The shortest not necessarily the best other path on the basis of the optimal path

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 10 | Oct-2014, Available @ http://www.ijret.org 322
THE SHORTEST NOT NECESSARILY THE BEST OTHER PATH ON
THE BASIS OF THE OPTIMAL PATH
Tomasz Neumann1
1
Gdynia Maritime University, Gdynia, Poland
Abstract
This paper presents a different perspective on the Dijkstra algorithm. In paper this algorithm is used to the further analyses to
find another paths between nodes in maritime traffic. In many cases, the best solution for a single criterion is not sufficient.
Finding more effective solutions can be the starting point to use for subsequent analysis or making decision by the captain of the
vessel. Using advanced reasoning mechanisms it is possible to create a decision support system based on well-known Dijkstra
algorithm.
Keywords: Sea Transport, Networks and Graphs, Intelligent Transportation System
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1. INTRODUCTION
Rapid and accurate calculation of the estimated time of
arrival at the port of destination of the ship at sea, is of great
importance in many areas of the ocean shipping industry.
For example, the route and schedule of ships on a day to
day, it is important to know when the ship reached the port
of destination and to be available for new loads. Estimated
time of arrival can also be important in the planning of port
operations. Give a reliable estimated time of arrival for ships
entering the port, planning port operations, such as work
assignments, loading/unloading equipment and harbours for
ships can be more efficiently done.
The traditional way is to base the estimate of estimated time
of arrival on ships. However, the new technology of satellite
position reporting combined with electronic map allows
users to land to check weather or update the master's
estimated time of arrival at regular intervals, not interfering
with the crew of the ship at all hours.
The paper presents an efficient algorithm for determining
the estimated time of arrival in port the ship is at sea. The
algorithm is implemented in a decision support system in
planning the operation of ships, one of which is installed and
used by several owners. By calculating the distance of the
route between the ship and the port of destination, estimated
time of arrival can be estimated by dividing the distance by
the speed sailing. Calculating the distance between the ship
and the port of destination may be considered to determine
the shortest path between two points in the presence of
polygonal obstacles, where one point corresponds to the
vessel and the other end to the port of destination. Sections
defining polygons are obstacles coast. Estimated time of
arrival accuracy can be improved by defining special
network structures in areas with limited speed, or are
waiting for the pilots [3].
The vehicle routing problem lies in the design of optimal
routes for a fleet of vehicles, usually in order to minimize
operating costs or the number of vehicles used. Several
variations of this problem has been extensively studied in
the literature optimization as efficient routing of vehicles
have a great impact on logistics costs [7].
2. THE PROBLEM
Given that the total linear programming model of a
simplified version of the problem of routing the vessel
presents an unacceptable solution times for a typical daily
planning process, taken a heuristic approach, deciding on
your hand. Author decided on this approach for its
implementation relatively simple calculation, as well as its
record of good results with similar problems to the present.
There are several algorithms such as Dijkstra's algorithm,
which is a single source-single destination shortest path
algorithm, the Bellman-Ford algorithm to solve the shortest
path algorithm with a free hand, A* algorithm solves the
single pair shortest path problems using a heuristic
algorithm and Floyd Warshall algorithm to find all pairs of
Johnson-perturbation and the shortest path algorithm to find
the shortest path locally. Genetic algorithms are also used to
finding shortest path [1]. In this paper to calculation will be
used Dijkstra algorithm.
2.1 Dijkstra's Algorithm
For a given source vertex (node) in the graph, the algorithm
finds the path with lowest cost (ie the shortest path) between
that vertex and every other vertex. It can also be used for
finding the shortest cost path from one vertex to a
destination vertex by stopping the algorithm is determined
by the shortest path to the destination node. For example, if
the vertices of the graph represent the city and are the costs
of running paths edge distances between pairs of cities
connected directly to the road, Dijkstra's algorithm can be
used to find the shortest route between one city and all other
cities. As a result, the shortest path algorithm is widely used

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routing protocols in a network, in particular the IS-IS and
Open Shortest Path First.
Short characteristic of Dijsktra algorithm [2].
 The input of the algorithm consists of a weighted
directed graph G and a source vertex s in G
 Denote V as the set of all vertices in the graph G.
 Each edge of the graph is an ordered pair of vertices
(u,v)
 This representing a connection from vertex u to
vertex v
 The set of all edges is denoted E
 Weights of edges are given by a weight function w:
E → [0, ∞)
 Therefore w(u,v) is the cost of moving directly from
vertex u to vertex v
 The cost of an edge can be thought of as (a
generalization of) the distance between those two
vertices
 The cost of a path between two vertices is the sum
of costs of the edges in that path
 For a given pair of vertices s and t in V, the
algorithm finds the path from s to t with lowest cost
(i.e. the shortest path)
 It can also be used for finding costs of shortest paths
from a single vertex s to all other vertices in the
graph.
2.2 Proposed to Use
As indicated above, the algorithm is well known and widely
used. Finding the shortest path between two vertices in
graphs is not difficult. But not always the shortest path is the
best. It is proposed to fast search method inferior
alternatives. In such situation, decision maker can choose
one of the alternatives and take all the consequences.
After finding the shortest path is proposed to remove from
the graph piece belonging to the founded path. Disposal
should be carried out as long as there is a lot of segments in
the founded path. For each new graph is necessary to find
the shortest path. Founded new path should be saved to an
array of solutions.
Fig 1: Scheme of traffic among islands

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First edge of optimal path
Next edge of
optimal path?
Remove edge from array of edges
Find new shortest path
Remove duplicate paths
Y
N
Fig 2: Diagram of searching new paths
The proposed scheme is shown in figure 2. Provides an
overview of the optimal path, the removal of all further
edges.
Resulting array can contain many of the same tracks. It is
therefore removed from the same tracks. Of course, such
removal is not a problem.
3. NUMERICAL EXAMPLE
The figure 1 shows an example of the unreal maritime
restricted area. It consists of eight obstacles (in the form of
islands), 21 turning points and 29 edges. Each edge is
described by value of the distance between two vertices.
All connections are shown in the Table 1. Number of edge
corresponds to the edge shown in Figure 1. Each connection
is between initial node and final node. The distance between
nodes describes a dimensionless measurement of the
distance between the nodes.
Table 1: Table of all edges
Number
of edges
Initial
vertex
Final
vertex
Distance between
the vertices
0 0 1 295
1 0 4 257
2 4 5 415
3 5 6 215
4 4 9 207
5 9 10 98
6 10 7 73
7 7 6 183
8 7 8 160
9 10 8 187
10 8 16 203
11 16 17 181
12 17 18 139
13 18 3 130
14 17 15 107
15 15 19 148
16 19 20 183
17 9 11 168
18 9 12 137
19 1 11 210
20 11 12 102
21 12 13 212
22 1 14 176
23 14 13 225
24 13 19 216
25 13 15 293
26 14 2 452
27 2 20 343
28 20 3 362
Result of the algorithm is a path with a length equal 1365.
The algorithm indicated that the shortest distance between
the vertex labelled 0 and 3 leading by edges: 0, 22, 23, 25,
14, 12, 13. The shortest path is presented in Table 2 and in
Figure 3.
Table 2: Description of shortest path
Number
of edges
Initial
vertex
Final
vertex
Distance between the
vertices
0 0 1 295
22 1 14 176
23 14 13 225
25 13 15 293
14 17 15 107
12 17 18 139
13 18 3 130
Total 1365

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Fig 3: Shortest path
An easy way to find another quick way from the source to
the target is to modify the optimal path, found a particular
method. The article proposes to remove one edge. The cycle
was repeated for each edge of the optimal path. In this way
calculated two other paths 1,4,5,9,10,11,12,13 and
0,22,23,24,16,28:. Detailed data are shown in the Figures
and tables.
Fig 4: Second path
Table 3: Description of second path
Number
of edges
Initial
vertex
Final
vertex
vertices
1 0 4 257
4 4 9 207
5 9 10 98
9 10 8 187
10 8 16 203
11 16 17 181
12 17 18 139
13 18 3 130
Total 1402
Fig 5: Third path
Table 4: Description of third path
Number
of edges
Initial
vertex
Final
vertex
vertices
0 0 1 295
22 1 14 176
23 14 13 225
24 13 19 216
16 19 20 183
28 20 3 362
Total 1457
For the purposes of demonstration and calculations
developed computer application [6] which graphically
created schema presented in the article. For middle-class
computer all the calculations were done in less than 150ms.
Such a short calculation time can be a prerequisite for
further research into the search for alternative paths.
The results require further calculations. According to the
author to be in the discussion to consider not only the
dimensionless values describing the edges, but also values
such as time, cost, security etc. It is necessary to use the
mechanism of multiple-choice decision or data fusion [4,5].
4. CONCLUSIONS
The Dijkstra algorithm is well known. It was first published
half a century ago. To this day, finding connections between
vertices is used. But not always the shortest path is the best.
It is to consider various criteria. This paper is an
introduction to further research.
It has been shown that with the use of today's computers to
find paths can be easy and quick.
REFERENCES
[1]. Bagheri H., Ghassemi H., Dehghanian A., 2014:
Optimizing the Seakeeping Performance of Ship Hull Forms
Using Genetic Algorithm. TransNav, the International
Journal on Marine Navigation and Safety of Sea
Transportation, Vol. 8, No. 1, pp. 49-57

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[2]. Dijkstra, E.W., 1959: A note on two problems in
connexion with graphs. Numerische Mathematik. 1, 269–
271.
[3]. Fagerholt, K., Heimdal, S., Loktu, A., 2000. Shortest
path in the presence of obstacles: an application to ocean
shipping. Journal of the Operational Research Society 51,
683–688.
[4]. Gopika, N.A., Deeoa, S. 2013. A survey on optimal
route queries for road networks, International Journal of
Research in Engineering and Technology, 02, 12, 447-450
[5]. Neumann T., 2008: Multisensor Data Fusion in the
Decision Process on the Bridge of the Vessel. TransNav, the
International Journal on Marine Navigation and Safety of
Sea Transportation, Vol. 2, No. 1, pp. 85-89
[6]. Neumann T., 2011: A Simulation Environment for
Modelling and Analysis of the Distribution of Shore
Observatory Stations - Preliminary Results. TransNav, the
International Journal on Marine Navigation and Safety of
Sea Transportation, Vol. 5, No. 4, pp. 555-560
[7]. Romeroa, G., Duran, G., Marenco, J. Weintraub, A.
2013. An approach for efficient ship routing. International
Transactions in Operational Research 00, 1-28

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