Optimization of Routes for Road Surface Inspection
An Application to the Portuguese National Road Network
Filipe F. Gomes
1
, Marta Castilho Gomes
2
and Alexandre B. Gonçalves
2
1
Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, Portugal
2
CERIS, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, Portugal
Keywords: Road Inspection Routing, Routing, Linear Programming, Geographical Information Systems (GIS).
Abstract: Infraestruturas de Portugal S.A. (IP) is responsible for managing the Portuguese rail network infrastructure
and a significant part of the road network. An annual inspection must be performed on every road segment
for which IP is responsible, which sums up around 14,000 km. This is a costly operation regarding time,
human and monetary resources. An optimization model that incorporates the problem technical constraints
was developed and a cost analysis performed to compare the distinct scenarios that IP may face in the
general layout of the inspection programme.
1 INTRODUCTION
Infraestruturas de Portugal, S.A. (IP) is a Portuguese
institution with the responsibility of managing the
rail network infrastructure and part of the road
network in Portugal. Every year, an inspection must
be conducted on the roads that IP manages, which
include national roads and some motorway
segments, in a total of ca. 14,000 km. The inspection
is done by directly registering a few parameters
related with pavement geometry and conditions, as
well as other relevant road events, by moving a
vehicle equipped with a device called Road Surface
Tester Laser (RST) and video registering travels
along the roads.
Additionally, there are technical constraints
related with the maintenance and calibration of the
RST device, which must be done every week in the
IP headquarters in the cities of Almada or Coimbra.
Another aspect concerns the inspection procedure
itself: for regular roads, i.e., with both directions and
at least two traffic lanes, it is assumed that road
surface conditions are equivalent in both sides, and a
single lane, the rightmost one, has to be travelled
along. In motorways, however, both directions must
be inspected. IP performs the operation usually in
summertime and has implemented a travel diary that
covers the entire Portuguese road network which IP
must inspect, based on empirical plans adopted in
previous years.
The implementation of the entire work plan is a
costly operation, in time, human and monetary
resources. A total of 65 working days is needed to
cover the road network, at an average speed of 55
km/h. Plans are supported by spatial data stored and
analysed in the institutional geographical
information system (GIS), which details the
geometry and attributes of the entire road network,
and not only that which must be inspected. The GIS
datasets have ca. 14,200 segments in total.
The goal of this work is to develop and apply a
model to define the inspection routes for the road
network managed by IP, which complies with the
inspection technical constraints and minimizes the
total cost.
2 METHODOLOGY
To achieve the expressed goals, a methodology
following the steps below was developed:
Collection and processing of road network
data (namely, conversion to a format that the
optimization software can handle)
Development of an optimization model
embedding the technical constraints
Application of the model
Critical analysis of model results.
362
Gomes, F., Gomes, M. and Gonçalves, A.
Optimization of Routes for Road Surface Inspection - An Application to the Portuguese National Road Network.
DOI: 10.5220/0005711803620365
In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems (ICORES 2016), pages 362-365
ISBN: 978-989-758-171-7
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
3 DATA COLLECTION AND
PROCESSING
This section describes the data collection and
processing stage, which was required to obtain and
transform data from the original datasets to a format
compatible with the optimization software.
IP maintains an exhaustive GIS database with the
road features stored in geodatabases, providing
topologically coherent datasets and at a detailed
positional and cartographic scale (for instance,
complex intersections such as roundabouts have
their segments broken into several features).
IP also maintains a record of previous inspection
routes and has established an empirical plan based
on travel diaries to direct the inspection procedure.
In it the travel directions are kept for future
reference.
It was necessary to process these data to enable
its representation as inputs to the optimization
software. The first task was to consider the required
level of detail for an accurate representation of road
inspection plans. This implied the edition of data
with a cartographic purpose to a simplified version
but maintaining the topological detail: for instance,
there is no need to consider all the small road
segments that constitute a roundabout since there is
enough detail in a description where the circular
intersection is replaced with a single node on which
the adjoining roads converge. Data was processed
and validated manually by overlaying the
geographic datasets over publicly available satellite
imagery as a layer in ArcGIS (ESRI, 2011) a
desktop GIS (Figure 1).
Figure 1: Processing of spatial data features: breaking
converging nodes into separated nodes.
After this edition, the next task was to assign to
each feature that represents a segment, which must
be inspected, and to each of its two endpoints,
unique identifiers. This action breaks the nodes
where two or more road segments converge into
several nodes. Figures 2 and 3 illustrate this
operation: Node 2, which was the intersection of
several road segments, of which three must be
inspected, is broken into three nodes, each
connecting to the respective segment.
Next, the shortest distance between each pair of
nodes is calculated with the GIS software, using a
network analysis function that produces an origin-
destination distance matrix by applying a shortest
path algorithm. The internal distances between the
duplicated node instances such as the case of Figure
1 are set to zero. Note that these shortest paths may
use the entire road system, i.e., they are not limited
to the road segments that must be inspected.
A complete list of pairs of nodes with the
corresponding shortest distance between them,
which is an input to the optimization model, is then
available.
Figure 2: Processing of spatial data features: breaking
converging nodes into separated nodes.
Figure 3: Processing of spatial data features: breaking
converging nodes into separated nodes (continued).
Optimization of Routes for Road Surface Inspection - An Application to the Portuguese National Road Network
363
4 MODEL FOR ROAD
INSPECTION ROUTING
The problem under study was characterized, among
routing problems, as an arc routing problem, and
corresponds, in particular, to the Rural Postman
Problem (RPP) were a sub-set of the arcs in a graph
has to be visited (inspected).
An original linear programming formulation for
the problem was developed, based on the one
presented by Monroy-Licht et al. (2014) – model on
the nodes. For sub-routes elimination, the Miller-
Tucker-Zemlin formulation (Miller et al., 1960, also
described in Pataki, 2003) for sub-route elimination
in the travelling salesman problem (TSP) was
adapted to the present problem.
Decision variables are binary and equal 1 if a
vertex j is visited immediately after vertex i and 0
otherwise. Auxiliary variables (integer) were
included in the model to enable sub-routes
elimination. Given the cost of inspecting each arc
(i,j) that has to be visited, the objective function is
the total inspection cost, to be minimized.
Formulations for the directed and undirected
variants of the problem under study (described in the
next section) were developed, as well as a mixed
formulation that combines the two.
5 MODEL APPLICATION AND
RESULTS
This section describes the model application to
obtain optimal routes for road inspection with the
existing technical constraints. The Bragança district,
in the northeast of Portugal, was selected as the case
study, as it presents a mixture of topological
combinations of road segments to be inspected and
other roads, and of short and long arcs, and thus was
also able to serve as a test dataset to verify if the
model constraints were able to represent feasible
inspection plans. Network size was also considered
adequate for a first model application.
As global parameters, values for the average
inspection speed, average speed for connections
(non-inspection), fuel consumption, gas price, daily
wage and overnight accommodation costs were set
to provide realistic values for the global operation
budget.
The model was implemented in GAMS
modelling system and solved with CPLEX version
12.6.1.
Table 1 presents the numeric characteristics of
the model (number of variables and equations), the
CPU time and the number of iterations of the
branch-and-bound search to reach a solution, as well
as the corresponding optimality gap.
Table 1: Summary of numeric characteristics and results
of the model.
Characteristic/re
sult
Value
# variables
70,225
# equations
71,148
# iterations
8,128 39,348 147,303 765,369
CPU time (s)
2 10 30 60
Relative gap (%)
27.39 7.88 6.00 1.11
Absolute gap (km)
530 123 92 16
Solutions were obtained for two scenarios: (i) a
model where the directions defined in the current
inspection plan were fixed; and (ii) a model where
road inspection directions were free. The reason to
consider scenario (i) was that it might be interesting
to the infrastructure manager to have an inspection
plan where each road stretch is examined following
the same direction of previous plans, as direct
comparisons are easier to made, while (ii) might
produce solutions that minimize the overall costs,
without necessarily respecting the directions of
previous inspection plans.
Best solutions of both scenarios were then
compared with the currently implemented IP
inspection plan, which was obtained empirically.
By including constraints that regulate the
location of the vehicle at the end of each working
day, it is possible to manage overnight stays in
specific locations. Options of overnight stays either
in the city of Coimbra (the closest IP headquarters)
or in the city of Bragança (the district capital) were
considered. Results with overnight stays are
presented in Table 2.
Table 2: Results (total length and cost) and savings of
solutions with overnight stays in Bragança, for both
scenarios.
Value Reduction %
km €
Current empirical
solution
3,281 1,308 -
Fixed directions
(i)
1,834 731 44
Non-fixed
directions (ii)
1,718 685 48
ICORES 2016 - 5th International Conference on Operations Research and Enterprise Systems
364
6 CONCLUSIONS
The developed optimization model for the route
inspection problem was able to produce solutions
that represent significant reductions of costs when
compared to the currently adopted solution.
By controlling the direction of inspection for
each road segment to match the current empirical
plan, savings of 44% were obtained. An additional
saving of 4% is obtainable when the inspection
direction is not fixed. A note should be made on
these preliminary results, as the model only
considered the district of Bragança while the current
inspection plans are designed for a national scale
where the administrative division is not taken into
account. As such, these preliminary results should
now be analysed by the experts in practice of
Infraestruturas de Portugal.
A future development of this work is its
extension to the entire country (divided by zones), to
produce full-scale inspection plans comparable with
the current empirical solution. Another development
is the integration of the solution generator with in-
vehicle systems to consider real-time unpredictable
changes to the plan, e.g. due to road blockage
(accidents, traffic congestion, etc.) and produce
alternative work plans.
REFERENCES
ESRI, 2011. ArcGIS Desktop: Release 10. Redlands, CA:
Environmental Systems Research Institute.
Miller, C.E., Tucker, A.W., Zemlin, R.A., 1960. Integer
Programming Formulations and Traveling Salesman
Problems, Journal of the Association for Computing
Machinery, 7, 326-329.
Monroy-Licht, M., Amaya, C.A., Langevin, A., 2014. The
Rural Postman Problem with Time Windows.
Networks, 64(3), 169-180.
Pataki, G., 2003. Teaching integer programming
formulations using the traveling salesman problem.
SIAM Review, 45(1), 116-123.
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