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# Open Engineering

### formerly Central European Journal of Engineering

Editor-in-Chief: Ritter, William

1 Issue per year

CiteScore 2017: 0.70

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2391-5439
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Volume 7, Issue 1

# Heuristic Optimization Approach to Selecting a Transport Connection in City Public Transport

Jozef Kul’ka
• Corresponding author
• Technical University of Košice, Faculty of Mechanical Engineering, Institute of Design and Process Engineering, Letná 9, 042 00 Košice, Slovak Republic
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• Other articles by this author:
/ Martin Mantič
• Technical University of Košice, Faculty of Mechanical Engineering, Institute of Design and Process Engineering, Letná 9, 042 00 Košice, Slovak Republic
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• Other articles by this author:
/ Melichar Kopas
• Technical University of Košice, Faculty of Mechanical Engineering, Institute of Design and Process Engineering, Letná 9, 042 00 Košice, Slovak Republic
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/ Eva Faltinová
• Technical University of Košice, Faculty of Mechanical Engineering, Institute of Design and Process Engineering, Letná 9, 042 00 Košice, Slovak Republic
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• Other articles by this author:
/ Daniel Kachman
• Technical University of Košice, Faculty of Mechanical Engineering, Institute of Design and Process Engineering, Letná 9, 042 00 Košice, Slovak Republic
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Published Online: 2017-02-05 | DOI: https://doi.org/10.1515/eng-2017-0001

## Abstract

The article presents a heuristic optimization approach to select a suitable transport connection in the framework of a city public transport. This methodology was applied on a part of the public transport in Košice, because it is the second largest city in the Slovak Republic and its network of the public transport creates a complex transport system, which consists of three different transport modes, namely from the bus transport, tram transport and trolley-bus transport. This solution focused on examining the individual transport services and their interconnection in relevant interchange points.

## 1 Introduction

Every public transport operator seeks to provide regular shared-passenger transport which has to meet all necessary transport requirements to support the functioning of the entire settled areas and cities. As transport requirements and demands increase with the development of regions and cities, especially to preserve and to improve the quality of the environment, the necessity of good coordination of activities in the whole transport system gains more prominence. Growing settlement concentration and large urban agglomeration, along with developing individual motoring pose an increasing challenge for shared-passenger transport. For this reason, it is necessary to apply logistics to urban traffic control in order to prevent traffic collapse and to reduce the environmental impact.

The question of emissions produced by the various kinds of transport induces an increased interest concerning utilisation of the public transport and other environmental solutions [1,2]. Cities should respect nature, consider the urban ecological environment as an asset, integrate environmental issues into urban planning and administration, and accelerate the transition to sustainable development. They should promote the use of renewable energy sources and build low-carbon eco-cities. They should strongly advocate for conservation of resources and promote environmental-friendly manufacturing.Cities and their citizens should join together to create sustainable lifestyles and an ecological civilization in which people and environment co-exist in harmony [3-7]. An important strategic consideration is transportation planning. Questions regarding the sustainability of dispersed car dependent urban forms have led to a renewed interest in public transportation [8-11]. Optimisation of the public transport operation can be performed using various suitable computational methods. Some of them are presented in [12-15]. Another relevant aspect of the modern public transport is application of the navigation system [16].

## 2 How passengers choose which transport mode suits them when they use a transport network

Passengers who use the system of urban shared-passenger transport typically choose those connections that take them to their destination fastest and involve no transfers. When there is no such service, they choose the ones which are fastest and involve fewest transfers. For this reason, the city transport operator should schedule their services to link up at the interchange points to save passengers time they otherwise spend waiting between two services. Only then the passengers can be happy and will not look for other means of transport for their travels. If the passengers are to be happy with the shared-public transport, it has to be reliable, safe, adequately fast and affordable. Urban passengers mostly choose the transport services heuristically, i.e. they do not know when the service is due, which is something they find out at the stop. It is caused by the public shared-passenger transport that runs regularly and quite frequently.

A network of shared-passenger transport consists of transport roads which service regular routes. For the sake of simplicity, we can imagine the transport network as a graph G=(V, H), where V={v1, v2, …, vn} is a set of peaks, which represent a set of stops in the transport network, and H={h1, h2, ….., hm} represents a set of edges, i.e. a set of existing direct connections between two peaks. A transport service runs on a concrete route on a road that is defined by technical parameters, and terminus and intermediate stops. Similar to the transport network, the set of transport services L={L1, L2, …, Ln} also forms an oriented graph. Every service is specified by a set of peaks and edges, so that Lk ={Vk, Hk}, where ${\text{V}}_{k}=\left\{{\text{V}}_{i}^{k}\phantom{\rule{thinmathspace}{0ex}}\in \phantom{\rule{thinmathspace}{0ex}}\text{V};\left(\phantom{\rule{thinmathspace}{0ex}}{\text{V}}_{0}^{k},{\text{V}}_{1}^{k},{\text{V}}_{2}^{k},\dots ..,{\text{V}}_{l}^{k}\right)$ is a sequence in the graph $\text{G},\phantom{\rule{thinmathspace}{0ex}}{\text{V}}_{i}^{k},\phantom{\rule{thinmathspace}{0ex}}\ne \phantom{\rule{thinmathspace}{0ex}}{\text{V}}_{j}^{k},\right\}$ and ${\text{H}}_{k}\phantom{\rule{thinmathspace}{0ex}}=\left\{{\text{h}}_{i}^{k},\phantom{\rule{thinmathspace}{0ex}}\text{i}=1,2,\dots .,\text{l}\right)\right\}.$ The “l” indication denotes the number of stops on the Lk service. Figure 1 presents an oriented graph of the network G = (V, H), which comprises a network of transport services L = (L1, L2, …, L11). The sequence of peaks and edges that represent the specific services and transport service interval τk are illustrated in Table 1. We have set about to find the shortest way from the start peak V1 to the finish peaks V10, V11, V14 and V15 with specified start conditions.

Figure 1

Traffic network.

Table 1

Sequence of peaks and edges for individual services.

L1, L6, L7, L8 and L11 are bus services and L2, L3, L4, L5, L9 and L10 are tram services. There are also instances when the stops on parallel bus and tram routes take different time to reach, which is a fact that is important to consider, and choose the shortest time possible for travel.

## 2.2 How to choose an interchange point suitable for passengers transfer

To choose a suitable interchange point in the transport network, it was necessary to explore all possible transfer combinations in the individual interchange points and specify the most suitable interchange point for passengers to transfer from one vehicle to another based on the criteria we defined. In this case, the criteria were following:

• minimum number of transfers between the beginning and end of the journey,

• shortest amount of time spent waiting when passengers transfer from one vehicle to another at the interchange point.

First, we need to define the start conditions. We are working with a given set of bus and tram services, which we are going to examine for the amount of time it takes to travel from the beginning to the end of the journey with fewest number of transfers taking the least amount of time. The distances between the individual stops will be expressed in time [min.] and the graph will be adjusted for the time it takes to transfer between the individual services at the interchange points (transfer stops). Figure 2 illustrates the adjusted transport network where all transport services are uniquely coded.

Figure 2

Adjusted model of the transport network.

Because we were dealing with passengers who come to a stop at random and do not know the schedule, they reach the stop with equal probability as the bus or tram service would. Arrival time at the waypoint on the route corresponds to the equivalent distribution on the interval (0, τk). The random quantity “x” of this distribution is characteristic of the distribution concentration f(x) = 1/ τk, for x ∈ (0, τk); and f(x) = 0 for the other instances of x. If we assume that the service runs exactly as scheduled, then the mean value of the random quantity, which equals τk/2, is used to denote the time spent waiting for the Lk service on any of its stops.

Figure 3 illustrates the adjustment at the interchange point for two diverging services. We have split the Vi peak, in which the Lm and Ln meet and diverge, to the two peaks labelled as ${\text{V}}_{i}^{p}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\text{V}}_{i}^{0}$ for each service. The link between the peaks ${\text{V}}_{i}^{pn}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\text{V}}_{i}^{om}$ which is marked ${\text{t}}_{i}^{\left(n,m\right)}$ denotes the time spent waiting from the “n” service to the “m” service and its value equals τm/2. The same principle applies to calculating the amount of time to transfer from the “m” route to the “n” route, so ${\text{t}}_{i}^{\left(m,n\right)}\phantom{\rule{thinmathspace}{0ex}}=\phantom{\rule{thinmathspace}{0ex}}{\tau }_{n}/2$ [2]. Table 2 illustrates all possible combinations of connections from the V1 peak to the V10 peak for the particular transport network. We have applied the same principle to create the tables which show the outcome of examining the shortest journey between the starting V1 peak to the V11, V14 and V15 peaks.

Figure 3

The graph adjusted for diverging services at the interchange point.

Table 2

Combinations of connections from the V1 peak to the V10 peak.

## 3 Results and discussion

There are presented in the Table 2 the all possible connection combinations from the V1 peak to the V10 peak. It is necessary to emphasize that the term “Total travel time” denotes the time between the moment the passengers get on a bus or tram when they start their journey in V1 and the moment they get off when they reach their destination in V10, V11, V14 and V15. The net travel time denotes the amount of time the passengers spend travelling by bus or by tram. The real values of the travel times and waiting times are obtained from a case study, which was realized in a close cooperation with the Public Transport Company in the city Košice. The green line in the Table 2 represents the best results, whereas the red line means the worst result from the passenger’s point of view, whereas the term “best results” means the transport connection with the shortest total travel time, average waiting time for all connections as well as the shortest total waiting time for the all connections.

## 4 Conclusion

Our research has shown that the passengers who travel from the start peak V1 to any of the considered destinations, out of all possible interchange points, seem to prefer the transfer to the V2 peak the most. Apart from a single case (when there was a direct service from the beginning to the end of the journey) it was necessary to transfer at an interchange point at least once. Considering the total waiting time between services for all examined final destinations, our research has also found that the L4 services appeared to be the most suitable combination, since the time intervals between services on this route were the shortest of all. It is necessary to keep in mind that the growing number of transfers translates into longer travel time which consequently demotivates the passengers from using such a transport system. We would like to emphasize the application possibilities of the described method. This method could be utilized during development of the optimisation algorithms specified for searching of the above-mentioned “best results” for the transport interconnections, e.g. in the web- or smart-phone applications.

## Acknowledgement

This paper was elaborated in the framework of the projects VEGA1/0197/14 Research of new methods and innovative design solutions in order to increase efficiency and to reduce emissions of transport vehicle driving unit, together with evaluation of possible operational risks, VEGA 1/0198/15 Research of innovative methods for emission reduction of driving units used in transport vehicles and optimisation of active logistic elements in material flows in order to increase their technical level and reliability and KEGA 021TUKE – 4/2015 Development of cognitive activities focused on innovations of educational programs in the engineering branch, building and modernisation of specialised laboratories specified for logistics and intra-operational transport.

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Accepted: 2016-07-30

Published Online: 2017-02-05

Citation Information: Open Engineering, Volume 7, Issue 1, Pages 1–5, ISSN (Online) 2391-5439,

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