https://utilitasmathematica.com/index Our Journal has we strive to minimize barriers to access and participation, ensuring that opportunities within the statistical community are available to all, regardless of background. This includes addressing issues such as language barriers, geographical disparities, and financial constraints that may limit access to statistical education and resources.

1. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
201
Improving Crew Scheduling for Maintenance Routing Problem: A
Hyperheuristic Approach
Zainab marid Alzamili1, Hussein.M Jebur2, Ali Hasan Ali3
1
Education Directorate of Thi-Qar, Ministry of Education, Iraq, zainab.alzamili@utq.edu.iq
2
College of Information Technology, Imam Ja'afar Al-Sadiq University, Baghdad, Iraq,
hussein.mankhi@sadiq.edu.iq
3
Education Directorate of Thi-Qar, Ministry of Education, Iraq, ali.hasaan@sadiq.edu.iq
College of Information Technology, Imam Ja'afar Al-Sadiq University, Baghdad, Iraq
Abstract
Operators of the public switched telephone network (PSTN) provide infrastructure and services
for public telecommunication. Phone lines, fiber optic cables, microwave transmission links,
mobile networks, communications satellites, and undersea cellphone cables are all part of the
PSTN, which is interconnected via switching centers and allows most telephones to communicate
with one another. The PSTN, which began as a network of constant-line analog mobile programs,
is now a digital core network that includes mobile and other networks, as well as fixed
telephones. The complexity of the network and the exponential increase of phone and DSL
services usage growth indicates that PSTN requires daily maintenance. In this study, we are
interested in a real scenario of maintaining PSTN services. The problem appears as a variant of
vehicle routing problem (VRP), with some particularities such as heterogeneous demanded
services, heterogeneous teams' capabilities, working hours limit, and others. We will offer
maintenance planning and scheduling using a non-exact optimization technique called
hyperheuristic. In this study, we will propose an intelligent method as a heuristic selection
method, as well as simulated annealing acceptance criteria and non-deterministic termination
criteria. Our numerical experiments show that the hyper-heuristic solution method offered a high-
quality solution in a reasonable time.
Keywords: PSTN, VRP, hyperheuristic, simulated annealing. high-quality.
1. Introduction
In the past, subscribers' posts were hardwired to a PSTN commutator using a pair of wires that
were charged by a separate battery (la boucle locale), making up what is now known as a public
switched telephone network (PSTN). High-speed digital links (BPNs) or high-speed optical links
connect telephone commutators (PDHs or SDHs).

2. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
202
A PSTN is made up of switches that operate as nodes at network centralized facilities, allowing
exchange of information between two entities. After going through a series of switches, the
phone conversation finally connects. After that, you can use the appropriate telephone lines to
transmit your voice.The initial PSTN featured a star structure and a hierarchical architecture. A
local exchange connects individual subscriber lines to trunk exchanges, central exchanges, and
other local exchanges. Inside a given exchange, all phone numbers are assigned the same area
code. Calling a number outside of one's local exchange requires the dialing of an area code.. To
make an international call, the user needs first dial the country code.The companies that make up
the public switched telephone network's infrastructure and supply its services to the public.
Phone lines, fiber optic cables, microwave transmission connections, mobile networks,
communications satellites, and submarine telecom cables are all components of the Public
Switched Telephone Network (PSTN), which is interconnected via switching centers and allows
most telephones to communicate with others. The PSTN's original core network was made up of
constant-line analog mobility programs, but today the PSTN's core net is nearly entirely made up
of mobile and other networks in addition to fixed telephones.The PSTN requires daily
maintenance due to its complexity and the exponential growth in phone and DSL service
demand. This study focuses on real-world scenarios of preserving PSTN services.
The problem presented in this study appears to be a variation of the vehicle routing problem
(VRP), with several differences such as heterogeneous needed services, varied teams'
capabilities, and a working hours constraint, among others.
Vehicle routing problems are a sort of combinatorial optimization and operational research
challenge. To give a list of clients or to complete a route of interventions (maintenance, repair,
controls) or visits, it is required to identify the routes of a fleet of vehicles (medical, commercial,
etc.). The purpose is to lower the cost of delivery of products. This is a famous generalization of
the commercial traveler's dilemma, and it falls under the NP-complete problem category.
Typical variants of the vehicle routing problem include:
• Vehicle Routing Problems with Profits (also known as VRPP for Vehicle Routing
Problems with Profits): A problem of profit maximization in which it is necessary to select which
clients to visit while keeping in mind the vehicle's limited capacity.
• Capacity constraints (also known as CVRP for Capacitated Vehicle Routing Problem):
Vehicles have a limited capacity for import (quantity, size, weight, etc.);
• Constraints relating to resources and clients: availability, location, required skills, etc.;
vehicle routing with time windows: Each client is assigned a time window during which the
delivery must be completed;
• Routing vehicles with collect and delivering: A specified number of items must be moved
from pick-up locations to delivery locations.
It's difficult to solve large-scale examples optimally, as it is for the majority of NP-complete
problems. Then one is pleased with finding "good quality" solutions. To get solutions in a
reasonable amount of time, people usually turn to heuristic methods like Clarke and Wright's

3. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
203
algorithm to build a first solution, which they then improve with other heuristics or local search
methods. It's worth noting that many of the improvement methods used for the problem of the
business traveler can be applied to each of the tours individually to reduce the overall cost of the
solution.
The linear optimization allows for the precise resolution of some problems with the routing of
relatively small vehicles (about 200 clients at the moment). The developed methods include
Branch and Cut applications, as well as more recently, column generation.
Numerous metaheuristics have finally been used to this problem, such as tabou, but also genetic
algorithms, variable-neighbors searches, and so on. Several problems with up to 20,000 clients
have been successfully resolved as a result.
Here, in this paper, we will offer maintenance planning and scheduling using a non-exact
optimization technique called hyperheuristic. Hyperheuristics (HH) tries to automate the
invention of heuristic approaches to tackle difficult computational search issues. In the year
2000, it was more appropriately employed combinatorial optimization (Cowling, Kendall, &
Han, 2002) called heuristics to choose heuristics.
Given a specific issue instance and a set of low-level heuristics, As opposed to low-level
heuristics, strategy for solving difficult computational search problems by picking Using an
appropriate low-level criterion at each phase of the decision-making process. The Hyperheuristic
framework consists of several low-level-heuristics, which are problem dependent, in addition, to
move acceptance strategy, heuristic selection method, and termination criteria, which are
problem independent. Our main aim is to propose an intelligent method as a heuristic selection
method, as well as simulated annealing acceptance criteria and non-deterministic termination
criteria.
2. Problem Statement
The following is a description of the issue: A group of clients who require maintenance and are
dispersed throughout a geographic area. every order's two clients (i,j) has a distance of |dij| in
terms of trip time. A fleet of vehicles (i.e. mobile maintenance heterogeneity vehicle) is available
to assist clients as needed, and each vehicle has a service level q assigned to it.
All services with service level lq < l can be provided by any vehicle r with service level l.
At time zero, all of the cars are at their original places, as are all of the clients who require
service. The goal is to reduce the total time it takes to complete maintenance tasks.
As previously stated, the problem looks to be a version of the vehicle routing problem (VRP),
with certain differences such as:
• The heterogeneous client demanded services;
• Heterogeneous teams ‘capabilities with heterogeneous vehicles;

4. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
204
• Working hours limit;
• Client priority.
Solution Approach
Hyperheuristics (HH) automate the development of heuristic procedures to address difficult
computational search issues. Denzinger conducted research on computer-aided theorem provers
in 1997. and Scholz (1997) originated the phrase with an approach that combined a variety of
artificial intelligence techniques. According to Heuristics for selecting heuristics, Cowling et al.
Specifically, in the field of combinatorial optimization, (2001) were used more efficiently.A
hyperheuristic is a high-level heuristic that can be derived from a large number of low-level
heuristics for a given problem instance. strategy for solving complex computational search
problems by selecting by using the right amount of low- Every time you make a call, use a
heuristic. Even though the name is new, Crowston et al. conceived of it in 1963, throughout the
1960s. During the '90s, a collective of Scientists (Fang et al., 1993) created a system to automate
the development of heuristic methods. However, hyperheuristics are a step above metaheuristics.
The search space of hyperheuristics is not the typical answer space, but rather other heuristics or
metaheuristics. Hyperheuristics can be thought of as an extension of the concept of
(Meta)heuristics. It simplifies the classification of a significant body of previously difficult-to-
classify heuristics and metaheuristics literature. According to Ozcan et al., hyperheuristics are
methods for scanning the feasible space, which is constructed using a set of low-level heuristics
(2012a). Topcuoglu and colleagues (2005), On the other hand, it was proposed a method of
automating the selection and development of several low-level heuristics. Hyperheuristics are the
most effective approach for dealing with specific sorts of optimization problems. They only
require a minimal understanding of subject matter expertise to get started according to Cowling
et al. (2001), who define hyperheuristics as "heuristics for picking heuristics."
In hyperheuristics research, Ochoa et al. (2009) argue that improving the efficiency of the
solution technique is more important than finding the answer itself. They also maintained that,
unlike metaheuristics, hyperheuristics had a set of heuristics to look through instead of problem-
solving techniques, as Ross et al. (2005) asserted. A search method or learning process for
picking or generating heuristics to solve a combinatorial problem is known as hyperheuristics.
While the concept of automating heuristic design dates back to the 1960s, it is now used to pick
or construct heuristics To resolve a combinatorial issue. The primary objective is to present a
generalized approach that may be used for a variety of issues. Despite relying on low-level, easy
heuristicsWe anticipate superior results from this procedure result.
1) One of the two major hyperheuristic categories coming from the previous classification is
Heuristic Selection, which covers a method for picking a heuristic from a list of current

5. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
205
heuristics. The technique of generating new heuristics from existing heuristic components is
known as heuristic generation.
Burke et al. (2010) suggested a 2-dimensional hyperheuristic categorization that divides
hyperheuristics into groups depending on the parameters that comprise the heuristic search space
and the data used to guide the procedure. Creation and perturbations are two examples of low-
level strategies that can be combined with a hyperheuristic for intuitive selection and production.
The second dimension, however, reveals an orthogonal classification to the first. It creates new
categories based on the type of data it collects during the learning process.
The first is known as online learning hyperheuristics, and it occurs when a learning mechanism is
applied in response to an issue. The appropriate low-level heuristic is selected or created by the
higher-level approach depending on its success in practice. Off-line learning hyperheuristics are
the second sort of algorithm, and they work by analyzing a collection of training instances to
create a set of rules or computations. allowing the process to generalize to the point where it can
solve unseen models completely. There exist non-learning hyperheuristics, which do not use any
learning methods at all, in addition to the aforementioned classes.
We'll look at hyperheuristic selection in this study, which seeks to determine the optimal set of
heuristics for a good result. It is made up of a few simple rules of thumb. led by a specific
selection technique.
Constructively is a low-level heuristic that focuses on building a viable solution from the ground
up. 2) With improvement, it is possible to use intensification methodologies to make incremental
adjustments to the response.
3) Perturbation, which increases the size localized optimality in the solution space.
4) Partially deconstructs and reassembles the solution.

6. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
206
Figure 1: Classification of Hyperheuristics.
Heuristic selection method
Simulated Annealing (SA) is prompted by a resemblance to solid annealing and was inspired by
a work by Metropolis et al. (1953). It demonstrates how to model the annealing process, which
entails chilling chemicals in a hot tub.
After a solid has been melting point exceeded, the cooling pace has an impact on its structural
characteristics. When Because of how slowly it is cooling, the production of crystals can also be
detected. If the materials were rapidly cooled, there's a good probability the crystals would have
flaws.
Metropolis algorithm components included represented as a particle system. The temperature of
the system steadily decreased in the simulation until it reached a stable, frozen condition. The
initial optimization difficulties were documented in Kirkpatrick in 1982.
To uncover plausible possibilities that could eventually converge to an ideal solution, simulated
annealing was applied. The law of thermodynamics states that for a particular temperature, t, the
likelihood of an increase in vitality is equal to the square of the temperature, δE, is determined by
P(δE) = exp(−δE/kT)

7. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
207
Boltzmann's steady is defined as the constant k. In the Metropolis computation, the reenactment
calculates the framework's new vitality. The system enters this condition when the vitality level
falls below a specified threshold. The new situation is recognized using the likelihood returned
by the prior formula if the vitality has grown.
Before the temperature is dropped, a specified number of emphases are conducted at each
temperature. This process is done until the framework is stable. Although the Boltzmann constant
is usually ignored because it was simply given in the comparison to adapt to different materials,
this mathematical statement is very useful in reenacted toughening. In this line, consider the
following mathematical statement: The probability of accepting a worse circumstance and this
mathematical statement gives us the answer:
P = exp(−c/t) ≥ r (20)
Where:
o c denotes the changeability to evaluate;
o t denotes the temperature right now;
o r is an irrational number between 0 & 1.
The ability to tolerate a harsher move is influenced by the temperature of the framework as well
as the cost capacity adjustment. It's worth noting that The chance of permitting a more rapid
cooling of the framework increases as heinous maneuver reduces. In physical annealing, this is
the same as gradually progressing to a solidified state.
Remember that if the temperature dips below freezing, only the best moves will be identified,
resulting in successfully replicated strengthening activities such as hill climbing. SA was
employed in two ways in hyperheuristic techniques: first, in selection heuristics, and second,
when approving a potential answer. The SA heuristic selective hyperheuristic was used to select
a reward r heuristic, 1 > r > 0, having exp( −r t ) > random(1, 0).
Schedules for annealing are thought to be linear, with:
T[t] = T0 − ηt
Low-level-heuristic
This paper provides a highly strung-heuristic framework with a variety of low-level heuristics
and a learning mechanism for mechanism. The following is a list of low-level heuristics: a)
constructive techniques, which start from the beginning to generate complete feasible solutions,
b) improvement methods, which take a working solution and aim to improve it within a specific
neighborhood, c) perturbation techniques, which attempt to introduce noise into the process to
develop solutions, which may aid in the discovery of better solutions and possible escape from

8. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
208
local optima, and d) reconstruct techniques, which take a working solution and aim to improve it
within (randomly or deterministically).
We'll go through Every one of these simple biases quickly in the following sections.
a) Using a series of productive Heuristics, we piece together an initial viable answer.
predetermined limits, outside of attempting to enhance it. I C1 uses the instance
information to create a solution. We sort the client based on the decreasing client priority.
Following that, we begin with the highest-priority client and assign each client to the
least-used compatible vehicle among others.
b) Heuristics for improvement: The optimization procedure begins with a workable answer
and improves it by making successful adjustments in a given region. The following
movements are common in our neighborhoods:
a. Assign-Best-Route: We reorganize the sequence of allotted clients to be supplied
by a given vehicle (one job at a time) and shift to the best-found feasible solution
greedily among the improving options identified for that vehicle, as presented in
Algorithm 1.
b. Balance-Add-Drop: We examine three motions for two randomly picked vehicles
to achieve a balanced utilization and fair job allocation across vehicles: (1)
Transfer one work from vehicle vi to vehicle vj, then remove a client from a list of
customers serviced by a specific vehicle and place it in the correct order of clients
the least objectively useful mode of transportation.
Algorithm 1: Pseudo Code of Assign-Best-Route
Algorithm 1: Assign-Best-Route
Begin Assign-Best-Route(S)
//choose a random vehicle
v = random(0,length(S))
//find the best swap
for i=0, i< len(v)
S’= Best_Swap(v,i)
end for

9. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
209
if OF(S’) < OF(S) then
S = S’
end if
return S
End Function
c. Perturbation heuristics: During the search, the perturbation phase ensures a
diversification approach by attempting to get out of the local optimum, must
randomly traverse the search space. We employ in this study a variety of
perturbation heuristics, including:
1. Mutation-Swap: This appears to be the genetic operator that keeps population
diversity from generation to generation. A chromosomal configuration alteration
(a sequence of clients on each vehicle) that prevents premature convergence and
allows exploration of new portions of the search space is referred to by this
operator.
2. Crossover: The rigs (chromosome segments) are used to swap 'genetic
material,' whereas the mutation operator uses two clients, one for each
chromosome.
3. To improve the search space, we define an operator that destroys and
reconstructs sections of a randomly chosen solution (diversifying the search
process). As a result, the operator demolishes a section of the current solution
before rebuilding it using constructive methods.
Hence, the general algorithm of the proposed HH here is the following pseudo code (Algorithm
2).
Algorithm 2: Pseudo Code of HH.
Algorithm 2: HH
S  Constructive()
While not(Termination_criteria) do
h = Select_heuristic()

10. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
210
S’=Apply(h,S)
if (Acceptance_criteria) then
S = S’
end if
End while
3. Numerical Experiments
The outcomes of the HH algorithm are reported in this section. This method is put to the test on a
set of 40 test scenarios, each with a varied number of clients and maintenance vehicles that reach
neighboring clients at different times. In TABLE I, the test cases are depicted. the amount of test
cases, the amount of clients, and the amount of used vehicles are all displayed in this table.
We wanted to see how different combinations of clients assigned to vehicles affected
performance in these 34 test situations. Thus, in some test instances (e.g., TC1-TC3), we altered
the amount of clients while keeping the number of vehicles constant, while in others, the amount
of clients remained constant but the amount of vehicles varied. In addition, several test cases
were ramped up in size to put our approach to the test on small, medium, and large challenges.
Table 1: Test cases
TestCase
nb
Number
of Clients
Number
of
vehicles
TestCase
nb
Number
of Clients
Number
of
vehicles
TC1 8 1 TC18 50 10
TC2 12 3 TC19 75 7
TC3 16 3 TC20 75 9
TC4 16 5 TC21 75 10
TC5 21 5 TC22 100 7
TC6 27 3 TC23 100 9
TC7 27 5 TC24 100 10
TC8 27 7 TC25 100 12
TC9 30 3 TC26 150 7
TC10 30 5 TC27 150 9
TC11 30 7 TC28 175 10
TC12 35 3 TC29 175 12
TC13 35 5 TC30 200 7
TC14 35 7 TC31 200 9
TC15 50 5 TC32 200 10
TC16 50 7 TC33 200 12
TC17 50 9 TC34 250 15

11. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
211
4. Results and Discussion
The best outcomes of the HH approaches applied to the test cases TC1-TC34 are summarized in
Table 2. The Java language is used to implement the HH algorithm.
Table 2: Initial Objective function, the better one, and the execution time
Instance
Initial Objective
Function (OF)
Best Objective
Function
Execution Time
TC1 346.67 240.00 2.74
TC2 1573.33 1466.67 5.48
TC3 2893.33 2663.33 5.51
TC4 1823.33 1710.00 4.27
TC5 3140.00 2350.00 8.24
TC6 7916.67 7326.67 6.89
TC7 4916.67 4696.67 4.71
TC8 3643.33 3610.00 8.07
TC9 11376.67 10680.00 10.01
TC10 6963.33 6516.67 7.42
TC11 5286.67 4916.67 9.61
TC12 14466.67 13496.67 10.97
TC13 8883.33 8326.67 9.32
TC14 6600.00 5933.33 9.73
TC15 19240.00 17663.33 8.23
TC16 13720.00 12740.00 6.86
TC17 11040.00 10373.33 8.87
TC18 10006.67 9416.67 8.91
TC19 31853.33 28933.33 9.20
TC20 25006.67 22886.67 10.01
TC21 22506.67 20776.67 8.78
TC22 61856.67 58470.00 6.86
TC23 57910.00 53950.00 8.32
TC24 47483.33 43826.67 8.35
TC25 40720.00 37233.33 8.42
TC26 163883.33 151100.00 7.59
TC27 163520.00 153736.67 6.42
TC28 127980.00 119026.67 10.17

12. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
212
TC29 111293.33 102576.67 11.16
TC30 278370.00 254823.33 10.01
TC31 255933.33 227766.67 10.16
TC32 213386.67 190026.67 8.22
TC33 192206.67 173343.33 8.36
TC34 0.00 0.00 0.00
Table 2 summarizes a variety of metrics for each scenario, such as total time, the value of the
objective function at the start, the best value of the objective function found by the HH, and the
amount of time it took to run the suggested algorithm.
5. Conclusion
We provided our vision for solving the crew scheduling for maintenance routing challenge in this
paper. The problem comprises assigning a maximum number of priority clients to maintenance
vehicles to reduce the total time spent traversing vehicles. For this problem, we introduced a
hyperheuristic technique. HH is the first to use the maintenance vehicle routing challenge to
solve the assignment problem.
This paper contributes by developing and testing a method (HH) that wasn't ever used earlier to
address the issue at hand. Our HH approach yielded an answer that was at least 5% better in
about 10 seconds. according to the results. This is because the HH focuses on diversification and
then intensification strategies. To improve the quality of the original population, a new
constructive strategy was applied. Since this method helped provide the best-known response
earlier in the iterations, it influenced the results and gave it an edge over similar work and studies
that didn't prioritize achieving such enhanced solutions. The methods of improvement and
heuristic improvement have also been strengthened in order to achieve better outcomes.
References
[1] - Jörg Denzinger, Marc Fuchs, and Matthias Fuchs. High-performance ATP systems by
combining several AI methods. Citeseer, 1996.
[2] - Peter Cowling, Graham Kendall, and Eric Soubeiga. A hyperheuristic approach to
scheduling a sales summit. In Practice and Theory of Automated Timetabling III, pages 176–
190. Springer, 2001
[3] - Wallace B Crowston, Fred Glover, Jack D Trawick, et al. Probabilistic and parametric
learning combinations of local job shop scheduling rules. Technical report, DTIC Document,
1963.

13. UtilitasMathematica
ISSN 0315-3681 Volume 120, 2023
213
[4] - Hsiao-Lan Fang, Peter Ross, and David Corne. A promising genetic algorithm approach to
job-shop scheduling, rescheduling, and open-shop scheduling problems. University of
Edinburgh, Department of Artificial Intelligence, 1993.
[5] - E. Özcan, M. Misir, G. Ochoa, and E. K. Burke. A reinforcement learning-great deluge
hyper-heuristic for examination timetabling. International Journal of Applied Metaheuristic
Computing (IJAMC), 1(1):39–59, 2010.
[6] - Ender Özcan, Mustafa Mısır, Gabriela Ochoa, and Edmund K Burke. A reinforcement
learning: Great-deluge hyperheuristic. Modeling, Analysis, and Applications in
Metaheuristic Computing: Advancements and Trends: Advancements and Trends, page 34,
2012.
[7] - Haluk Rahmi Topcuoglu, Abdulvahid Ucar, and Lokman Altin. A hyper-heuristic-based
framework for dynamic optimization problems. Applied Soft Computing, 19:236–251, 2014.
[8] - Gabriela Ochoa, Rong Qu, and Edmund K Burke. Analyzing the landscape of a graph-based
hyper-heuristic for timetabling problems. In Proceedings of the 11th Annual Conference on
Genetic and evolutionary computation, pages 341–348. ACM, 2009.
[9] - Peter Ross. Search Methodologies, chapter Hyper-heuristics, pages 529–556. 2005.
[10] - Edmund K Burke, Matthew Hyde, Graham Kendall, Gabriela Ochoa, Ender Özcan, and
John R Woodward. A classification of hyperheuristic approaches. In Handbook of
Metaheuristics, pages 449–468. Springer, 2010.
[11] - Nicholas Metropolis, Arianna W Rosenbluth, Marshall N Rosenbluth, Augusta H Teller,
and Edward Teller. Equation of state calculations by fast computing machines. The Journal
of chemical physics, 21(6):1087–1092, 1953.
[12] - Scott Kirkpatrick. Optimization by simulated annealing: Quantitative studies. Journal of
statistical physics, 34(5-6):975–986, 1984.
[13]. Ali Hasan Ali 2023. Smart Fire System using IOT. CENTRAL ASIAN JOURNAL OF
MATHEMATICAL THEORY AND COMPUTER SCIENCES. 4, 3 (Apr. 2023), 88-113.