scieee Science in your language
[en] (orig)
International Journal for Quality Research 16(2) 375–394
ISSN 1800-6450
1 Corresponding author: Cristiano Fragassa
Email: cristiano.fragassa@unibo.it 375
Matej Babic
Cristiano Fragassa1
Dragan Marinkovic
Janez Povh
Article info:
Received 10.06.2021.
Accepted 05.01.2022.
UDC – 004.85
DOI – 10.24874/IJQR16.02-04
MACHINE LEARNING TOOLS IN THE
ANALYZE OF A BIKE SHARING SYSTEM
Abstract: Advanced models, based on artificial intelligence
and machine learning, are used here to analyze a bike-
sharing system. The specific target was to predict the number
of rented bikes in the Nova Mesto (Slovenia) public bike
share scheme. For this purpose, the topological properties of
the transport network were determined and related to the
weather conditions. Pajek software was used and the system
behavior during a 30-week period was investigated. Open
questions were, for instance: how many bikes are shared in
different weather conditions? How the network topology
impacts the bike sharing system? By providing a reasonable
answer to these and similar questions, several accurate ways
of modeling the bike sharing system which account for both
topological properties and weather conditions, were
developed and used for its optimization.
Keywords: Transportation Systems Engineering; Bike-
Sharing System (PBS); Artificial Intelligence (AI); Machine
Learning (ML); Hybrid Intelligent Systems; Weather
Conditions.
1. Introduction
1.1. Quality of Life
The efficiency of public transport operation has
a relevant and direct impact on the individual
Quality of Life, especially in the case of
crowded cities, where, due to a combination of
reasons (e.g., traffic, lack of parking), a private
car no longer guarantees sufficient mobility to
the owner (Berg et al., 2019; Ali et al., 2020).
Ensuring that anyone, regardless of the
social status, can easily move between
different destinations (e.g., to the places of
work, care, feed, study, recreation, etc.) can
be deemed as fundamental human right that
every public transport policy must assure
when addressed to support the development
of the individual sphere of life.
Moreover, even if the crucial role of the
public transport in the economic and social
growth of cities and districts is evident, it has
to be always considered including aspects of
ecology and safety. Sustainability, in fact, is
another important aspect in this equation
(Durmić et al., 2020).
However, solving problems related to the
public transport often represents a difficult
task since the systems complexity and the
potential impacts of any change. Hence, the
interest in developing suitable approaches to
model public transport systems and to
predict the effect of each change emerges,
including recent methods based on artificial
intelligence (AI) & machine learning (ML).
The Quality of Life comes back again,
finally, when, as in our case, mobility is
achieved through healthy and sustainable
means of transport, such as bicycles.
Cycling, like any other sport, has a positive
effect on the state of the athlete’s body,
helping to keep it young and healthy.
Babic et al., Machine learning tools in the analyze of a bike sharing system
376
Bicycling refers to a cyclic type of physical
activity that develops the cardiovascular
system, lungs, muscles, and increases the
general healthiness of the human body.
Medical evidence also exists that cycling can
help prevent many serious illnesses (Celis-
Morales, 2017) but it also improves overall
strength, balance, and coordination.
Hence, emerging together with a more active
and healthier lifestyle (Woodcock et al.,
2014), even extreme cycling events as
marathons (Menaspà et al., 2012) and
mountain biking (Weiss et al., 2016) have
also become quite popular in recent years.
In short, cycling is healthy, funny, cheap,
and practical. It is therefore understandable
why bike sales and rents are increasingly
spreading everywhere (DeMaio, 2009).
1.2. Bike Rental Services
Bike rental services (BRS) have shown a real
explosion in recent years, favored not only
by such an increased attention to health and
the environment benefits, but also by the
larger use of technology in terms of traction
(e.g., pedal assist) and control (e.g., geo-
localized APPs to locate, book, unlock, pay).
BRS operate in accordance with the
recognized technologies for managing rental
points by ICT services and allow to optimize
all the processes related to the customer
service. In this way, modern BRS are able to
offer an effective service response to an
increasing number of users who prefer bikes
to cars, especially during the warmer periods
of year (Barbour et al., 2019).
Bike travelling can provide several logistic
benefits to users, given the heavy traffic
during rush hours, constant traffic jams,
endless road works and parking limitations.
At the same time, a good quality bike can be
quite expensive while renting usually does
not cost much, even less than a bus ticket.
Therefore, many city dwellers find it easier
to rent bikes as needed instead of buying.
Approximately 18 million public bicycles
are available in 1608 cities around the world.
Thus, Public Bicycle Sharing Programs
(PBSPs) have become a prominent feature
across city spaces worldwide. In less than a
decade, PBSPs have grown from a small
number of European cities to include five
continents and more than 200 schemes. And
these public bikes have already proven their
positive effects in terms of
a) increasing cycling in many urban areas,
b) reducing traffic congestions of towns,
c) improving eco-sustainability in mobility,
especially in combination with a rational
public transport (IPCC, 2017; IEA. 2014).
Hence, PBSPs’ optimization, including bike
rental services, can be considered as a
priority for administrators of large and small
cities. It represents, in fact, an effective way
for reducing air pollution, congestion and
carbon emissions.
At the same time, most public transport
systems can also be seen as business
processes to be analyzed, modified, and
optimized. When their optimization has been
performed, these systems not only become
more efficient and profitable, but
environmentally friendly and safe too.
1.3. Design parameters
Optimizing the level of quality for bike
rental services (BRS) also means to find how
comfortable on-call transport should be from
the point of view of waiting for transport,
travel time and density of entry and exit
locations.
The waiting time for transport means the
longest time allowed while the user is still
ready to wait for transport. This time must be
competitive with other existing transport
options, such as public transport. According
to the experience of systems abroad, the
usual average waiting time for transport is
somewhere between 10 and 20 minutes.
Another parameter that needs to be
determined when designing a system is the
longest time a passenger can spend on the
journey. This means the difference in time if
an individual travels the route from point A
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
377
to point B on the usual (fastest) route and the
time if other passengers join in while driving
and the route is extended as a result of the
vehicle making a certain detour.
The density of entry and exit stops is the
third parameter. Stops are usually virtual
locations that are marked in the app, but they
do not have to exist physically (such as bus
stops). Virtual points are usually set at
various intersections, institutions, or other
striking locations. It is important that they
are recognizable, and that the vehicle can
stop there safely. It is recommended that the
walking time to the stops is not too long, but
on the other hand, the excessive density of
entry and exit stops can confuse people and
put more strain on the system.
It is also important that bus stops cover areas
where there are currently no existing bus
stops and increase density where existing
stops are placed too infrequently.
Some systems also provide door-to-door
service. Such a solution enables higher
accessibility of transport, which is especially
suitable for the elderly and disabled people.
On the other hand, for this level of service
with the same number of vehicles, it is
necessary to wait longer for transport, and
the travel time is also extended (Bodini et
al., 2013).
1.4. System modelling
The optimal design and management of BRS
should take into consideration a huge array
of variables and situations related to
topology, population and behavior. In this
way it should be possible, for instance, to
recognize and optimize aspects as docking
stations (e.g., positions, distances) on the
territory and bikes (distributions).
However, a different optimization approach
would also be possible, without entering in
such a level of details: it is exclusively based
on the overall number of bicycles and aims
to provide an adequate number of bikes to
the users accounting for expected situations.
This is what is also reported in the present
study where the investigation is not intended
to modify the pre-existing network structure.
Whatever the approach chosen, and the level
of detail used, every sort of optimization
brings up the possibility to make use of
engineering analysis in order to model the
transport systems (van Wee, 2015). In this
manner, it is possible to predict the impact of
every change in the system and identify the
most effective ones in terms of cost, safety,
traffic capacity and other factors.
Several recent methods for transport system
optimization are based on Information &
Communication Technology. This trend is
called digital transformation or digitalization
of transport and involves several alternative
approaches. Among them, Machine learning
(ML) (Char et all, 2018) represents one of
the most promising approaches, as it
involves the concepts such as artificial
intelligence (AI) and expert systems.
1.5. Weather conditions
Among the various external conditions to be
included in every transport optimization,
weather forecast is quite a relevant one,
especially because of its direct influence. So,
an open problem consists in the estimation of
bikes demand with respect to different
weather conditions and the answer to this
problem is not straightforward. It calls for
development of an expert system based on
machine learning. And it is by no means a
small problem given the potential effects on
local transport.
In (Corcoran et al., 2014), the impact of local
weather conditions and calendar events on
the spatial-temporal dynamics of a PBSP
was explored by using novel spatial
analytical techniques. In (Rixey, 2013) the
effects of demographic and environmental
factors near 3 bike sharing stations on the
bike sharing ridership levels in three
operational US systems were investigated.
Results highlight how the ridership levels is
strongly affected by the topological
Babic et al., Machine learning tools in the analyze of a bike sharing system
378
properties of the bike sharing station
network, with a robust, statistically
significant relationship between the systems
and bike use, and independent from other
variables, such as demography and age
distribution.
Another research (Fuller et al., 2019) has
also examined the potential of actions and
changes on highly constrained transportation
systems and their potential impact on
cycling. In the period November 1-7th, 2016,
Philadelphia's transit workers went on strike,
stopping all transit services in the city. The
authors used the strike event as a natural
experiment to examine the impact of public
transit strikes on the use of Philadelphia's
bicycle share program. Two separate
approaches were used for this investigation:
interrupted time series and Bayesian
structural time series models. However, the
interdependencies between bicycle sharing
and public transportation systems were not
totally clear in that analysis.
In (Saberi at al., 2018), authors found that
the disruption of public transportation in
London increased the total number of
bicycles sharing trips by 85% from an
average 38,886 to 72,503 trips per day.
Considering similar situations, Lin et al.
(2018) proposed a novel Graph
Convolutional Neural Network with Data-
driven Graph Filter (GCNN-DDGF) model
that can learn hidden heterogeneous pairwise
correlations between stations to predict
station-level hourly demand in a large-scale
bike-sharing network.
Partially in line with the mentioned works,
this research presents an approach based on
expert systems for modeling a bike sharing
system, but it uses other machine learning
(ML) tools with the aim at finding the best
way for merging the topological properties
of the network with the weather conditions.
2. Materials and Methods
2.1. The location
The present work aims at predicting the
variability of bikes demand in the specific
case of Nova Mesto (Slovenia) bike-sharing
system (GoNM), including in this prediction
environmental factors, in order to optimize
offer and help reduce the use of cars.
According to the national Statistical Office,
in 2019 in the Municipality of Novo Mesto,
Slovenia, there were living slightly more
than 37.000 inhabitants, on an area of 236
km2, resulting in a density of 157
inhabitants/km2. This population makes the
Municipality of Novo Mesto the 6th largest
one in the country, with a population density
higher (+52%) with respect to the national
average (103 inhabitants/km2).
The City of Novo Mesto, approximately 33.3
km2, is the urban center of the Municipality
and the administrative, educational, health,
economic and cultural center of the wider
region of South-Eastern Slovenia. With its
industry, this area is the carrier of the fastest
economic development in the region. A
strong automotive, pharmaceutical, and
cosmetic industry has developed, as well as
the insulation materials industry (Krka,
Revoz, Adria Mobil, TPV), which also
provides private labor silos from elsewhere.
The old town is nestled between the Krka
riverbeds. From the central part, the city
extends outwards along the main city
entrances. Settlement outside the city center
is quite dispersed. Population density in the
municipality is shown in Fig. 1.
As in other parts of Slovenia and EU, the
population is rather elderly discouraging the
use of bikes: 107 inhabitants are over 64
years old per 100 young people, under 15.
This value is less compared to the Slovenian
average (of 132) but the gap is closing fast.
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
379
Figure 1. Population density (per 100m2) in
Novo Mesto, Slovenia
2.2. The system
GoNM bike-sharing system was established
in 2017 when the city acquired an automatic
bicycle rental system, making bike renting
easy. It is enough to be registered and, by an
appropriate card, it is possible to pick up the
bike at 1 of the 14 docking stations and leave
there or at another station (Figs. 2 and 3).
Figure 2. GoNM bike rental system with its
14 stations and distances
Figure 3. A GoNM bike docking station
2.3. Data and information
Anonymous information related to GoNM
users (who rent a bike) during the 30-week
period since 25th April 2020 till 20th
November 2020, were provided by the
Municipality of Novo Mesto. Data included
approximately 7,000 items with user IDs,
Renting & Returning stations, Renting &
Returning Time and user’s birth year (see
Table 1).
Similarly, the total number of bicycles used
each week were also provided (see Table 2).
As displayed in Fig. 4, the number of bikes
changes a lot during the observation period,
from 11 to 132 bikes, with an average value
of 30 and standard deviation of 34. This
variability in the service demand highlights
the need to enable frequent adjustments of
the bikes’ availability.
Table 1. Sample data of GoNM public bicycle system.
User ID
Renting Station
Returning
Station
Returning Time
Birth
year
6*1**-
20
Ragovska ulica
Avtobusna
postaja
Topliška cesta
26.05.2020
17:56:24
1999
6*4**-
20
Novi trg
Šolski center
Novo mesto
31.03.2020
19:15:21
1957
6*2**-
20
Drska - Šegova
ulica
Podbreznik
26.05.2020
17:17:34
1989
6*3**-
20
Ločna-Seidlova
cesta
Kandijski most
02.06.2020
14:05:39
1970
Babic et al., Machine learning tools in the analyze of a bike sharing system
380
Table 2. Weekly rented bikes vs weather conditions as temperature (T); wind velocity (WV);
cloudy (C); relative humidity (RH); air pressure (AP); rainfall (R); sun time (SD).
Week
Bikes
T
WV
C
RH
AP
R
ST
N.
(n)
[°C]
[m/s]
[%]
[%]
[hPa]
[mm]
[h]
1
28
14.27
1.56
64.86
73.57
984.57
4.49
4.57
2
43
14.30
1.77
25.71
60.00
992.57
1.67
10.54
3
132
14.76
2.49
73.86
72.00
988
3.03
4.66
4
98
15.63
1.78
70.08
74.62
992.15
2.94
4.7
5
108
14.96
1.44
66.63
73.84
995.68
3.83
5.29
6
72
17.54
1.55
52.43
66.86
984.71
1.19
7.59
7
68
18.11
1.73
34.14
73.00
985.29
5.04
8.47
8
39
18.80
1.33
75.14
80.00
986.25
7.63
5.59
9
40
20.74
1.29
42.29
66.29
992.29
2.13
10.2
10
56
21.73
1.39
43.29
75.86
988.43
2.09
8.79
11
112
21.24
1.37
16.71
65.29
990.57
3.06
12.19
12
101
17.60
1.63
48.63
72.63
991.88
4.68
10.05
13
80
21.30
1.00
42.57
77.57
990.14
6.93
8.64
14
58
25.03
1.20
21.71
73.43
990.29
1.33
11.41
15
52
20.36
1.49
67.71
84.71
989.00
6.99
5.21
16
71
23.16
1.03
29.86
79.14
990.14
2.64
8.89
17
90
19.58
1.36
46.8
73.85
990.46
3.90
8.27
18
78
21.91
1.59
49.43
70.43
987.43
0.13
8.33
19
91
17.44
1.27
39.57
80.29
991.00
11.13
6.23
20
77
18.83
1.36
29.57
76.00
994.57
0.00
8.57
21
131
10.72
1.35
66.54
85.03
992.26
4.97
3.98
22
119
15.71
1.30
79.00
83.57
983.83
6.53
4.79
23
78
13.4
1.56
51.57
83.86
982.71
5.51
5.57
24
106
12.79
1.56
53.71
83.43
989.43
9.79
5.66
25
70
8.64
1.50
87.29
86.71
986.43
11.69
1.96
26
47
11.39
1.71
41.57
81.71
995.00
0.07
5.13
27
12
12.13
1.27
64.71
83.71
990.71
4.19
3.96
28
22
10.00
1.09
56.57
80.14
1001.14
0.11
5.06
29
11
5.57
1.05
90.57
91.29
1000.71
0.13
1.13
30
21
5.72
1.03
82.83
93.17
999.67
7.78
1.48
In this regard, it is important to underline
that those bikes are meant to be used several
times during the same day.
On average, 30 bicycles were able to satisfy
the request mobility coming from about 230
users per week, hence nearly 1 ride per day.
Therefore, even at a first glance, it is evident
the GoNM bike-sharing system is subject to
a very strong variability that, if not properly
managed by mitigation actions, leads to a
general underutilization of the bikes.
It follows that a system optimization can
really provide tangible benefits, but it cannot
be done without including further boundary
conditions, such as the weather.
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
381
Weather data during the same 30 weeks were
acquired (from Weather Society Zeus,
Slovenia) including: Temperature [C],
Wind Velocity [m/s], Cloudy [%], Relative
Humidity [%], air Pressure [hPa], Rainfall
[mm] and Sun Duration [h] (see Table 2). A
part of this information is shown in Fig. 4
where Temperature, Wind Velocity, Cloudy,
Rainfall and Sun Duration trends are
displayed against the rented bikes.
Figure 4. Rented bikes vs temperature, wind
speed, cloudy, rainfall and sunny time.
Even from a preliminary data analysis, no
clear relationship emerges between rented
bikes and weather conditions. A rather weak
correlation can be numerically estimated (by
Pearson correlation coefficients) between the
bikes rented and weather conditions:
Temperature (0.25), Wind Velocity (0.4),
Cloudy (-0.11), Relative Humidity (-0.21),
air Pressure (-0.33), Rainfall (0.21) and Sun
Duration (0.20). This is apparently illogical:
for instance, it is clear that rain reduces the
number of riders. On the other hand, these
same correlation values, never negligible,
suggest that a certain relationship still exists.
In correlating these data, it is necessary to
consider that the effect of weather conditions
onto the bicycle rental demand should be
examined on a daily (rather than weekly)
basis. However, the management of the
service (i.e., change in the number of
bicycles available in the area) does not allow
for a sampling period shorter than a week.
This difference makes machine learning
even more interesting. The analysis will
provide data about its ability to find patterns
among data available on weakly basis (in
contrast to data available on daily basis).
2.4. Topological properties
In this research, we use the graph theory
(Vecchio, 2017) as a mathematical tool. The
graph theory (as a part of the network theory
(Saleh et al., 2018)) is a section of discrete
mathematics that examines the properties of
finite sets and the relationships between their
individual elements. In mathematics, graph
theory or network theory, a graph or network
is a structure amounting to a set of vertices
(nodes or points) in which some pairs of the
vertices are in relationship with edges. In the
public transport system, we denote a station
as a node. If a passenger rents a public
bicycle at station X and returns it to station
Y, there is a directed edge pointing from X
to Y. On the other hand, the weight of this
edge is equal to the number of cycling
records from X to Y, which can show how
0
0.5
1
1.5
2
2.5
3
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Wind Speed [m/s]
Bikes
Week
Wind speed
SUMMER AUTUMN
SPRING
0
2
4
6
8
10
12
14
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sunny Time (h)
Bikes
Week
Sunny Time
SUMMER AUTUMN
SPRING
Babic et al., Machine learning tools in the analyze of a bike sharing system
382
close the relationship between X and Y is.
Hence, a PBN is a directed weighted
network. Graphs form the basis upon which
semantic networks (Sun & Zhuge, 2018),
cognitive maps (Warren et al., 2017), neural
networks (Garrido et al., 2014) and
economic models (Emmert-Streib et al.,
2018) are constructed and transport problems
(van Lierop et al., 2018) are solved. In Fig. 5
one example of an artificial network
representing the bike renting system with its
14 stations is depicted. The present analysis
is strictly in line with previous studies of the
authors (Babic et al., 2018 and 2020).
Figure 5. Artificial network representing
the bike-sharing system with 14 stations
Four topological properties were considered
in order to schematize the transportation
systems network: Degree, Network Density,
Betweenness centrality and Clustering
coefficient of the network. They are defined
in the following.
Degree (D)
The total degree of a node i (𝑘𝑖𝑡𝑜𝑡𝑎𝑙) is equal
to the sum of its in-degree 𝑘𝑖𝑖𝑛 and out-
degree 𝑘𝑖𝑜𝑢𝑡:
𝑘𝑖𝑖𝑛=∑𝑎𝑖𝑗𝑗 𝑘𝑖𝑜𝑢𝑡=∑𝑎𝑖𝑗𝑗 ()
𝑘𝑖𝑡𝑜𝑡𝑎𝑙= 𝑘𝑖𝑖𝑛+𝑘𝑖𝑜𝑢𝑡 ()
where 𝑎𝑖𝑗 is the adjacency matrix element
corresponding to its nodes. Out-degree
𝑘𝑖𝑜𝑢𝑡 represents the number of bikes, rented
from station i, that are returned to any
destination station. In-degree 𝑘𝑖𝑖𝑛 represents
the number of bicycles, rented from any
origin station, that are returned to station i.
Network Density (ND)
The ND measures the territorial occupation
of a transport network in terms of km of
links (L) per square kilometers of surface
(S). The higher it is, the more a network is
developed:
=𝐿𝑆 ()
Betweenness centrality (BC)
The BC is an important statistical property of
a network, applied in many real-world
problems, such as finding border-crossing
points that have most extensive traffic or a
trade flow. It measures the accessibility that
is the number of times a node is crossed by
the shortest paths in the graph. An
anomalous value of centrality is detected
when a node has a high betweenness
centrality and a low order (degree centrality).
The betweenness centrality of a node i is
given by the expression:
∑ 𝜎𝑠𝑡(𝑖)
𝜎𝑠𝑡
𝑠≠𝑖≠𝑡 ()
where σst is the total number of the shortest
paths from node s to node t and σst(i) is the
number of those paths that pass through i.
Clustering coefficient (CC)
The CC, also known as the network
transitivity, shows how well the neighbors of
a node are connected to each other. For node
i with degree ki, 𝑒𝑖𝑗 is distinct from 𝑒𝑗𝑖. The
local clustering coefficient for a directed
network is defined as
ci=|{𝑒𝑗𝑘:𝑣𝑗,𝑣𝑘∈ 𝑁𝑖,𝑒𝑗𝑘∈𝐸 }|
𝑘𝑖(𝑘𝑖−1) ()
Then, the clustering coefficient is the
average value of network clustering
coefficients, defined as:
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
383
CC=1
𝑛∑ci
n
𝑖=1 ()
2.5. Standard models
Several conventional methods (Gomes et al.,
2017) are considered first:
a) Genetic Programming (GP)
GP is a collection of methods for the
automatic generation of computer programs
that solve carefully specified problems by
using highly abstracted principles of natural
selection. At the beginning, we have some
randomly written programs, which represent
the initial population. In the next steps, by
crossing and selection, we get the next
generations. Additional details are available in
(Kovačič et al., 2020; Pavlović et al., 2019).
Table 3 lists the used parameters for GP: the
population size of organisms, the maximum
number of generations, reproduction and
crossover probability, the maximum
permissible depth in the creation of
population and after the operation of
crossover of two organisms, the smallest
permissible depth of organisms in generating
new organisms and tournament size used for
the selection of organisms.
Table 3. Input parameters of the Genetic
Programming (GP)
Size of the population of organisms
500
Maximum number of generations
100
Reproduction probability
0.6
Crossover probability
0.5
Maximum permissible depth in the
creation of the population
8
Maximum permissible depth after
crossover between two organisms
10
Smallest permissible depth in
generating new organisms
4
Tournament size used for selection of
organisms
6
b) Artificial neural network (NN)
NN consists of a configurable stratification
of nodes (input, hidden, and output layers),
connected by artificial neurons, typified by
developed weights that modulate signals’
crossing. Additional details are available in
(Le et al., 2020; Albu et al., 2019).
Table 4 lists the used parameters for NN:
learning speed, inertial coefficient, learning
set tolerance, test mass tolerance and number
of layers.
Table 4. Input parameters of the Artificial
Neural Network (NN)
Learning speed
0.7
Inertial coefficient
0.6
Test mass tolerance
0.03
Tolerance of the learning set
0.02
Number of layers
6
c) Multiple Regression (MR)
MR analyzes the relationship between one
dependent variable and several independent
variables by an equation of the following
form:
Y = b0+b1×X1+…+b6×X6+e, (7)
where Y is the dependent variable, the b's are
the regression coefficients for the
corresponding X (independent) terms, b0 is a
constant (or intercept,) and e is the error term
reflected in the residuals. Additional details
are available in (Saldana-Perez et al., 2019).
2.6. Hybrid models
Hybrid machine learning models aim at
combining the strengths offered by different
AI models (Vadlamani et al., 2013). It makes
sense as long as these methods offer
independent predictions.
In the present research, several numerical
combinations of predicted values coming
from the three conventional models (MR, GP
and NN) were considered and compared
with the scope to search for an accurate
combination. For instance, hybrid outputs
were set, time by time, as minimum, mean or
maximum between MR, GP, NN, or between
only two of them. Rounding up, down and to
the nearest integer operators were involved.
More advanced approaches were also taken
in consideration such as, e.g., a 'two out of
three' system logic able to identify which
Babic et al., Machine learning tools in the analyze of a bike sharing system
384
estimator was to be eliminated (given a
prediction very far from the others and,
therefore, probably incorrect), averaging the
values of the remaining two.
The comparison (with respect to real values
and to the other estimators) was carried out
using various immediate criteria, such as:
• error in predicting the total number
of rented bikes in the entire period;
• error in predicting the average
weekly value of bikes used;
• linear correlation between
predictions.
similarly to (Fragassa et al. 2019 & 2020).
3. Results and discussion
GoNM consists of a transport network
conveniently representable by an artificial
network with 14 nodes (one per station), as
already shown in Figure 5. One can see there
directed edges between the nodes (stations),
and the weights are the number of public
bicycles rented or returned. Table 5 reports
the topological properties of the network (D,
ND, BC and CC), also highlighting max. and
min. values. For instance, the Network
Density (ND) is maximum (8.210-2) at the
2nd week and minimum (4.310-2) at the 27th
and 29th weeks.
Figure 6. Topological properties.
3.1. Degree
The average out-degree is 64 with the
maximum being 132 and the minimum 11.
Fig. 7 presents, as an example, the
distribution degree and log-degree for the 3rd
week. In a log–log plot, the least square
estimation was applied to estimate the out-
degree distribution, the in-degree
distribution, and the regression equations
with the coefficient of determination R2,
which showed a fitting effect. All graphs
have R2 = 1.
Figure 7. Degree/log-degree distribution of
the network: (a) Out-degree; (b) In-degree;
(c) log-Out-degree; (d) log-In-degree.
b
c
d
a
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
385
Table 5 also reports k coefficient of graph
log-Out-degree distribution and log-In-
degree distribution of the bike sharing
network. The network has the maximum k in
the 27th and 29th week and the minimum is in
the 3rd week.
Table 5. Bike sharing network topological properties.
Week
Topological properties
k – coefficient
N
D
ND
BC
CC
Out
In
1
2.125
0.0664
0.0908
0.1042
0.0345
0.0345
2
2.625
0.0820
0.0879
0.0000
0.0233
0.0238
3
7.125
0.2227
0.2954
0.2667
0.0076
0.0076
4
5.250
0.1641
0.0816
0.2593
0.0133
0.0103
5
6.125
0.1914
0.2759
0.2422
0.0096
0.0093
6
4.125
0.1289
0.1734
0.1228
0.0152
0.0152
7
4.125
0.1289
0.1765
0.1837
0.0147
0.0145
8
3.000
0.0938
0.0849
0.2581
0.0278
0.0278
9
3.250
0.1016
0.1597
0.1136
0.0263
0.0263
10
4.000
0.1250
0.1905
0.2688
0.0179
0.0179
11
6.250
0.1953
0.1452
0.1598
0.0090
0.0090
12
5.500
0.1719
0.1295
0.2204
0.0111
0.0108
13
4.125
0.1289
0.1013
0.2727
0.0133
0.0133
14
3.125
0.0977
0.0454
0.3000
0.0192
0.0192
15
3.500
0.1094
0.0615
0.2856
0.0192
0.0217
16
3.750
0.1172
0.0876
0.2750
0.0164
0.0164
17
5.125
0.1602
0.1172
0.2458
0.0116
0.0114
18
5.625
0.1758
0.1504
0.3311
0.0135
0.0135
19
5.875
0.1836
0.1379
0.2840
0.0115
0.0114
20
5.500
0.1719
0.1225
0.3100
0.0132
0.0132
21
6.125
0.1914
0.0893
0.2731
0.0526
0.0079
22
6.125
0.1914
0.1213
0.2655
0.0093
0.0087
23
5.875
0.1836
0.1619
0.2480
0.0128
0.0128
24
5.500
0.1719
0.1522
0.0235
0.0089
0.0091
25
3.875
0.1211
0.2785
0.2245
0.0143
0.0139
26
2.875
0.0898
0.1333
0.2931
0.0217
0.0208
27
1.375
0.0430
0.0384
0.1545
0.0909
0.0909
28
2.000
0.0625
0.0533
0.0000
0.0500
0.0556
29
1.375
0.0430
0.0137
0.0000
0.0909
0.0909
30
1.750
0.0547
0.0473
0.0000
0.0526
0.0476
3.2. Network Density
A network’s density is the number of
connections divided by the number of
potential connections. The density of a graph
is a measure of how many ties between
actors exist compared to how many ties
between actors are possible, given the graph
size (number of nodes) and the graph order
(number of links).
As such, the density of an undirected graph
is quite simply calculated as the ratio of the
observed number of edges (the cardinality of
Babic et al., Machine learning tools in the analyze of a bike sharing system
386
the edge set) to the graph maximum size.
Another way to think about density is as
giving the probability that, if we were to
choose two random nodes in the network,
this random dyad will have probability p of
being connected (as opposed to null). To
compute the density of a directed graph,
there is no need to multiply the numerator by
two, as each edge does single duty.
Fig. 8 shows the network density during the
period of 30 weeks. The regression equation
is:
y = −0.00014x + 0.1536, (8)
with the coefficient of determination of
R2 = 0.0558. (9)
In statistics, a moving average is a
calculation used to analyze data points by
creating a series of averages of different
subsets of the full data set. The reason for
calculating the moving average is to help
smoothing out the sharing data by creating a
constantly updated average price. By
calculating the moving average, the impacts
of random, short-term fluctuations on the
bike sharing of a stock over a specified
period are mitigated. The line in Fig. 8
represents a moving average.
Figure 8. Network density.
3.3. Clustering coefficient
Clustering coefficient is, as previously
mentioned, the overall probability for the
network to have adjacent nodes
interconnected, thus revealing the existence
of tightly connected communities. Fig. 9
represents the clustering coefficient over the
30-week period. In this density plot, the
regression equation was:
y = −0.00018x + 0.2272, (10)
with the coefficient of determination:
R2 = 0.0222. (11)
Figure 9. Clustering coefficient trend
3.4. Formula
The formulation of the Genetic programming
(GP) and Multiple regression (MR) models
in the specific case of the network under
investigation is reported in, respectively, Eq.
8 and 9 (see Appendix A). For instance,
between the four topological properties, the
highest impact on the model is due to ND
(since rather high coefficients as 639.378).
3.5. Predictions
Table 6 reports predictions from different
estimation models against real data. Results
are also shown in Fig. 10. Moreover, Table 7
also reports predictions for weather forecast,
topology properties and expected number of
rented bikes during the different periods
(spring, summer, and autumn) in terms of
min, max and average seasonal values. One
hybrid model, between several available,
was also here included (explicitly defined as
MIN (GP, NN)).
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
387
Figure 10. Real vs predicted data.
Table 6. Real data (RD) vs predictions by multiple regression (MR), genetic programming
(GP), artificial neural network (NN) and hybrid machine learning models (H).
Week
RD
Predictions
Error
N
MR
GP
NN
H
MR
GP
NN
H
1
28
26
27
52
26
-7.1%
-3.6%
85.7%
-7.1%
2
43
44
43
112
43
2.3%
0.0%
160.5%
0.0%
3
132
127
132
126
126
-3.8%
0.0%
-4.5%
-4.5%
4
98
91
92
95
91
-7.1%
-6.1%
-3.1%
-7.1%
5
108
106
115
132
106
-1.9%
6.5%
22.2%
-1.9%
6
72
63
68
78
63
-12.5%
-5.6%
8.3%
-12.5%
7
68
66
67
79
66
-2.9%
-1.5%
16.2%
-2.9%
8
39
47
42
52
42
20.5%
7.7%
33.3%
7.7%
9
40
48
53
58
48
20.0%
32.5%
45.0%
20.0%
10
56
57
56
57
56
1.8%
0.0%
1.8%
0.0%
11
112
109
111
105
105
-2.7%
-0.9%
-6.3%
-6.3%
12
101
103
94
89
89
2.0%
-6.9%
-11.9%
-11.9%
13
80
70
81
71
70
-12.5%
1.3%
-11.3%
-12.5%
14
58
48
54
71
48
-17.2%
-6.9%
22.4%
-17.2%
15
52
56
51
48
48
7.7%
-1.9%
-7.7%
-7.7%
16
71
53
60
58
53
-25.4%
-15.5%
-18.3%
-25.4%
17
90
90
85
77
85
0.0%
-5.6%
-14.4%
-5.6%
18
78
95
89
68
68
21.8%
14.1%
-12.8%
-12.8%
19
91
106
90
106
90
16.5%
-1.1%
16.5%
-1.1%
20
77
89
84
112
84
15.6%
9.1%
45.5%
9.1%
21
132
114
117
109
109
-13.6%
-11.4%
-17.4%
-17.4%
22
119
112
123
56
56
-5.9%
3.4%
-52.9%
-52.9%
23
78
102
97
119
97
30.8%
24.4%
52.6%
24.4%
24
106
96
105
89
89
-9.4%
-0.9%
-16.0%
-16.0%
25
70
64
66
106
66
-8.6%
-5.7%
51.4%
-5.7%
26
47
39
36
36
36
-17.0%
-23.4%
-23.4%
-23.4%
27
12
13
14
11
11
8.3%
16.7%
-8.3%
-8.3%
28
21
24
23
18
18
14.3%
9.5%
-14.3%
-14.3%
29
11
14
12
21
12
27.3%
9.1%
90.9%
9.1%
30
21
26
17
19
17
23.8%
-19.0%
-9.5%
-19.0%
Average
70
69
70
74
63
2.2%
0.6%
14.0%
-7.4%
Babic et al., Machine learning tools in the analyze of a bike sharing system
388
Table 7. Seasonal predictions (in terms of average, maximum and minimal values) of weather
conditions - temperature (T); wind velocity (WV); cloudy (C); relative humidity (RH); air
pressure (AP); rainfall (R); sun time (SD) - and rented bikes.
Weather conditions
Topological properties
Bikes
T
WV
C
RH
AP
R
SD
D
ND
BC
CC
N
Spring
Avg
16.04
1.70
57.85
71.7
988.6
3.72
6.42
4.31
0.134
0.15
0.17
73
Max
18.80
2.49
75.14
80.0
995.6
7.63
10.54
7.12
0.222
0.29
0.26
132
Min
14.27
1.33
25.71
60.0
984.5
1.19
4.57
2.12
0.066
0.08
0.00
28
Summe
r
Avg
21.26
1.335
40.90
73.9
990.0
3.38
9.19
4.42
0.138
0.11
0.24
73
Max
25.03
1.63
67.71
84.7
992.2
6.99
12.19
6.25
0.195
0.19
0.33
112
Min
17.60
1.00
16.71
65.3
987.4
0.13
5.21
3.12
0.097
0.04
0.11
40
Autumn
Avg
10.61
1.34
67.43
85.2
992.1
5.07
3.87
3.68
0.115
0.10
0.14
61
Max
15.71
1.71
90.57
93.1
1001.1
11.69
5.66
6.12
0.191
0.27
0.29
131
Min
5.57
1.03
41.57
80.1
982.7
0.07
1.13
1.375
0.042
0.01
0.00
11
3.6. Accuracy
Several techniques were used to compare
predicting models in terms of accuracy as:
regression analysis, analysis of variance
(ANOVA), Pearson correlation and so on.
For instance, Table 8 reports main statistical
properties referring to the application of a
regression analysis (Multiple R, R Square,
etc.) in the case of the multiple regression
(MR) model, but parallel evaluations were
done for each model. Similarly, Table 9
reports main statistical properties of
ANOVA on the same model.
Table 8. Regression statistical properties for
the multiple regression model.
Regression Statistics
Multiple R
0.959
R Square
0.921
Adjusted R Square
0.872
Standard Error
12.326
Observations
30
Table 9. ANOVA statistical properties for
the multiple regression model.
ANOVA
df
SS
MS
F
SF
Regression
11
31920
2901
19
1E-07
Residual
18
2734
152
Total
29
34654
Finally, Table 10 outlines the methods’
accuracy where the best approximation is
offered by GP, followed by MR.
Table 10. Comparing model accuracy.
MR
GP
NN
H
87.39%
91.49%
70.52%
87.88%
3.7. Hybrid vs Conventional Models
The accuracy of hybrid methods was finally
investigated. In Table 11 it is possible to find
a comparison between predictions offered by
conventional (MR, GP, NN) and hybrid
models where the last ones were a
combination of predictions from the previous
ones. In particular, these rules were used in
the definition of the hybrid models:
• Hmin = Min (MR, GP, NN)
• Hmax = Max (MR, GP, NN)
• Hmean = Mean (MR, GP, NN)
Table 11. Comparing accuracy of prediction
for conventional and hybrid models.
Mean
Total
Correl
RD
70
2111
1
MR
69
2098
0.959
GP
70
2104
0.979
NN
74
2230
0.758
Hmin
63
1908
0.921
Hmax
80
2426
0.875
Hmean
71
2133
0.947
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
389
Other formulations were also considered, but
not here reported since they do not add much
information to the general discussion.
The comparison was done considering the
accuracy in predicting the weekly use of
rented bikes and the number of bikes rented
inside the whole period. Linear correlation
was also used.
In short it is possible to highlight that:
• The conventional methods (i.e.,
MM, GP, NN) already allow to
obtain an excellent estimation. This
accuracy can be observed by the
mean and total values which differ
slightly. The best model (i.e., GP)
guesses the weekly average and
slightly underestimates (-0.3%) the
total number of bikes rented in the
period. Even the worst of the three
models (i.e., NN) makes an error of
less than 6%.
• Since the good accuracy offered by
these conventional methods respect
to the mentioned reference values,
their combination could easily
provide a good estimation of the
same values. It is therefore
necessary to understand the possible
added value of hybrid models. In
these terms, hybrid models could
add better overall correlation
alongside the whole period.
However, it does not seem to be
happening in the present case.
The correlation coefficient of hybrid
methods, in fact, does not suggest an
improvement in the offered accuracy.
However, the use of a hybrid model that
averages the values predicted by the other
conventional models (Hmean) makes it
possible to save an excellent accuracy (error
<1.5%), also avoiding the risk of selecting of
an inappropriate predictive model. This is
the reason why its adoption is suggested.
4. Conclusion
One of the main goals of every valid strategy
aiming at the development of transport is to
increase the sustainability of the transport
system and, at the same time, provide a
public transport solution that will be
accessible to most of the population.
In this sense, transport systems involving the
use of shared bikes appear very attractive.
Moreover, promoting active transportation is
an important public health objective. Regular
cycling stimulates the heart, improves the
circulatory system, reduces the risk of
cardiovascular disease and stroke, and
lowers blood pressure.
Therefore, with the growing complexity of
such systems (e.g., increase in the number of
bikes, stations, popularity in using bikes),
new network analysis methods and tools
have to be considered for their optimization.
Application of the concepts of artificial
intelligence and expert systems is expected
to provide a deeper understanding of the
public transport and organizational
phenomena.
This paper elaborates the application of
conventional methods, including Multiple
Regression (MR), Genetic Programming
(GP) and Artificial Neural Network, and an
additional hybrid machine learning ensemble
to modelling the bicycle rental system of the
town of Novo mesto in Slovenia. The GP
model gives the best results with a very high
accuracy, but also the hybrid machine-
learning ensemble offered quite solid
estimations. In particular, as it was expected,
the analysis measured the system as
oversized in terms of number of bikes (and,
as a consequence, with single little-used
bikes). However, in accordance with the
general goals of the Municipality for
sustainable mobility, every action toward the
implementation of a shared transport should
be supported since they are much more
environmentally friendly than private
vehicles with petrol or diesel engines.
Babic et al., Machine learning tools in the analyze of a bike sharing system
390
Thus, an initial oversizing was preferred
with the scope to support spreading this new
service among users. The idea is that the user
should wait a minimum of time for an
available bike, otherwise the service will no
longer be attractive.
Funding: The investment is co-financed by
European Regional Development Fund.
Conflicts of Interest: The authors declare
no conflict of interest.
Acknowledgments: Research supported by
the Central European Initiative (CEI) within
the ‘ATC.EVO’ transfer of technology
project.
References
Albu, A., Precup, R.-E., & Teban, T.-A. (2019). Results and challenges of artificial neural
networks used for decision-making and control in medical applications. Facta Universitatis-
Series: Mechanical Engineering, 17(3), 285-308.
Ali, Y., Mehmood, B., Huzaifa, M., Yasir, U., & Khan, A. U. (2020). Development of a new
hybrid multi criteria decision-making method for a car selection scenario. Facta
Universitatis-Series Mechanical Engineering, 18(3), 357-373.
Babic, M., Calì, M., Nazarenko, I., Fragassa, C., Ekinovic, S., Mihaliková, M., Janjić, M., &
Belič I. (2018): Surface Roughness Evaluation in Hardened Materials by Pattern Recognition
Using Network Theory. International Journal on Interactive Design and Manufacturing,
13(1), 211-219. Doi: 10.1007/s12008-018-0507-3.
Babic, M., Fragassa, C., Lesiuk, G., & Marinkovic, D. (2020) New method for complexity
determination by using fractals and its applications in material surface characteristic.
International Journal for Quality Research, 14(3) 705-716.
Barbour, N., Zhang, Y., & Mannering, F. (2019). A statistical analysis of bike sharing usage
and its potential as an auto-trip substitute. Journal of Transport & Health, 12, 253-262.
Berg, J., & Ihlström, J. (2019). The importance of public transport for mobility and everyday
activities among rural residents. Social Sciences, 8(2), 58.
Bodini, I., Lancini, M., Pasinetti, S., & Vetturi, D. (2013). Techniques for on-board vibrational
passenger comfort monitoring in public transport. In 12th IMEKO TC10 Workshop on
Tecnical Diagnostics, (pp. 118-123).
Celis-Morales, C., Lyall, D. M., Welsh P., Anderson, J., Steell, L., Guo, Y., ... & Gill, J. M.R.
(2017). Association between active commuting and incident cardiovascular disease, cancer,
and mortality: prospective cohort study. BMJ, 357 doi: https://doi.org/10.1136/bmj.j1456.
Char, D. S., Shah, N. H., & Magnus, D. (2018). Implementing Machine Learning in Health
Care—Addressing Ethical Challenges. New England Journal of Medicine, 378(11), 981-983.
doi:10.1056/nejmp1714229.
Corcoran, J., Li, T. B., Rohde, D., Charles-Edwards, E., & Mateo-Babiano, D. (2014). Spatio-
temporal patterns of a Public Bicycle Sharing Program: The effect of weather and calendar
events. Journal of Transport Geography, 41, 292-305.
DeMaio, P. (2009). Bike sharing: History, impacts, models of provision, and future. Journal of
public transportation, 12, 41-56.
Durmić, E., Stević, Ž., Chatterjee, P., Vasiljević, M., & Tomašević, M. (2020). Sustainable
supplier selection using combined FUCOM–Rough SAW model. Reports in Mechanical
Engineering, 1 (1), 34-43. doi: 10.31181/rme200101034c
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
391
Emmert-Streib, F., Tripathi, S., Yli-Harja, O., & Dehmer M. (2009). Understanding the World
Economy in Terms of Networks: A Survey of Data-Based Network Science Approaches on
Economic Networks. Frontiers in Applied Mathematics and Statistics, 4(37). doi:
10.3389/fams.2018.00037.
Fragassa, C., Babic, M., Bergmann, C. P., & Minak, G. (2019). Predicting the tensile behaviour
of cast alloys by a pattern recognition analysis on experimental data. Metals, 9, 557.
Fragassa, C., Babic, M., Pavlovic, A., & do Santos, E. D. (2020). Machine Learning
Approaches to Predict the Hardness of Cast Iron. Tribology in Industry, 42(1), 1-9.
Fuller, D., Luan, H., Buote, R., & Auchinclossd, A. H. (2019). Impact of a public transit strike
on public bicycle share use: An interrupted time series natural experiment study. Journal of
Transport & Health, 13, 137-142.
Garrido, C., De Oña, R., & De Oña, J. (2014). Neural networks for analyzing service quality in
public transportation. Expert Systems with Applications, 41(15), 6830-6838.
Gomes, M., Silva, F., Ferraz, F., Silva, A., Analide, C., & Novais, P. (2017). Developing an
Ambient Intelligent-Based Decision Support System for Production and Control Planning. In
Intelligent Systems Design and Applications, Springer: Berlin, Germany, pp. 984-994.
IEA. (2017). CO2 Emissions from Fuel Combustion 2017—Highlights. IEA: Paris, France.
IPCC. (2014). Summary for Policymakers. IPCC: Geneva, Switzerland, ISBN 9789291691432.
Kovačič, T., Kovačič, M., Ovsenik, R., & Zurc, J. (2020). The impact of multicomponent
programmes on balance and fall reduction in adults with intellectual disabilities: a
randomised trial. Journal of intellectual disability research, 64(5), 381-394.
Le, L. T., Lee, G., Park, K.S., & Kim, H. (2020). Neural network-based fuel consumption
estimation for container ships in Korea. Maritime Policy & Management, 47(5), 615-632.
Lin, L., He, Z., & Peeta, S. (2018). Predicting station-level hourly demand in a large-scale
bike-sharing network: A graph convolutional neural network approach. Transportation
Research Part C: Emerging Technologies, 97, 258-276.
Menaspà, P., Rampinini, E., Bosio, A., Carlomagno, D., Riggio., M., & Sassi, A. (2012).
Physiological and anthropometric characteristics of junior cyclists of different specialties and
performance levels. Scandinavian Journal of medicine & science in sports, 22(3), 392-398.
Pavlović, M., Nikolić, V., Simonović, M., Mitrović, V., & Ćirić, I. (2019). Edge detection
parameter optimization based on the genetic algorithm for rail track detection. Facta
Universitatis-Series Mechanical Engineering, 17(3), 333-344.
Rixey, R. (2013). Station-level forecasting of bike sharing ridership: Station network effects in
three U.S. systems. Transportation research record, 2387, 46-55.
Saberi, M., Ghamami, M., Gu, Y., Shojaei, M.H., & Fishman, E. (2018). Understanding the
impacts of a public transit disruption on bicycle sharing mobility patterns: A case of Tube
strike in London. Journal of Transport Geography, 66, 154-166.
Saldana-Perez M. (2019). Miguel Torres-Ruiz, & Marco Moreno-Ibarra, Geospatial Modeling
of Road Traffic Using a Semi-Supervised Regression Algorithm. IEEE Access, 7, 177376-
177386, doi: 10.1109/ACCESS.2019.2942586,
Saleh, M., Esa, Y., & Mohamed, A. (2018). Applications of Complex Network Analysis in
Electric Power Systems. Energies, 11(6), 1381. doi:10.3390/en11061381.
Sun, X., & Zhuge, X. (2018). Summarization of Scientific Paper through Reinforcement
Ranking on Semantic Link Network, IEEE ACCESS.
Babic et al., Machine learning tools in the analyze of a bike sharing system
392
Vadlamani, R., Nekuri, N., & Mayank, P. (2013). Hybrid classification and regression models
via particle swarm optimization auto associative neural network based nonlinear PCA.
International Journal of Hybrid Intelligent Systems, 10 (3).
van Lierop, D., Badami, M. G., & El-Geneidy, A. M. (2018). What influences satisfaction and
loyalty in public transport? A review of the literature. Transport Reviews, 38(1), 52–72.
van Wee, Bert. (2015). Viewpoint: Toward a new generation of land use transport interaction
models. Journal of Transport and Land Use, 8(3).
Vecchio, F. (2017). Small World architecture in brain connectivity and hippocampal volume in
Alzheimer's disease: a study via graph theory from EEG data. Brain Imaging and Behavior,
11(2), 473-485. doi:10.1007/s11682-016-9528-3.
Warren, W. H., Rothman, D. B., Schnapp, B. H., & Ericson, J. D. (2017). An empirical
articlethat outlines the cognitive-graph theory alternative to cognitive-map theory.
Weiss, F., Brummer, T., & Pufal, G. (2016). Mountain bikes as seed dispersers and their
potential socio-ecological consequences. Journal of Environmental Management, 181, 326-
332.
Woodcock, J., Tainio, M., Cheshire, J., O’Brie, O., & Goodman, A. (2014). Health effects of
the London bicycle sharing system: Health impact modeling study. British Medical
Journal, 348, g425.
Matej Babic
Faculty of Information Science
in Novo mesto,
Novo mesto, Slovenia
[email protected]
ORCID 0000-0002-5446-5087
Cristiano Fragassa
Department of Industrial
Engineering, Alma Mater
Studiorum University of
Bologna, Bologna, Italy
[email protected]
ORCID 0000-0003-0046-8810
Dragan Marinkovic
Department of Structural
Mechanics, Institute of Mechanics,
Technical University of Berlin,
Germany
[email protected]
ORCID 0000-0002-3583-9434
Janez Povh
Faculty of Mechanical
Engineering, University of
Ljubljana, Novo mesto,
Slovenia.
[email protected]
ORCID 0000-0002-9856-1476
International Journal for Quality Research, 16(2), 375–394, 2022, doi: 10.24874/IJQR16.02-04
393
Appendix A
𝑌=9.08502𝑁𝐷(−1.51133+𝐶𝐶+𝑁𝐷+𝑆𝐷+𝑇𝑇+2𝑊𝑉+𝑁𝐷(𝐵𝐶+𝐶(𝑁𝐷+𝑊𝑉))+
𝑁𝐷(4.13212+𝐶+(𝐵𝐶+𝐶)𝑁𝐷+𝑆𝐷+𝐶 𝑁𝐷(𝐶+𝑊𝑉+0.110071 𝐴𝑃
𝑇𝑇+𝑁𝐷+𝐶𝐶−4.13212)
𝑇𝑇 )
+𝐴𝑃
𝐶+𝑆𝐷+𝑄+𝑁𝐷 𝑆𝐷(𝑁𝐷+𝑁𝐷 𝑊𝑉(𝐶+𝑁𝐷(2𝐶+𝑁𝐷+3𝑊𝑉)))
−𝐶𝐶(𝑇𝑇+ 𝐶 𝑁𝐷(𝑁𝐷+𝑊𝑉(𝑊𝑉+𝑁𝐷2(2𝐶 𝑁𝐷+𝑁𝐷(𝐶𝐶+𝑇𝑇+𝑊𝑉−𝑁𝐷))))))
Q
=0.110071 𝐴𝑃
(𝑁𝐷+𝑊𝑉)(𝑁𝐷 (𝐵𝐶+𝐶𝐶 𝑁𝐷)+𝑁𝐷 𝑅𝐻 (𝑁𝐷+𝑇𝑇+2𝑊𝑉+𝐵𝐶 (𝑁𝐷+𝑊𝑉))−0.110071𝐴𝑃(𝐵𝐶+𝐶+𝑊𝑉+𝐴𝑃
(9.08502+𝐵𝐶)(𝐶𝐶+𝑁𝐷+𝑇𝑇+𝑊𝑉−4.13212))
𝐶𝐶+𝑇𝑇+𝑊𝑉 )
(8)
Y = - 406.6192311+ 0.00076234×D + 639.3785287×ND - 46.72088091×BC +
9.015791733×CC -0.747814175×T + 4.569795467×WV + 0.236921533×C -
0.043525382×RH + 0.372085427×AP + 1.012797827×R + 2.716867132×SD (9)
Babic et al., Machine learning tools in the analyze of a bike sharing system
394