School Bus Routing in the City of Denpasar using Differential

Evolution Algorithm

I Wayan Suasnawa, I Ketut Gede Sudiartha, I Gusti Ngurah Bagus Caturbawa,

Anak Agung Ngurah Gde Sapteka, I Nyoman Eddy Indrayana and I Gusti Agung Made Sunaya

Department of Electrical Engineering, Politeknik Negeri Bali, Kampus Bukit Jimbaran, Badung, Indonesia

Keywords: Bus Routes, Differential Evolution, Mutation, Crossover, Selection.

Abstract: The Denpasar City Transportation Office has launched school buses for school students since 2017. Through

this school bus, The Denpasar City Transportation Office has helped parents to pickup students. The problem

that often occurs in the transportation system is finding the optimal route. The purpose of this study is to

create a method to get an effective route, namely, in the form of the shortest route. Route selection uses the

Differential Evolution algorithm. At the initialization stage, the Differential Evolution algorithm generates a

population (random route). The random route generated has a distance of between 46.976602126788194 km

to 9999 km. A score of 9999 is not the true distance, but the score assigned to a bad individual candidate.

Considered as a bad individual candidate because the random route generated was the pickup location as the

final destination. Furthermore, each individual goes through a process of mutation, recombination, selection

with a certain number of iterations. The system will produce a better population, with shorter routes with each

iteration. With the selection process, shorter route variations that result from iterations replace routes with

longer distances. The Differential Evolution algorithm is very effective to use to get the minimum value.

Based on the final results obtained from the application, the optimal route candidates are obtained. The farthest

route is 26.624917440178955 km, and the route with the shortest distance is 25.75039590845092 km.

1 INTRODUCTION

The Denpasar City Transportation Office has

launched school buses and provided bus stops as

places to pick up students since 2017. This program

is very useful in providing a sense of security for

students and parents of students. Through this school

bus, the Transportation Office has helped parents to

pick up and drop off.

One of the problems that often occur in the public

transportation system is determining an effective

route, finding the path between the departure location,

pickup location, and final destination location. In this

research, an application is made that can provide the

shortest alternative route for school buses in Denpasar

City. Route selection uses the Differential Evolution

Algorithm. This algorithm is one of the evolutionary

algorithms, which is famous for its convergence

speed (Leung, et al., 2007). The application can

generate an effective route for each school bus so that

the driver takes students to school with faster travel

time.

2 THEORY

2.1 Evolutionary Computation

Evolutionary Computation is one of the fields of

artificial intelligence. Evolutionary Computation is

an abstraction that requires specific engineering to

produce an optimization algorithm to solve the

problem (Leung, et al., 2007). Evolutionary

Computation adopts various theories and fields of

science. For example, physics, statistics, probability,

but Evolutionary Computation is part of computer

science (Eiben, et al., 2003). Optimization algorithms

are becoming important techniques in many

disciplines (Lin, 2013). Many practical engineering

or decision-making problems involve optimization to

find the best design solution. In the case of multi-

objective optimization gives rise to a Pareto-optimal

solution because of the interactions between various

conflicting objectives (Deb, 2001).

There are several algorithms that are included in

the Evolutionary Computation family. Algorithms

that are included in the Evolutionary Algorithm are

Suasnawa, I., Sudiartha, I., Caturbawa, I., Sapteka, A., Indrayana, I. and Sunaya, I.

School Bus Routing in the City of Denpasar using Differential Evolution Algorithm.

DOI: 10.5220/0010964600003260

In Proceedings of the 4th International Conference on Applied Science and Technology on Engineering Science (iCAST-ES 2021), pages 1327-1333

ISBN: 978-989-758-615-6; ISSN: 2975-8246

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

1327

Genetic Algorithm, Genetic Programming,

Evolutionary Strategies, Differential Evolution,

Evolutionary Programming, and Grammatical

Evolution (Suyanto, 2008). Besides, there are many

more systems that combine various features or

characteristics of the algorithms mentioned above,

making it difficult to classify.

2.2 Differential Evolution Algorithm

Differential Evolution is a population-based

algorithm. First developed by Storn and Price (Storn,

et al., 1997). With the advantages of simplicity and

fewer parameters, the Differential Evolution

algorithm has been widely used in various fields, such

as engineering, electricity, data mining,

biogeography, structural optimization, and so on

(Gong, et al., 2014). Differential Evolution is an

optimization method to find the minimum value of a

nonlinear and non-differentiable continuous space

function (Storn, et al., 1997). Differential Evolution

is considered the latest study to solve the problem of

finite optimization, multi-purpose global

optimization, and other complex real-world

applications.

In the Differential Evolution Algorithm,

individuals have a real value, which is the true value

of the solution being sought. This real value can then

be considered a vector. Differential Evolution

generates new vectors (individuals) by involving

three vectors (individuals) as parents. The generation

of new vectors is done by adding one vector (1st

parent) with the difference between the other two

vectors (2nd and 3rd parent). This process is called

Differential Mutation.

In the mutation process for each vector x

i,G

0,1,2,…, NP-1, a new vector is generated based on the

formula:

v = x

r1,G

+ F(x

r2,G

- x

r3,G

)

Where r1, r2, r3 ∈ [0,NP-1] are integers randomly

selected in the interval [0, NP-1]. Whereas F is called

a scale vector in the form of a real number which is a

constant that controls the gain of the differential

variation (x

r2,G

– x

r3,G

). To increase the diversity of the

parameter vectors, the vector v is recombined

(crossover) with an arbitrary vector in the population

i,G

). The crossover process produces the following

vector u.

u = ( u1, u2,...,u

)

(2)

where

‹n›

, ‹n + 1›

, ...,‹n + L - 1›

;

(

i,G

)

for other

The symbol ‹›

represents the Modulo function,

which is a function that issues the remainder of the

division. From the above equation, it can be seen that

certain vector elements in a certain order are the same

as the vector v. The remaining elements of the vector

u are derived from x

i,G

. The prefix index n in the

above equation is randomly selected in the interval [0,

D-1]. The integer L is randomly selected in the

interval [0, D-1] with the probability Pr(L=v) = (CR)

where CR ∈ [0,1] is the crossover probability and

represents a control variable for the Differential

Evolution scheme. Generating random numbers for n

and L is done every time the generation of a new

vector v. When (n+L–1) is greater than maximum j

then j returns equal to 0.

3 RESEARCH METHODOLOGY

Basically, the Differential Evolution algorithm will

find the shortest route based on the given criteria

value. The route search process can be described, as

shown in Figure 1. Some of the processes that this

algorithm goes through to obtain the optimal route are

initialization, mutation, recombination, and selection.

Figure 1: Flowchart of routing with differential evolution.

iCAST-ES 2021 - International Conference on Applied Science and Technology on Engineering Science

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3.1 Initializing Chromosomes

At the initialization of the population, each point

(location), namely the departure location, school

location, and pickup location, will become the genes

forming individual chromosomes. The number of

individuals who are raised randomly in a certain

number. The individual refers to the solution

candidate as parents. The solution candidate

(individual) is coded into the chromosome. Each

chromosome consists of genes that are located in

random positions and are assigned a certain value.

3.2 Mutation

The mutation process makes use of existing

chromosomes to get better individuals. In Differential

Evolution, individuals are considered as vectors. In

the mutation process, the generation of a new vector

will involve three vectors (individuals) as parents.

This vector generation uses Formula 1.

3.3 Crossover

The crossover process increases the diversity of

existing vectors (individuals). Vector v is recombined

(crossover) with an arbitrary vector in the population

i,G

). The crossover process generates new

(individual) vectors.

3.4 Selection

The crossover result vector replaces the parent vector

if it has a greater fitness value. This means that the

vector u will replace the vector x

i,G

in the next

generation. But if u has a fitness value smaller than

i,G

, then vector u does not replace x

i,G

. In other words,

i,G

will still appear in the next generation. A greater

fitness value will be obtained from the vector with the

shortest route distance.

3.5 The Shortest Route

In the last stage, when the specified number of

iterations has been reached, there will be a number of

individuals who have shorter routes than the

individuals who were raised during initialization. The

individual candidates selected are the individuals who

have the shortest route.

4 RESULTS AND DISCUSSION

4.1 First Population

At the initialization, a number of random populations

were generated. This random population is generated

from the data entered into the application. This data

includes the location of departure, location of

destination schools, and pickup locations. Table I

shows some of the population formed. In the initial

population, the route distance obtained will vary

greatly. The route distance obtained is between

46.976602126788194 km to 9999. The value of 9999

does not reflect the actual route distance. The largest

value, 9999 km, indicates a bad route candidate. This

route produces the pickup location as the final

destination in the overall route. In contrast, the

expected final destination location on the route is a

school.

Table 1: First population.

Route

Distance

UPT Pelayanan Transportasi Darat - Jl.

Meduri - SMP PGRI 9 Denpasar - Toko

Chaca - Jl. Astasura - SMP Negeri 8

Denpasar - Jl. Gadung - SDN 28 Dangin

Puri - Banjar Tulangampiang - Apotek

Cempaka - Jl. Antasura - SD Dwijendra

Denpasar - Jl. Nangka - SMP PGRI 2

Denpasar - WR. Supratman - SD Saraswati

6 Denpasar - Jl. Patimura - Indomaret

A.Yani - SD Saraswati 2 - Jl. Suradipa -

Indomaret Antasura - Jl. Lembusora

9999

UPT Pelayanan Transportasi Darat - SMP

PGRI 9 Denpasar - Indomaret Antasura - Jl.

Meduri - SD Dwijendra Denpasar - Banjar

Tulangampiang - SD Saraswati 6 Denpasar -

Jl. Antasura - Indomaret A.Yani - Jl.

Patimura - WR. Supratman - SMP Negeri 8

Denpasar - Jl. Astasura - Toko Chaca - Jl.

Gadung - SD Saraswati 2 - Jl. Nangka -

SDN 28 Dangin Puri - Jl. Suradipa - Apotek

Cempaka - Jl. Lembusora - SMP PGRI 2

Denpasar

64.55675

03867861

UPT Pelayanan Transportasi Darat - SD

Saraswati 2 - SMP PGRI 9 Denpasar - Jl.

Meduri - SMP PGRI 2 Denpasar - Jl.

Nangka - SMP Negeri 8 Denpasar - WR.

Supratman - Jl. Astasura - Jl. Gadung - SDN

28 Dangin Puri - Jl. Antasura - SD

Saraswati 6 Denpasar - Jl. Patimura -

Apotek Cempaka - Jl. Lembusora - Jl.

Suradipa - Banjar Tulangampiang - Toko

Chaca - Indomaret Antasura - Indomaret

A.Yani - SD Dwijendra Denpasar

47.87273

01594511

UPT Pelayanan Transportasi Darat - SMP

PGRI 9 Denpasar - Jl. Patimura - Jl. Gadung

- SD Saraswati 6 Denpasar - Jl. Antasura -

SMP PGRI 2 Denpasar - SMP Negeri 8

Denpasar - Jl. Meduri - Jl. Lembusora - Jl.

Astasura - Jl. Nangka - Jl. Suradipa -

9999

School Bus Routing in the City of Denpasar using Differential Evolution Algorithm

1329

Route

Distance

Indomaret A.Yani - Banjar Tulangampiang -

Indomaret Antasura - SD Saraswati 2 - WR.

Supratman - SDN 28 Dangin Puri - Toko

Chaca - SD Dwijendra Denpasar - Apotek

Cempaka

UPT Pelayanan Transportasi Darat - SMP

PGRI 9 Denpasar - Jl. Gadung - Jl. Antasura

- Jl. Suradipa - WR. Supratman - Banjar

Tulangampiang - Apotek Cempaka - Toko

Chaca - Jl. Nangka - Indomaret A.Yani - Jl.

Lembusora - SMP PGRI 2 Denpasar - SD

Saraswati 6 Denpasar - Jl. Meduri - Jl.

Astasura - SD Dwijendra Denpasar - SDN

28 Dangin Puri - SMP Negeri 8 Denpasar -

SD Saraswati 2 - Jl. Patimura - Indomaret

Antasura

9999

UPT Pelayanan Transportasi Darat - SMP

PGRI 9 Denpasar - Indomaret Antasura - Jl.

Lembusora - Jl. Gadung - SMP PGRI 2

Denpasar - Jl. Meduri - Indomaret A.Yani -

SD Saraswati 6 Denpasar - Jl. Patimura - Jl.

Astasura - SDN 28 Dangin Puri - Banjar

Tulangampiang - Jl. Nangka - WR.

Supratman - SD Dwijendra Denpasar - Jl.

Suradipa - SD Saraswati 2 - Apotek

Cempaka - Toko Chaca - Jl. Antasura -

SMP Negeri 8 Denpasar

64.77384

79124430

UPT Pelayanan Transportasi Darat - Banjar

Tulangampiang - SMP Negeri 8 Denpasar -

Jl. Lembusora - SDN 28 Dangin Puri - Jl.

Meduri - SMP PGRI 2 Denpasar - WR.

Supratman - Apotek Cempaka - Jl. Nangka -

Jl. Patimura - SD Dwijendra Denpasar -

SMP PGRI 9 Denpasar - SD Saraswati 2 -

Jl. Astasura - SD Saraswati 6 Denpasar - Jl.

Suradipa - Indomaret A.Yani - Toko Chaca

- Jl. Gadung - Indomaret Antasura - Jl.

Antasura

9999

UPT Pelayanan Transportasi Darat - SDN

28 Dangin Puri - Banjar Tulangampiang - Jl.

Patimura - Jl. Astasura - Jl. Nangka - Jl.

Meduri - Jl. Suradipa - Jl. Antasura - SD

Saraswati 2 - Toko Chaca - SD Saraswati 6

Denpasar - SMP PGRI 2 Denpasar - Jl.

Gadung - Apotek Cempaka - SMP Negeri 8

Denpasar - SMP PGRI 9 Denpasar -

Indomaret Antasura - Indomaret A.Yani -

SD Dwijendra Denpasar - WR. Supratman -

Jl. Lembusora

9999

UPT Pelayanan Transportasi Darat - Banjar

Tulangampiang - Apotek Cempaka - Jl.

Astasura - SDN 28 Dangin Puri - SMP

Negeri 8 Denpasar - Toko Chaca - Jl.

Suradipa - Indomaret A.Yani - Jl. Gadung -

Jl. Patimura - SD Dwijendra Denpasar -

SMP PGRI 2 Denpasar - Jl. Lembusora -

Indomaret Antasura - Jl. Antasura - SMP

PGRI 9 Denpasar - SD Saraswati 2 - Jl.

Meduri - WR. Supratman - Jl. Nangka - SD

Saraswati 6 Denpasar

52.95430

26973108

UPT Pelayanan Transportasi Darat - Jl.

Suradipa - Toko Chaca - Jl. Nangka - SD

Dwijendra Denpasar - Jl. Lembusora -

Apotek Cempaka - SDN 28 Dangin Puri -

SD Saraswati 6 Denpasar - Jl. Astasura - SD

Saraswati 2 - Jl. Gadung - Jl. Meduri - SMP

59.77698

70774727

Route

Distance

PGRI 2 Denpasar - Banjar Tulangampiang -

SMP Negeri 8 Denpasar - Jl. Antasura -

WR. Supratman - Jl. Patimura - Indomaret

Antasura - Indomaret A.Yani - SMP PGRI 9

Denpasar

UPT Pelayanan Transportasi Darat - Jl.

Meduri - Jl. Astasura - Banjar

Tulangampiang - Apotek Cempaka - SDN

28 Dangin Puri - Indomaret A.Yani - Jl.

Nangka - Jl. Gadung - Jl. Suradipa - SMP

PGRI 2 Denpasar - Jl. Patimura - Jl.

Antasura - Jl. Lembusora - SD Dwijendra

Denpasar - SD Saraswati 2 - SD Saraswati 6

Denpasar - WR. Supratman - Indomaret

Antasura - Toko Chaca - SMP PGRI 9

Denpasar - SMP Negeri 8 Denpasar

60.06778

92287021

UPT Pelayanan Transportasi Darat - Jl.

Patimura - Apotek Cempaka - Indomaret

A.Yani - SMP Negeri 8 Denpasar - SD

Saraswati 2 - Jl. Astasura - WR. Supratman

- SMP PGRI 2 Denpasar - Indomaret

Antasura - Jl. Nangka - Jl. Antasura - Jl.

Lembusora - Jl. Meduri - Jl. Suradipa -

Banjar Tulangampiang - Jl. Gadung - SMP

PGRI 9 Denpasar - Toko Chaca - SD

Saraswati 6 Denpasar - SDN 28 Dangin Puri

- SD Dwijendra Denpasar

63.02498

53063988

UPT Pelayanan Transportasi Darat - SD

Dwijendra Denpasar - Jl. Nangka - SMP

Negeri 8 Denpasar - SMP PGRI 2 Denpasar

- Jl. Patimura - Toko Chaca - SD Saraswati

2 - Indomaret A.Yani - Jl. Gadung - SDN 28

Dangin Puri - Jl. Lembusora - Apotek

Cempaka - WR. Supratman - SD Saraswati

6 Denpasar - Indomaret Antasura - Jl.

Antasura - SMP PGRI 9 Denpasar - Banjar

Tulangampiang - Jl. Suradipa - Jl. Astasura

- Jl. Meduri

9999

UPT Pelayanan Transportasi Darat - SD

Dwijendra Denpasar - Jl. Meduri - SD

Saraswati 6 Denpasar - Jl. Nangka - Jl.

Astasura - Banjar Tulangampiang -

Indomaret A.Yani - SD Saraswati 2 -

Indomaret Antasura - Toko Chaca - SDN 28

Dangin Puri - SMP Negeri 8 Denpasar -

WR. Supratman - Jl. Antasura - SMP PGRI

2 Denpasar - Jl. Gadung - Jl. Lembusora -

Apotek Cempaka - Jl. Patimura - SMP

PGRI 9 Denpasar - Jl. Suradipa

9999

UPT Pelayanan Transportasi Darat - Toko

Chaca - SD Saraswati 6 Denpasar - SMP

PGRI 2 Denpasar - SD Dwijendra Denpasar

- Jl. Patimura - SMP PGRI 9 Denpasar -

SMP Negeri 8 Denpasar - Jl. Suradipa -

WR. Supratman - Jl. Gadung - Jl. Meduri -

Indomaret Antasura - Indomaret A.Yani -

Apotek Cempaka - Jl. Astasura - Jl. Nangka

- Jl. Lembusora - SD Saraswati 2 - Jl.

Antasura - Banjar Tulangampiang - SDN 28

Dangin Puri

64.78412

89352247

UPT Pelayanan Transportasi Darat - SD

Saraswati 2 - Jl. Suradipa - SD Dwijendra

Denpasar - Jl. Antasura - SDN 28 Dangin

Puri - Toko Chaca - Indomaret A.Yani - Jl.

Nangka - Jl. Gadung - Jl. Lembusora - Jl.

Astasura - SMP PGRI 2 Denpasar - SMP

9999

iCAST-ES 2021 - International Conference on Applied Science and Technology on Engineering Science

1330

Route

Distance

PGRI 9 Denpasar - Indomaret Antasura - Jl.

Patimura - Jl. Meduri - Apotek Cempaka -

WR. Supratman - SMP Negeri 8 Denpasar -

SD Saraswati 6 Denpasar - Banjar

Tulangampiang

UPT Pelayanan Transportasi Darat - Jl.

Patimura - Banjar Tulangampiang - SMP

PGRI 2 Denpasar - Jl. Lembusora - Jl.

Suradipa - WR. Supratman - Toko Chaca -

SMP Negeri 8 Denpasar - SD Saraswati 2 -

Apotek Cempaka - SD Dwijendra Denpasar

- Jl. Antasura - Jl. Astasura - SMP PGRI 9

Denpasar - Jl. Gadung - SD Saraswati 6

Denpasar - Indomaret A.Yani - Jl. Nangka -

Jl. Meduri - Indomaret Antasura - SDN 28

Dangin Puri

66.07797

15707438

UPT Pelayanan Transportasi Darat - SMP

Negeri 8 Denpasar - Banjar Tulangampiang

- Jl. Lembusora - Jl. Antasura - SDN 28

Dangin Puri - SD Saraswati 6 Denpasar -

SD Dwijendra Denpasar - Apotek Cempaka

- Jl. Patimura - SMP PGRI 2 Denpasar - Jl.

Astasura - SMP PGRI 9 Denpasar -

Indomaret Antasura - Indomaret A.Yani - Jl.

Meduri - WR. Supratman - SD Saraswati 2 -

Toko Chaca - Jl. Nangka - Jl. Gadung - Jl.

Suradipa

9999

UPT Pelayanan Transportasi Darat - Jl.

Nangka - Indomaret Antasura - Toko Chaca

- Jl. Lembusora - Apotek Cempaka - SD

Saraswati 6 Denpasar - WR. Supratman - Jl.

Patimura - SD Saraswati 2 - SD Dwijendra

Denpasar - SMP PGRI 2 Denpasar - Jl.

Suradipa - Indomaret A.Yani - Jl. Antasura -

SDN 28 Dangin Puri - Jl. Gadung - Jl.

Meduri - Banjar Tulangampiang - Jl.

Astasura - SMP PGRI 9 Denpasar - SMP

Negeri 8 Denpasar

48.36256

59710800

UPT Pelayanan Transportasi Darat - Banjar

Tulangampiang - Indomaret Antasura - Jl.

Antasura - Toko Chaca - SD Dwijendra

Denpasar - Jl. Meduri - Jl. Patimura - SMP

PGRI 2 Denpasar - SD Saraswati 6

Denpasar - Jl. Lembusora - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Astasura - Jl.

Suradipa - Jl. Gadung - Apotek Cempaka -

SDN 28 Dangin Puri - Indomaret A.Yani -

WR. Supratman - SMP Negeri 8 Denpasar -

SD Saraswati 2

46.97660

21267881

4.2 Final Population

Applications that have been built using the

Differential Evolution algorithm. The output of the

application is a route candidate that is getting shorter

and shorter. Table II shows the final population

results. The last population has the same number as

the population that was raised at the time of initial

initialization. In the last population, a more optimal

route candidate has been obtained with varying route

distances. The resulting difference in route distance is

much smaller than that of the first population route.

Table 2 shows the minimum route distance value

obtained is 25.75039590845092 km, and the

maximum is 26.624917440178955.

Table 2: Final population.

Route

Distance

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP Negeri 8

Denpasar - SMP PGRI 2 Denpasar - Jl.

Meduri - WR. Supratman - Apotek

Cempaka - Jl. Patimura - SD Saraswati 6

Denpasar - Jl. Antasura - Jl. Astasura -

Indomaret Antasura - Jl. Suradipa - SMP

PGRI 9 Denpasar - Jl. Nangka - Jl. Gadung -

SD Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.28123

79401957

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP Negeri 8

Denpasar - SMP PGRI 2 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.24865

28273547

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Apotek Cempaka - Jl. Gadung -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.28879

54928038

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Apotek Cempaka - Jl. Gadung -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.28879

54928038

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Apotek Cempaka - Jl. Gadung -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.28879

54928038

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

26.39077

67633963

School Bus Routing in the City of Denpasar using Differential Evolution Algorithm

1331

Route

Distance

Meduri - WR. Supratman - Apotek

Cempaka - Jl. Gadung - SD Saraswati 6

Denpasar - Jl. Antasura - Jl. Astasura -

Indomaret Antasura - Jl. Suradipa - SMP

PGRI 9 Denpasar - Jl. Nangka - Jl. Patimura

- SD Dwijendra Denpasar - SDN 28 Dangin

Puri - SD Saraswati 2

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.24865

28273547

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Apotek Cempaka - Jl. Gadung -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SDN

28 Dangin Puri - SD Dwijendra Denpasar -

SD Saraswati 2

26.04539

31569802

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Apotek Cempaka - Jl. Gadung -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SDN

28 Dangin Puri - SD Dwijendra Denpasar -

SD Saraswati 2

26.04539

31569802

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.24865

28273547

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Apotek Cempaka - Jl. Gadung -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.28879

54928038

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

26.24865

28273547

Route

Distance

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - WR. Supratman -

Apotek Cempaka - SD Saraswati 6

Denpasar - Jl. Antasura - Jl. Astasura -

Indomaret Antasura - Jl. Suradipa - SMP

PGRI 9 Denpasar - Jl. Nangka - Jl. Patimura

- SDN 28 Dangin Puri - SD Saraswati 2 -

SD Dwijendra Denpasar

26.19511

97169122

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Toko Chaca - Banjar

Tulangampiang - Jl. Lembusora - SMP

PGRI 2 Denpasar - SMP Negeri 8 Denpasar

- Jl. Meduri - Jl. Gadung - Jl. Patimura -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Apotek Cempaka -

SD Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

27.33332

78207907

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP Negeri 8

Denpasar - SMP PGRI 2 Denpasar - WR.

Supratman - Jl. Gadung - Apotek Cempaka -

Jl. Meduri - SD Saraswati 6 Denpasar - Jl.

Antasura - Jl. Astasura - Indomaret Antasura

- Jl. Suradipa - SMP PGRI 9 Denpasar - Jl.

Nangka - Jl. Patimura - SDN 28 Dangin Puri

- SD Dwijendra Denpasar - SD Saraswati 2

26.43319

43464800

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - WR. Supratman -

Apotek Cempaka - SD Saraswati 6

Denpasar - Jl. Antasura - Jl. Astasura -

Indomaret Antasura - Jl. Suradipa - SMP

PGRI 9 Denpasar - Jl. Nangka - Jl. Patimura

- SD Dwijendra Denpasar - SDN 28 Dangin

Puri - SD Saraswati 2

26.62491

74401789

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SD Saraswati

6 Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SMP PGRI 2 Denpasar -

Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SDN

28 Dangin Puri - SD Dwijendra Denpasar -

SD Saraswati 2

26.44615

42127098

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang

- Toko Chaca - Jl. Lembusora - SMP PGRI

26.24865

28273547

iCAST-ES 2021 - International Conference on Applied Science and Technology on Engineering Science

1332

Route

Distance

2 Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - Jl. Gadung - Apotek Cempaka -

WR. Supratman - SD Saraswati 6 Denpasar

- Jl. Antasura - Jl. Astasura - Indomaret

Antasura - Jl. Suradipa - SMP PGRI 9

Denpasar - Jl. Nangka - Jl. Patimura - SD

Saraswati 2 - SDN 28 Dangin Puri - SD

Dwijendra Denpasar

26.24865

28273547

UPT Pelayanan Transportasi Darat -

Indomaret A.Yani - Banjar Tulangampiang -

Toko Chaca - Jl. Lembusora - SMP PGRI 2

Denpasar - SMP Negeri 8 Denpasar - Jl.

Meduri - WR. Supratman - Jl. Gadung -

Apotek Cempaka - SD Saraswati 6

Denpasar - Jl. Antasura - Jl. Astasura -

Indomaret Antasura - Jl. Suradipa - SMP

PGRI 9 Denpasar - Jl. Nangka - Jl. Patimura

- SDN 28 Dangin Puri - SD Dwijendra

Denpasar - SD Saraswati 2

25.75039

59084509

Based on the data from the Differential Evolution

algorithm in Table II, the shortest route obtained is

the minimum distance route of 25.75039590845092

km. The route obtained is as follows:

UPT Pelayanan Transportasi Darat - Indomaret

A.Yani - Banjar Tulangampiang - Toko Chaca - Jl.

Lembusora - SMP PGRI 2 Denpasar - SMP Negeri 8

Denpasar - Jl. Meduri - WR. Supratman - Jl. Gadung

- Apotek Cempaka - SD Saraswati 6 Denpasar - Jl.

Antasura - Jl. Astasura - Indomaret Antasura - Jl.

Suradipa - SMP PGRI 9 Denpasar - Jl. Nangka - Jl.

Patimura - SDN 28 Dangin Puri - SD Dwijendra

Denpasar - SD Saraswati 2.

5 CONCLUSIONS

Based on the data of the initial population and the

final population from the Differential Evolution

algorithm, it was found that the individual candidates

(routes) in the final population were much better with

a shorter route than the initial population. We can

conclude, the Differential Evolution algorithm is

effectively used to find the minimum value in the case

of route search.

REFERENCES

Leung, J., Kern, K. and Dawson, J. (2007). Genetic

Algorithms and Evolution Strategies, presentation

slide.

Eiben, A. E. and Smith, J. E. (2003). Introduction to

Evolutionary Computing. Springer-Verlag Berlin

Heidelberg, New York.

Lin, Y.C. (2013). Mixed-integer constrained optimization

based on memetic algorithm, Journal of Applied

Research and Technology, vol 11, pp. 242-250.

Deb, K. (2001). Multi-Objective Optimization Using

Evolutionary Algorithms. John Wiley, NJ.

Suyanto, (2008). Evolutionary Computation: Komputasi

Berbasis Evolusi dan Genetika. Informatika, Bandung.

Storn, R. and Price, K. (1997). Differential Evolution – A

Simple and Efficient Heuristic for global Optimization

over Continuous Spaces, Journal of Global

Optimization, vol. 11, pp. 341–359.

Gong, W. et al., (2014). Engineering optimization by means

of an improved constrained differential evolution,

Computer Methods in Applied Mechanics &

Engineering, vol 268, pp. 884-904.

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