' research was to
address the timetabling challenges faced by universities
each academic year and mitigate the significant costs
associated with generating near-optimal timetables.
The genetic algorithm serves as a useful
approach for obtaining an optimal solution to scheduling
problems. In the reviewed papers, the system
administrator begins by signing into the system and
entering the courses along with their respective course
codes and units [2]. The administrator can continue
adding courses until the required number is reached,
and they also have the ability to delete any incorrectly
imported courses. Once the courses are entered, the
administrator proceeds to input all the rooms to be
utilized. Upon entering this information, the system
generates the timetable.
To expedite convergence, an adaptive mutation
scheme was used. The system design is compatible with
various operating systems, starting from Windows Vista.
However, for existing systems, the installation of the
XAMPP server is necessary. Popular internet browsers
such as Internet Explorer, Microsoft Edge, Google
Chrome, Opera Mini, and UC Browser are supported. The
development of the system utilized the following tools:
Supernatural Test 3 and XAMPP for implementing
existing software.
Although the genetic algorithm is widely
recognized as a highly effective approach for generating
schedules, it does not provide a guarantee of achieving a
100% optimal schedule. The degree of optimality is
contingent upon the specific constraints applied and the
adaptability of the parameters' adjustment function.
Despite involving multiple steps and potentially slower
execution, the utilization of the genetic algorithm is
favored due to its efficiency in generating schedules.
Timetable schedulers created through the
utilization of genetic algorithms may not be able to
address all given constraints, but they are proficient in
handling significant constraints, such as avoiding clashes
between two teachers within the same time slot. In the
study conducted by Shruthi. B (2020), the developed
system generates timetables specifically with a duration
of 1 hour, and it achieves an accuracy level of 80% [3].
A Genetic Algorithm (GA) problem involves
candidate solutions that are not necessarily optimal but
represent possible solutions. These solutions are
composed of one or more individual traits known as
chromosomes or genotypes, which undergo crossover or
mutation operations to generate new solutions for the
same problem [7]. Mutation is a divergent operation that
aims to explore new regions by altering one or more
members of the population, potentially leading to
improved solutions outside of the local minimum or
maximum space. In the crossover process, two parent
solutions are combined to produce offspring for each
case [4].
The crossover function plays a crucial role in
genetic algorithms (GA). It involves pairing genes from
each chromosome using a crossover operator to create
new generations. These offspring are then judged based
on their fitness scores to determine their qualification
for the next generation. Orong, Sison, and Medina [8]
proposed a new crossover mechanism known as cross-
average crossover. They integrated a rank-based
selection approach that enhances the effectiveness of
variable minimization, leading to promising results.
Qiongbing and Lixin [8] conducted a separate
study that introduced a distinct crossover mechanism
known as Same Adjacency crossover in the context of
genetic algorithms with variable-length chromosomes.
Same Adjacency crossovers aim to find more efficient
crossing pairs between parental chromosomes.
However, this mechanism requires additional
computational work, and the determination of
intersection points relies on information from
neighboring nodes.
A Java-based system was proposed by Shraddha
Shinde, Saraswati Gurav, and Sneha Karme [6] to
automate the process of generating timetables. In
addition to timetable generation, the system provides
additional features allowing users to request leave by
specifying the leave date, reason, and alternative faculty.
To implement this system, the installation of JSP and

MYSQL is required. The framework developed by the
authors appears to have broad applicability to various
other scheduling problems beyond timetabling.
According to Shraddha Thakare, Tejal Nikam,
and Mamta Patil [5], the key modules in the scheduling
procedure include:
1. Data encoding and decoding
2. Initial population
3. Evaluation of population
4. Crossover evolution
5. Mutation
6. New population
These modules are essential in the scheduling process
and serve as fundamental steps to generate efficient
schedules. The application of these modules extends to
various areas and timetable generation of any
organization.
After an extensive study of the papers on
timetable generation and scheduling, it is apparent that
the genetic algorithm plays a vital role in producing
optimal schedules while considering all the constraints
and rules. This algorithm not only saves time but also
eliminates the complexity associated with manual
timetable creation and management. Instead of relying
on tedious paperwork, students and faculty can access
the timetable quickly. By implementing a user-friendly
interface and utilizing a well-designed database, the
issue of manual timetable creation can be effectively
resolved. This approach enhances the efficiency of the
scheduling process and provides a convenient solution
for students and faculty to access and view timetables.
III. PROBLEM STATEMENT
The process of time scheduling is of the utmost
importance as it involves creating schedules that adhere
to specific constraints based on the given scenario. The
aim is to generate timetables that effectively
accommodate all relevant requirements and limitations.
While manual scheduling is still prevalent for small-scale
operations, larger ones often require computer-assisted
solutions. The rapid progress of computational capacities
has enabled artificial intelligence to arise as an appealing
informatic means for improving existing solutions or
exploring novel possibilities that had hitherto remained
unexplored owing to a plethora of constraints. In this
project, a university timetable scheduler will be
developed using a genetic algorithm that incorporates
adaptive and elitist traits. The objective is to generate a
solution that is both valid and optimal while satisfying
certain constraints.
IV. PROPOSED SYSTEM
A. Genetic Algorithm
A genetic algorithm (GA) is an
optimization algorithm of a numerical nature that arises
from the combination of natural selection and genetics.
Unlike conventional procedural methods, the approach
employed in this method is of a versatile nature, allowing
it to be applied to a broader spectrum of problems.
Genetic algorithms are instrumental in solving practical
real-life problems on a day-to-day basis. The algorithms
are straightforward to comprehend, and the
corresponding computer code is simple to implement.
Despite the growing number of enthusiasts, genetic
algorithm engineering (GA) has not garnered as much
attention as artificial neural networks, hill climbing, and
various other methods. Its relative lack of attention is
not due to any inherent limitations or a dearth of
powerful analogies. The concept of evolution, deeply
rooted in biodiversity observed in the world around us,
serves as a potent and inspiring paradigm for addressing
complex problems. From the early stages, the utilization
of genetic algorithms became apparent as computer
scientists envisioned systems that imitate and replicate
various characteristics of life. During the 1950s and
1960s, the concept of employing a collection of solutions
to address practical engineering optimization problems
was explored repeatedly. John Holland is credited with
the essential invention of the genetic algorithm (GA)
during the 1960s. The primary motivation behind the
development of these algorithms by John Holland was to
tackle problems of broad significance and general
interest. John Holland's visionary approach to the
concept was extensively documented in his 1975 book,
"Adaptation in Natural and Man-made Systems"
(recently republished with additional content). This
publication is highly recommended due to its insightful
perspective. According to David (1999), the application
of genetic algorithms has demonstrated its efficacy as a
potent method for estimating various unknown
parameters in physical system models. However, its
versatility extends to a wide range of practical
optimization issues, particularly those that are of utmost
relevance to us, such as the specific scheduling problem
within the context of this project.
A genetic algorithm is a computational
technique inspired by the natural process of biological
evolution, known as natural selection. The process
follows an iterative approach and can be effectively
visualized through a flowchart. In genetic algorithms, a
solution is referred to as a chromosome, rather than an
individual. The provided diagram illustrates the
fundamental steps of the genetic algorithm. However, in
practice, an additional step is included after the

evaluation, which involves adjusting the environment in
response to the evaluated solutions.
The generation of the population should involve
a combination of random selection and greedy
approaches. A random point will be selected as the
starting point, and the array will be filled with suitable
real values, following a deliberate and systematic
approach. During the population creation process, it is
crucial to ensure that all hard constraints are satisfied.
Significant effort will be dedicated to addressing medium
constraints, whereas soft constraints may be disregarded
entirely.
Evaluation refers to the computation of the
fitness value for a chromosome. Fitness is a metric that
assesses the quality of the chromosome in relation to the
desired solution. This event also serves as a termination
criterion, indicating the completion of the process when
a certain form or condition is achieved. Fitness
calculations involved evaluating each chromosome
under various moderate and mild stress levels. This
assessment considered factors such as subject
alignments, lunch breaks, rest sections, section idle time,
people rest instructions, instructor load balancing, and
meeting models.
The fitness calculation will largely be based on
the number of objects drawn compared to the objects
required. However, the calculation will still depend on
the rating matrix provided by the user. An evaluation
matrix is a set of constraint weights capable of shaping
solutions. This is a list containing the priority of the
constraints using a one hundred percent (100%)
distribution.
Genetic algorithm is one of the most efficient
schedule generation methods, though it cannot provide
an assurance of a 100% flawless schedule. The degree of
optimality achieved by genetic algorithms depends on
the specific constraints utilized and the effectiveness of
the adaptation function applied to the parameters. Using
the genetic algorithm is relatively slow because of the
steps involved but being the most efficient schedule
generation method, its use is more convenient [2].
V. METHODOLOGY
Fig.- 2. Process flow
A genetic algorithm is used to generate the
timetable. As shown in Figure 2, 4 input fields i.e.,
Instructors, rooms, sections and subjects are fed. Before
starting the program, various settings are fixed like
section rest time, instructor rest time, lunch break timing
etc. The genetic algorithm is subsequently applied to
generate results by evaluating the fitness of individuals.
After a candidate solution is generated the program
checks if all the constraints are satisfied. If it does not
satisfy all the constraints then the process continues
unless an optimal solution is generated.
The timetable is encoded as a set of
chromosomes or individuals, where each chromosome
represents a potential timetable solution. A fitness
function is defined that quantifies the quality or fitness
of a given timetable solution. The fitness function
evaluates how well a timetable satisfies the defined
constraints and objectives. It could consider factors like
minimizing conflicts, maximizing resource utilization,
and meeting preferences. An initialization method is
developed to generate an initial population of timetable
solutions. This could involve random assignment of
classes to timeslots and rooms, ensuring that the initial
solutions adhere to the defined constraints. Genetic
operators, including crossover and mutation, are
employed during the implementation process, to
manipulate the solutions in the population. A selection
mechanism is designed to choose individuals from the
population for reproduction based on their fitness
values. Individuals with higher fitness values have a
higher probability of being selected, mimicking the
natural selection process. Fitness of the newly generated
offspring solutions are evaluated using the fitness
function. Assess their performance in terms of satisfying
the defined constraints and objectives. The solution with
highest Fitness is selected as a final solution.
A. Requirement Analysis
1) Data Format and Collection: The application takes five
major inputs namely Instructors, rooms, subjects,
Fig.- 1. GUI of the Software

sections and settings. First three inputs are given to
the system in the form of CSV files.
a) CSV Formatting: When working with CSV files,
it's important to use line 1 of the file as a file
indicator, which should be one of the following:
"instructors", "rooms", or "subjects".
Additionally, the second line of the file should be
dedicated to defining the table columns in the
same format.
Example of subject CSV file-subjects.csv:
Subjects
Code, title, type, hours, splitable
BI, Business Intelligence1, lec,3,1
HPC, High performance computing, lec,3,1
NLP, Natural language processing, lec,3,1
DL, Deep Learning, lec,2,1
2) Minimum System Requirements: Following is the list of
minimum system requirements that must be
available to run this application.
a) Operating System: Windows 7 and Above
b) CPU: 2.0+ GHz with multithreading support
c) RAM: 1 GB (This still relies on the scenario size
and algorithm configuration)
d) Disk Space: At least 1 GB Available Space (User
generated files are excluded in assessment and
minimum space is also subject to application
usage)
B. Table Of Constraints
Table 1 shows constraints that are taken into
consideration for generating a timetable.
TABLE 1: Table Of Constraints
Sr.
No.
Soft
Constraints
Medium
Constraints
Hard constraints
1. A set of rules
that can be
broken
without
affecting the
validity of the
output.
A set of
guidelines may
exist that, if
breached, could
affect the
accuracy of the
output.
However, these
There may be a
set of rules that, if
disregarded or
broken or not
followed, would
result in an
invalid solution.
guidelines
should only be
violated if the
scenario is
logically
impossible or
invalid
2. Instructors
should not
get workload.
Sections’
subjects are
placed on the
schedule.
The schedule
should ensure
that classes do
not overlap or
clash with each
other.
3. Students
should have
only 30
minutes
break for
every two
hours of
session per
day
Sections should
have at least 30
minutes vacant
time between.
Instructors teach
at their available
schedule.
4. Some
instructors
prefer not to
have
consecutive
lectures.
Sections should
have at least 30
minutes vacant
time between.
Instructors can
only take N
number of
subjects
dependent on
their maximum
amount of load.
5. Some
instructors
have
preferred
hours for
their lectures.
The seating
capacity of a
classroom should
be adequate to
accommodate the
enrolled number
of students for a
given course
6. Instructors
should have
normalized
distributed
load based on
the instructor
pool of
subjects.
It is not feasible to
schedule two
practical classes
simultaneously in
a single
laboratory
7. Lectures
should not
exceed three
hours (pre-
defined time
slot).
A student cannot
attend more than
one class
simultaneously

8. Adequate and
separate
halls should
be allocated
for lectures.
Sections will stay
in one room
unless taking a
laboratory
subject.
9. Students
should have
free periods
between
lectures.
Sections with
subjects that are
shared to other
sections should
produce a
schedule that is
compatible to all
sharing
participant.
C. Half Hour Algorithm
Most of the current systems do not provide the flexibility
of scheduling a class of half hour duration. Given below is
the algorithm for scheduling a half hour class.
Algorithm selectTimeDetails (subject,
forceRandomMeeting)
Step 1. Initialize variables
- meetingPatterns = [[0, 2, 4], [1, 3]]
- days = [0, 1, 2, 3, 4, 5]
- hours = data['subjects'][subject][1]
Step 2. Check if hours can be split into minimum
sessions of 1 hour or 2 timeslots
- if hours > 1.5 and ((hours / 3) % .5 == 0 or (hours /
2) % .5 == 0) and data['subjects'][subject][5]:
a. If hours is divisible by two and three
- if (hours / 3) % .5 == 0 and (hours / 2) % .5 ==
0:
- meetingPattern = random.
choice(meetingPatterns)
- if len(meetingPattern) == 3:
- meetingPattern = days[0:3] if
forceRandomMeeting else meetingPattern
- hours = hours / 3
- else:
forceRandomMeeting else meetingPattern
- hours = hours / 2
b. If hours is divisible by three
- if (hours / 3) % .5 == 0:
forceRandomMeeting else meetingPatterns[0]
- hours = hours / 3
c. If hours is divisible by two
- else:
forceRandomMeeting else meetingPatterns[1]
- hours = hours / 2
Step 3. Select a random day slot if hours cannot be split
- else:
- meetingPattern = [random. randint(0, 6)]
Step 4. Convert hours into timetable timeslots
- hours = hours / .5
Step 5. Select a starting timeslot
- startingTimeslot = False
- startingTime = settings['starting_time']
- endingTime = settings['ending_time']
- while not startingTimeslot:
- candidate = random.randint(0, endingTime -
startingTime + 1)

- if (candidate + hours) < endingTime -
startingTime:
- startingTimeslot = candidate
Step 6. Generate output
- return [meetingPattern, startingTimeslot,
int(hours)]
D. Applications
The main goal of the Timetable generator is to
optimize the allocation of resources, minimize conflicts,
and improve overall efficiency and productivity in that
specific domain.
Timetable generator have various applications
across different domains. Here are some common
applications:
1) Small scale Applications:
a) Education Institutions: It is widely used in
schools, colleges, and universities to plan and
organize class schedules for students and
teachers. It helps in optimizing the allocation
of resources such as classrooms, teachers,
and subjects, ensuring a balanced and
efficient timetable for the institution.
b) Event Planning: It can play a significant role
in event planning, whether it's conferences,
seminars, or festivals. It can help in
coordinating multiple activities, sessions, and
speakers within a given time frame.
Timetable scheduling ensures that all the
components of the event are properly
organized and synchronized.
2) Large scale Applications:
a) Public Transportation: It can be crucial for
public transportation systems like buses,
trains, and airlines. It involves determining
the routes, departure and arrival times, and
frequency of services. It can help passengers
plan their journeys and ensures smooth
operations of public transportation
networks.
b) Manufacturing and Production Planning: It
can be employed in manufacturing and
production industries to plan and coordinate
various production activities. It involves
scheduling tasks, machine usage,
maintenance activities, and material
availability. It can help in maximizing
production efficiency, meeting deadlines, and
reducing downtime.
c) Healthcare Services: It can be used in
hospitals and clinics to manage patient
appointments, surgeries, and other medical
procedures. It helps in minimizing waiting
times, optimizing the utilization of healthcare
resources, and improving overall patient
care.
VI. RESULTS
A schedule is produced as shown in Fig. 3 by a
predictive algorithm that utilizes a hybrid approach of
the genetic algorithm and particle swarm optimization
algorithm to fulfill specific constraints, both mandatory
and desirable. The algorithm ensures that subjects are
assigned in a sequential manner without overlapping.
Fig.- 3. Generated Timetable
Here is a comparison between the outcome of
the expected and actual outcome of the proposed system
in Fig. 4. All the tests were conducted on a system with
configuration of 4Gb RAM, AMD Ryzen 3 processor.
Values may change with the size of the dataset and the
system’s configuration.
TABLE 2: Results Comparison
Metrics
Expected
results
Actual
Results
total fitness 100 99.98
sub placement 100 100
section rest 90 100
section idle time 23.21 37.29
Instructor Rest 100 97.56
Instructor load 50 63.7
Lunch break 100 100
Meeting pattern 95 100

Fig.- 4. Result analysis of expected and actual results
Also, as the Genetic algorithm is based on
evolution therefore the following results in the Table. 3,
also signifies the generation time for timetable with the
same input is comparatively less than the earlier
generation meanwhile the average CPU usage is higher
and average memory usage is lower.
TABLE 3: Output generation comparison
Metrics Test1 Test2
Generation time 04:01 min 03:43 min
Average CPU usage 27 70
Average memory usage 110 Mb 74 Mb
In Fig. 5 and Fig. 6, the following results are the
comparison of different chromosomes generated in the
Generation of test data sets in Table. 4 as well real-world
applications Table. 5 respectively. From the following
results we can conclude that chromosome 1 is most
likely to be the most optimal solution but it also differs
on the real-world applications.
TABLE -4: Results data
Metrics chr 1 chr 2 chr 3 chr 4 chr 5
total fitness 100 99.88 99.87 99.83 99.83
sub placement 100 100 100 100 100
section rest 100 100 100 98.25 98.25
section idle time 23.21 37.29 34.69 36.84 36.84
Instructor Rest 100 97.56 97.37 100 100
Instructor load 61.51 63.7 44.87 56.9 56.9
Lunch break 100 100 100 100 100
Meeting pattern 100 100 100 100 100
Fig. - 5. Analysis of Chromosome fitness and optimality
of testing dataset
TABLE- 5: Results data
Metrics Chr 1 Chr 2 Chr 3 Chr 4 Chr 5
Total Fitness 100% 95.27% 95.27% 95.27% 95.27%
Subject
Placement 100% 94.74% 94.74% 94.74% 94.74%
Section Rest 64.71% 82.35% 53.33% 53.33% 64.71%
Section Idle
Time 47.06% 41.18% 60% 40% 58.82%
Instructor Rest 100% 100% 100% 100% 100%
Instructor
Load 100% 75% 100% 100% 100%
Lunch Break 100% 100% 100% 100% 100%
Meeting
Pattern 100% 93.33% 100% 100% 100%
Fig.- 6. Analysis of Chromosome fitness and optimality of
real-life applications

VII. CONCLUSION
The use of the model is to measure intelligence
ability. It is observed from our results that the system
has overcome the limitations of the existing systems and
has performed more efficiently. Efficiency compared to
the model; the system can generate solutions with at
least 80% exercise (as the maximum solution for any
situation). Timetable generated using genetic algorithm
provides optimal outputs which enhances the in better
management of classes and organization.
Moreover, the genetic algorithm-based timetable
generation has had a profound impact on educational
institutions' day-to-day operations. The optimized
outputs provided by the algorithm enable administrators
to allocate resources more effectively, minimize conflicts
in scheduling, and maximize student and teacher
productivity. Consequently, the intricate machinations
and multifaceted operations of academic establishments
have benefitted from fluid functionality, an amplified
immersion of pupils, and advanced total execution.
Additionally, the optimized timetable generated by
the genetic algorithm has potential applications in areas
such as event management, transportation logistics, and
healthcare scheduling. If the system can adeptly
apportion assets and mitigate frictions, it may heighten
functioning, decrease expenditures, and better the total
organizational proficiency in these realms.
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