Effects of drivers’ evasive behavior on the placement of automated enforcement equipment in highway systems

1Transportation and Logistics Laboratory, Federal University of Santa Catarina, franceschi.lucas@gmail.com 2Transportation and Logistics Laboratory, Federal University of Santa Catarina, otto.gus@gmail.com 3Transportation and Logistics Laboratory, Federal University of Santa Catarina, luciano.kaesemodel@gmail.com 4Transportation and Logistics Laboratory, Federal University of Santa Catarina, amir.labtrans@gmail.com


INTRODUCTION
For any entity that is responsible for maintaining highway infrastructure, a core concern is monitoring the vehicles that use the roads in order to ensure user safety. Hazards on highways can arise, among many situations, from the presence of vehicles that are in poor maneuverability condition or from damages caused by such vehicles to the road infrastructure itself. Especially in freight-heavy traf ic, overweight or speeding trucks represent a grave danger to other users, due to the increased possibility that these trucks would lose control and cause catastrophic crashes. Besides this, overweight trucks also cause exponential damage to the pavement, creating defects that can compromise the safety of other users and demand infrastructure interventions much earlier than planned, which represent an expressive cost increase for the maintenance of the service level of the highway system.
However, carriers that disobey the transport regulations often do so in a conscious manner. They seek, for instance, to optimize their costs by increasing the amount of cargo hauled in each truck over the legal limits. In doing so, however, these individuals are obtaining pro it at the expense of society, since they are causing danger to other users and exponentially increasing the roadway's maintenance cost, which is ultimately paid by the users themselves via tollbooth fares or taxes (Transportation Research Board, 1990). Upon the creation of enforcement measures on the highways, such as automated weighing stations, the violating vehicles are motivated to ind ways in which they can avoid enforcement and carry on with illegal transportation. In fact, a few studies have observed the practice of such evasive tendencies, which include traveling at weighing stations' closed hours or even making detours to avoid them (Cottrell, 1992;Cunagin et al., 1997;Strathman and Theisen, 2002). Another study has also applied the System Dynamics method in order to show that the practice of overloading vehicles does indeed increase productivity and pro it for carriers, and that such pro it comes with disadvantages to society, such as infrastructure deterioration and increased accident rates (Ghisol i et al., 2019).
As a solution to this problem, technological advancement has allowed the creation of automated monitoring stations, which are capable of measuring various characteristics (such as size, speed, total weight and its distribution along the axles) on-track automatically. Such technologies have a potential not only for enforcement, but also for continuous data collection, since the measuring process is completely automated, and in many cases does not require additional infrastructure beyond the installation of on-track equipment (Jacob and Feypell-de La Beaumelle, 2010).
Given the possibility of creating such continuous monitoring stations and the problem of enforcement evasion by the vehicles, it is imperative to properly plan the locations of enforcement stations on the highway system, in order to effectively capture the vehicle lows without allowing simple detours to exist around the monitoring stations. This problem consists in optimally locating a minimal number of enforcement stations, with the objective of intercepting as many vehicles as possible (Mirchandani et al., 1995), while also considering that the vehicle lows might react to the installation of monitoring stations and change their original routes.
Thus, if the objective of the monitoring system is to intercept vehicles that may present evasive behavior, it is not enough to use location models that are based on maximum vehicle interception, but rather it is necessary that the evasive behavior of the vehicles also be considered in the mathematical modelling of the problem (Marković et al., 2015). Otherwise there is a risk that the system may not be effective for enforcement. This kind of mathematical problem is commonly known as evasive low-capturing problem (EFCP). Motivated by this scenario, this paper presents an overview of EFCP and how they have been solved in recent literature. Moreover, numerical experiments are performed with real data that allow an analysis of how effective an enforcement system is when subjected to evasive lows in relation to the number of monitoring stations that are installed and also how the number of necessary monitoring stations increases with the increase in evasive tendency of the vehicles.
Other numerical experiments are also performed that investigate the effects of considering a different evasion tendency in planning than that which is shown by vehicles in practice, and show that underestimating the evasive behavior may lead to an ineffective enforcement system, whereas overestimation guarantees that the vehicles are covered, and does not require a significant increase of investment in infrastructure.
It is not the goal of this paper to advance the mathematical state-of-the-art on EFCP problems and their solution, but rather to review and discuss the practical applications of the theory and the currently existing techniques of EFCP and its solution alternatives, with special focus on transportation planners which deal with any kind of system where the users could actively try to evade enforcement by using different routes.
As such, the main contribution of this paper is to show how the evasive behavior of illegal vehicles changes the way that enforcement systems should be planned, and the consequences of not considering such behavior when planning. Another contribution of this paper is providing an up-to-date review of the currently existing formulae and solution algorithms for this problem.
The next sections are organized as follows: in Section 2, an overview of the mathematical models that deal with this problem is presented, as well as other works in which the problem of locating monitoring stations is also addressed. In Section 3, the methodology used to conduct the current study is presented. Section 4 presents and discusses the results obtained in our experiments. Finally, Section 5 presents the conclusions of this paper, along with the limitations of this study and recommendations for future works.

LITERATURE OVERVIEW
Many problems in transportation and logistics are well represented mathematically by "facility location problems", which are models that seek to optimally locate facilities in a given network so as to maximize an objective function. The ields in which these problems are used include the location of emergency services (Boonmee et al., 2017), refueling stations (MirHassani andEbrazi, 2012;Yildiz et al., 2016), traf ic counting equipment (González et al., 2019), distribution centers (Yan and Shuzhi, 2012) and railway stations (Xiang et al., 2010).
A subclass of location problems is called " low capturing problems" (FCP), in which the demand is characterized by traf ic lows, and the number of captured vehicles is obtained considering not only the volumes in the network, but also the routes that the vehicles take from their origin to their destinations, hence maximizing the number of vehicles that encounter at least one facility in their trip, and disregarding repeated interception of the same trips (Berman et al., 1992;Hodgson, 1990). Upon proposing the mathematical formulation for such problems, Hodgson (1990) offered a few examples of facilities for which the demand is characterized by vehicle lows instead of traf ic volumes, which include: convenience stores, refueling stations, automated teller machines and billboards. For these problems, if a low capturing model is not considered and the allocation is performed based on the links with higher volumes, then a "cannibalism" effect may occur, in which the demand of one facility is impaired by the existence of others of the same type at nearby locations. The FCP formulation has been used to solve several applications (Gendreau et al., 2000;Hodgson et al., 1996;Liu et al., 2019;MirHassani and Ebrazi, 2012;SE elmić et al., 2010;Yang and Zhou, 1998).
An extension of low capturing problems have been proposed by Marković et al. (2015), called "evasive low-capturing problem" (EFCP). In this case, it is assumed that vehicles may travel by many pre-determined routes, as long as the detour from its original path is not greater than a determined distance. Furthermore, it is also assumed that vehicles choose to travel through the shortest path which is not covered by a monitoring facility. Marković et al. (2015) demonstrated that EFCP problems are structurally different from FCP problems, and that algorithms that are successfully used to solve FCP problems may not be effective in solving EFCP problems.
The problem of locating monitoring stations to capture evasive lows can be represented by a bilevel optimization problem (Hooshmand and MirHassani, 2018), which is a special case of game theory (Stackelberg, 1952). Bilevel optimization problems are typically composed of a "leader" and a "follower", which possess different, con licting objective functions which are dependent on shared variables. The "leader" is the party which irst sets decision variables in order to optimize its objective function, and the "follower" reacts to the leader's decision and sets its own decision variables in order to optimize its own objective function. A few reviews of multilevel programming problems can be found in literature (Colson et al., 2007;Hongli et al., 2011;Lu et al., 2016).
In the EFCP applied to freight monitoring on highway networks, the transportation planning and enforcement agency is the leader, and the freight carriers which are in violation of transport regulations are the followers. The goal of the leaders (enforcement agency) is to minimize the occurrence of uncaptured illegal traf ic lows, and it does that by locating enforcement equipment that monitors all vehicles passing through a certain link in the network. The goal of the followers (illegal carriers), on the other hand, is to travel from origin to destination without being captured by any enforcement equipment and with the least possible transportation cost. They do that by looking for the shortest, un-monitored route from origin to destination.
Bilevel optimization problems, however, are intrinsically very dif icult to solve. Literature shows that even the simplest instances of this problem are classi ied as NP-hard (Colson et al. 2007). For this reason, Marković et al. (2015) have made a few assumptions that allow the problem to be reduced to a single level. The assumptions are: 1. For every trip that is made in the network, there is an associated cost, which represents two quantities simultaneously: the cost of transportation for the carrier, and the cost of illegal transportation for the planner. Both quantities are proportional to the low volume and to the trip's distance; 2. The followers attempt to minimize the cost of travel for every origin-destination pair, by choosing the shortest, un-monitored route. The leader attempts to minimize the costs of illegal transportation in the whole network, by locating enforcement stations that capture illegal vehicles. As such, the objectives of both leader and follower models coincide; 3. The cost associated with a certain vehicle low increases linearly with the distance traveled by unmonitored vehicles; 4. A certain vehicle low (de ined as a set of vehicles with the same origin and destination) may travel along the shortest paths between its origin and destination. The number is determined so that the ( + 1) th shortest path would represent and excessive detour (that is, the cost of making such detour would exceed the bene it obtained from the illegal transportation); 5. A vehicle low is considered captured if there is at least one monitoring station in each of its shortest paths. Furthermore, it is assumed that captured lows do not represent any cost to the highway system; and 6. An uncaptured vehicle low travels along the shortest of its shortest paths that is not covered by any monitoring station, since this minimizes its travel costs. As a result of making these assumptions, the minimization of the travel distance of the vehicles (which is the objective of the followers) coincides with the minimization of the total cost associated with the illegal lows (which is the objective of the leader) and so the problem can be expressed as a one-level program.
The mathematical model proposed by Marković et al. (2015) is a binary integer programming model, which has an exact solution. One limitation of this model, however, is that its solution depends on the preprocessing of the shortest paths between each origin-destination (OD) pair of the network being studied, a process which has a potentially prohibitive computational cost. Other subsequent works have evolved from Marković et al. (2015) to propose more computationally ef icient models and also to consider scenarios in which equipment installation spans over a long time, considered as one of the decision factors the order of equipment installation over time (Arslan et al., 2018;Hooshmand and MirHassani, 2018;Marković et al., 2017).
Another work has also approached the evasive low-capturing problem, with the goal of relaxing assumptions made in the original paper (Lu et al., 2018). In this case, the authors dispute the assumption that the vehicles travel along one of a set of shortest paths for each OD pair, and instead consider that the route choice is made considering the whole roadway network. In order to solve this model, Lu et al. (2018) present a bilevel model and a solution algorithm based on heuristics.
Upon evaluating Markovic's work, however, Lu et al. (2018) have considered a constant number of shortest paths between the OD pairs (denoted as k), chosen to represent the majority of cases. If this approach is changed, and k is chosen dynamically in relation to the route possibilities between each OD pair, then the authors' argument that the vehicles may ind alternative viable paths beyond the given set of shortest paths is invalid, since there is certainty that all viable paths between origin and destination are included in the set of k shortest paths (in this case, a viable path is de ined as one whose distance is within a given maximum allowed detour from the shortest path). Hence, the bene it obtained via the bilevel formulation does not compensate for the loss of certainty that the solution is going to be optimal. It can be used, however, as a good alternative to deal with large problems, where pre-processing is prohibitive.

METHODOLOGY
In order to explore the problem of positioning monitoring stations in highway networks considering evasive behavior, the deterministic EFCP model presented by Marković et al. (2015) will be used, which is presented in this section. With this model, a few numerical experiments will be carried out with a real network, which represents the highway network on the state of Espıŕito Santo, in Brazil.

Problem formulaBon by Marković et al. (2015)
Consider ( , ) as a bidirectional road network, where is the set of nodes in the network and is the set of links, identi ied by ( , ) pairs, which represent the origin ( ) and destination ( ) nodes of the link. Also, consider as the set of vehicle lows, and the set of possible paths for each low ∈ , composed by its shortest paths. In this context, a "vehicle low" is de ined as a trip with an origin, a destination, and the transported volume. is de ined as the set of links that compose the path ∈ of low ∈ . In addition, is the cost of installation of an enforcement station at the link ( , ), and is the cost associated to low ∈ if it travels unmonitored along path ∈ .
Moreover, de ine as a binary variable which is equal to 1 if a monitoring station is located in the ( , ) link, and 0 otherwise. In order to allow formulation as a single-level problem, three sets of auxiliary variables are introduced. These variables are used to determine whether or not a certain vehicle low should be considered captured, and also to determine which path is chosen, amongst all the available paths, for each vehicle low. The auxiliary variables are de ined as follows: The auxiliary variables and have their values set by the choice made for the variable . However, is also a decision variable, which represents the choice of path for each low, and is restricted by the location of the monitoring stations. With these de initions, it is possible to write the evasive low-capturing model as a binary programming model: (2) The objective function (1) is composed of two terms. The irst term minimizes the investment cost of installing new monitoring stations. The second term minimizes the cost associated by truck lows whose paths are not covered by at least one enforcement equipment. Constraints (2)-(4) de ine the auxiliary variable, by ensuring: that the path must be considered unmonitored ( = 0) if there aren't any enforcement stations in its links (constraint 2); that if there are any enforcement stations on a given path ( = 1) then the path mustn't be considered unmonitored ( = 0) (constraint 3); and that the path must be considered monitored ( ≥ 1) if any of its links contain an enforcement station ( = 1) (constraint 4). In constraint (4), 4 4 denote the number of elements on the set of links that compose a path. Constraint (5) de ines the auxiliary variable , by stating that, if any of the paths for a certain low ∈ are un-monitored ( = 0 for any ∀ ∈ , ∈ ), then the low must also be considered unmonitored ( = 0). Constraint (6) makes sure that all unmonitored lows ( = 0) contribute to the cost function ( ≥ 1).
Through this formulation, it is possible to ind the exact optimal solution for the location of enforcement stations on highway networks accounting for evasive behavior. In practice, the solution is obtained in two steps: irst, the network must be pre-processed in order to ind all shortest paths within a given maximum detour from the shortest path (this can be done with Yen's algorithm (Yen, 1971). Second, the problem must be solved with any solver equipped with branch-and-bound based algorithms.

Concepts and definiBons
In this section, a few concepts of interest to this study are de ined in order to facilitate the explanation of the following experiments and results obtained. Firstly, we assume that the cost of transportation for each low is equal to the distance traveled by the vehicles multiplied by the low volume. In doing so, we assume a unitary cost per vehicle and per distance unit. As such, the cost of each path for each vehicle low ( ) is calculated as the distance traveled by the vehicles on each path multiplied by the low volume. The origin of this de inition is on weight enforcement problems, in which the damage is the loss in service-life of the pavement, which is linearly increasing with the distance traveled by overweight vehicles. This de inition is still applicable on other contexts, such as hazardous material transportation, in which the cost is not related to pavement infrastructure, but rather on the risk such vehicles represent to other highway users. In this context, the risk also increases with the distance traveled by the vehicles (SE elmić et al. 2011).
For a scenario in which a certain enforcement solution is evaluated, the "resulting damage" of the solution is the sum of the cost of all unmonitored lows. This coincides with the second term of the Objective Function (1). For all the scenarios analyzed, a baseline case will be created in which there are no enforcement stations in the network (hence all vehicles travel unmonitored along their shortest paths), and the resulting total cost is noted as a reference value.
We then denote the "damage reduction" of an enforcement system as the percentual difference between the resulting damage of the system and the resulting damage of the baseline case. The complementary amount is called the "residual damage" which is the cost that still exists after the installation of the enforcement system. Therefore, if a certain scenario presents a damage reduction of 80%, for instance, that means that the enforcement system has successfully accounted for 80% of the total cost that existed in the baseline case, and the residual damage is 20%.
Vehicles that are captured by enforcement stations are considered to not represent any cost, since it is assumed that the vehicles know where the enforcement stations are and they know of the penalties of overloading, in which case they will cease their illegal practices if there is no viable unmonitored route. This is indeed a simpli ication; however, it is justi ied by considering that the planning of enforcement systems usually spans over a long timeframe, in which there would be time for carriers to learn the location of the stations and to react accordingly.
As previously mentioned, the number of shortest paths will be chosen for every OD pair as a function of a parameter called "maximum allowed detour". The maximum allowed detour quanti ies the tendency of the vehicles to evade monitoring stations. The meaning of this parameter is that, if a maximum deviation detour of 5% is prescribed, then all vehicles will accept traveling distances up to 5% greater than the shortest possible distance between origin and destination in order to avoid the monitoring stations. This means that is such that the ( + 1) th shortest path have a distance at least 5% greater than the shortest possible path.

Numerical experiments
A few experiments will be carried out, in which some input parameters will be controlled in order to study the sensitivity of the optimal solution and investigate the problem. The experiments will be described in this section, and their results presented in Section 4.

Experiment 1: reduction of total damage in relation to the number of stations located.
The goal of this experiment is to verify the ef iciency of locating a variable number of monitoring stations in the damage reduction of the system. The model will be adapted in order to locate a given maximum number of stations. In order to achieve this, the installation costs will be considered null, and Constraint (7) will be added to the model: The shortest paths will be found using a modi ied version of Yen's algorithm (Yen 1971), that inds not a given number of shortest paths, but all shortest paths within a maximum allowed detour. The modi ied model will be solved repetitively, varying the number of monitoring stations in the system ( ) and observing the inal value of the objective function.

Experiment 2: effects of the increase of the evasion tendency on the number of monitoring stations needed to cover all lows.
In this case, the goal is to study the impact of the variation of maximum allowed detour (in practical terms, this varies the tendency of the vehicles to evade enforcement) in the number of monitoring stations that is necessary to cover all lows in the network. To this end, the installation costs receive much lower (but non-zero) values than the cost associated with unmonitored lows. Thus, the second term on the Objective Function (1), that represents the cost associated with unmonitored lows have a much greater importance than the term that represents installation costs. Therefore, the model will locate the least possible number of stations that are needed in order to eliminate the occurrence of unmonitored traf ic.
With the model modi ied in this way, the maximum allowed deviation will be varied and the number of stations necessary to eliminate unmonitored traf ic will be observed.

Experiment 3: consequences of planning without considering evasive behavior.
In order to investigate the need to consider evasive behavior on the planning of automated monitoring systems for enforcement, another experiment is carried out, in which an initial planning is made with a maximum allowed deviation of 0%. Thus, only the shortest paths for every OD pair will be considered in this initial planning, which re lects the way the problem has been solved in a few works (AlGadhi, 2002;Mahmoudabadi and Seyedhosseini, 2013;SE elmić et al., 2011). When solving this model, the installation costs are set in the same way as Experiment 2. Hence, the minimum amount of stations necessary to capture all lows will be located. After this, the location of the monitoring stations from this initial planning will be kept constant, and a simulation carried out in which the vehicles receive a greater maximum allowed detour than the one considered in planning (up to 50%).
Furthermore, additional instances of this experiment will be carried out, in which the initial maximum allowed deviation also varies between 0% and 50%, and the resulting locations are used in the simulation of lows with varying maximum allowed detours. With this, it is possible to observe the effects of evasive behavior in a system that did not completely account for it in the planning of the stations' locations.

RESULTS AND DISCUSSION
The experiments described previously were carried out on a personal computer with an Intel® Core™ i5-8400 processor with 2.80GHz frequency, with RAM memory of 16.0 GB and Windows 10 64 bits operational system. The models were implemented with the "PuLP" python library (Mitchell et al., 2011). This library allows for the modelling of the optimization problem and provides an interface to a few solvers, of which the COIN-OR CBC solver was used (Forrest et al., 2018).
The results obtained allow a few observations to be traced regarding the effects of evasive behavior in the problem of optimally locating monitoring stations for enforcement purposes. As a irst point of discussion, it is possible to observe the potential that the model presented by Marković et al. (2015) has in being used for the planning of the locations of monitoring stations for evasive low capture. The usefulness of this model is mainly in the fact that the optimal solution to this otherwise very complex problem is possible to ind, limited only by network complexity and computing capacity. Finding the optimal solution means that all the possible paths contained in the input vector will be accounted for. The pre-processing of all the viable paths between each OD pair, however, can be prohibitive.

Results of Experiment 1
The network used in this experiment represents the federal, state and municipal highway  (Figure 1). The origin and destination nodes (which correspond to municipalities), the OD pairs and the transported volumes were obtained from of icial data for the state of Espıŕito Santo in 2017. The shortest paths for all OD pairs were pre-processed for a maximum allowed detour of 20% (it is possible to consider lower values simply by iltering the input set ). This resulted in a total of 107,920 considered paths. The number has varied in the following way: 61% of the lows had fewer than 10 viable paths, 25% between 10 and 100 viable paths, 10% between 100 and 1000 viable paths, and 4% of the lows had more than 1000 viable paths, including two OD pairs with over 26,000 viable paths. The solution of the model was obtained with three computational processes running in parallel. Each process executed a sequence of processing tasks that correspond to instances of the problem solution. A common queue of processing tasks was created, and each one of the three processes pulled from the same queue.
For each processing instance, a number of located monitoring stations was prescribed. The average time needed to solve the model with the COIN-OR CBC solver (Forrest et al., 2018) was 14 hours. This time does not include the time it took to pre-process the shortest paths, which was of approximately 13 hours for the maximum allowed detour of 20%. Figure 2 shows the damage reduction obtained as a function of the number of monitoring stations located in the network.
It is observed that, in the three cases of maximum allowed detours, a reduction of more than 95% on the damage associated with unmonitored lows was obtained with 20 monitoring stations, with 78 stations needed to increase this reduction to 100%. This may be explained by the fact that the highest damages are associated with the longest trips, which possess a greater number of links in common between themselves. Besides which, a concentration of the highest volume lows in a few origins or destination nodes is observed in reality, which can also contribute to the majority of the damage being eliminated with a few stations, since covering these regions would account for a large part of the traf ic.

Discussion of Experiment 1
An analysis of the results presented on Section 4.1 (Experiment 1) shows the ef iciency of increasing the number of monitoring stations on reducing the damage associated with unmonitored lows. Figure 2 shows a drastic reduction on the resulting damage with a relatively low number of monitoring stations. This observation is due to the fact that the model's exactness guarantees that in any scenario the maximum possible damage reduction will be obtained, so even with a low number of stations, the solution will prioritize locations where it inds the best results with the limited number of stations. Another fact that collaborates this result is that, usually, highway systems present a clustering of nodes with high volumes, which may be located near production or consumption centers, large cities or large transportation terminals such as ports, railway stations, etc.
Note that, for Experiment 1, every number of located stations was run as a new solution to the model, independent from the ones found previously. Therefore, the increase in number of stations does not represent the evolution of a system that is gradually built, but rather the increase in effectiveness of increasing the total investment on the system.

Results of Experiment 2
The network used in this experiment represents the south-central region of the state of Espıŕito Santo, Brazil. This network includes the largest cities of the state and the OD pairs with the highest volumes. The reduction in network size was performed in order to lower the computational cost of the analysis, since pre-processing of the ES network with more than 20% maximum allowed detour was inviable.
The graph used in this experiment has 146 nodes, 368 links and 147 OD pairs (Figure 3). Preprocessing of this network was carried out with up to 50% maximum allowed detour, which resulted in a total of 78,137 possible paths between OD pairs. Figure 4 shows the results obtained in this experiment.

Discussion of Experiment 2
Looking at results from Section 4.3 (Experiment 2), it is possible to observe that considering evasive behavior on the planning of automated monitoring systems did not signi icantly increase the number of monitoring stations needed in order to achieve total coverage. This result is due to the fact that many of the possible paths between origin-destination pairs, including those with high detours, have a great number of common links. Especially if there is some kind of junction between origin and destination, the increase in the maximum allowed detour would still be covered by a monitoring station located in the appropriate link. As such, it is possible to observe that the consideration of evasive lows in the planning of automated monitoring systems does not mean that a signi icantly greater investment would be needed on building new stations, but rather that the choice of installation links would be performed in a more intelligent way, so that the links that cover a greater number of paths are chosen. Another important consideration on this Experiment is the fact that, in order to consider the allowed detour with values up to 50%, it was necessary to reduce the network to a smaller region. The reason is that with such high values of allowed detour percentage, the number of paths that are possible for each vehicle low increases greatly and makes it prohibitive to carry out this experiment on a larger network. This is also due to the model that was chosen to perform this study. This paper uses the deterministic model presented in Marković et al. (2015) because it presents an exact solution and is simple to implement. However, there are different models to solve the same problem, including the one presented by the authors of Arslan et al. (2018), which also presents an exact solution without preprocessing.

Results of Experiment 3
The same network used in Experiment 2 was used in this case. An initial planning was carried out with 0% maximum allowed detour, and the total cost associated to lows with an increasing maximum allowed detour was observed. The residual damage of the system was observed with the varying lows. Results are found in Figure 5.  The same analysis was also run with varying values of maximum allowed detour both for the initial planning and for the vehicle lows. The results of this analysis are shown in Table 1. This table is structured in the following way. Each column represents the value of maximum allowed detour that was used in order to plan the system and locate the enforcement equipment. In turn, each row represents the maximum allowed detour that was used to simulate the lows' response to the initial planning. The value in each cell represents the residual damage in the network, which quanti ies the ability of the vehicles to evade the system. For instance, the irst column represents a case where the location of the equipment was chosen without considering evasive tendencies. The values in this column mean that, for instance, if the vehicles are willing to perform detours of up to 50% their total travel distance, then 68.8% of the low is able to continue travelling without being captured. The last column shows, however, that if the initial planning is done considering a 50% tolerance on the vehicle's detours, then all the vehicles which are willing to perform detours of up to 50% their total distance will be captured.

Discussion of Experiment 3
Results from Section 4.5 (Experiment 3) show that, in the event that carriers do have a disposition of avoiding enforcement stations by changing their routes, and such behavior was not considered in planning, the system might be ineffective in capturing these vehicles, and the investment made in installing monitoring stations might not have an adequate return. For the network considered in Experiment 2, it is seen that the system planned without consideration for the evasive behavior (maximum allowed detour in planning was 0%) suffered a signi icant loss of ef iciency when the vehicles had an allowed detour greater than 30%. In reality, the pro its obtained by vehicles with illegal practices such as truck overloading might compensate for a 30% detour in routes.
The results from Table 1 show that if, during planning stages, the maximum allowed detour is considered to be less than the detours that the vehicles might perform in reality, the effectiveness of the system is unpredictable. Because the effectiveness of the system depends on choices of location for the monitoring stations, it is possible that the choice made for lower allowed detours is already a good candidate for dealing with more evasive lows, which was the case for the scenarios planned with 20% maximum allowed detour in Table 1.
The same table shows, however, that all the lows with a maximum allowed detour lower than the value considered in planning were completely captured. For this reason, it is possible to say that, in the planning of monitoring stations' locations for enforcement purposes, the evasion tendency must be overestimated. Doing this, there is no doubt that all the considered lows along the accounted paths will be captured by the enforcement stations. The cost of such overestimation is not in excessive investments needed in the system (as seen by Experiment 2), but rather on the computational effort that is needed for proper planning of the system. This computational effort, however, is minimal when compared to the magnitude of the timeframes that are considered in the planning of transportation systems, which usually span for multiple decades.

CONCLUSIONS
The goal of this study was to show how the evasive tendencies of illegal vehicles change the way that the placement of enforcement equipment in highway networks should be performed. It was also the goal of this paper to present relevant references as to how this placement may be performed in order to address evasive behavior. By analysis of literature and the performance of numerical experiments, this paper has arrived at the following conclusions: • Considering evasive behavior in the positioning stages of automated monitoring systems does not signi icantly increase the number of stations that are needed to cover the lows, but rather optimizes the chosen locations; • With the evasive low-capturing model, a signi icant reduction in the cost associated with unmonitored lows can be obtained even with a reduced number of monitoring stations. For instance, in the real case of the state of Espıŕito Santo, Brazil, the location of 20 stations reduced the total network cost in more than 95%, while 78 monitoring stations were needed to further increase this reduction to 100%; • If the targeted lows for a certain enforcement system do present an evasive behavior, and such behavior was not accounted for in the planning stages, then it is possible that there are escape routes which allow the vehicles to avoid enforcement by making relatively short detours, and the enforcement system might not be effective in promoting compliance to traf ic regulations; and • On the other hand, if the planning of the enforcement stations locations considers an evasion tendency that is greater than the one actually presented by the vehicles, then all the vehicle lows will still be accounted for, and such consideration will not generate excessive costs in infrastructure. Therefore, evasion tendencies must be overestimated in practice. This study also presents a few limitations, that are listed below, along with recommendations for future works.
• Firstly, the model that was used to perform the studies (Marković et al., 2015) requires that all the possible paths considered between each origin-destination pair be preprocessed. This is very costly, and as such, the size of the networks that were analyzed was limited. Future studies in this subject might consider using different models, which in turn could allow larger networks to be considered; • This study did not consider real costs of transportation or equipment installation, rather used proportional quantities that guaranteed the optimality of the solution for the experiments that were performed. As such, future studies could factor in the real installation and transportation costs for a speci ic application, in order to obtain more speci ic insights regarding the inancial planning of said application; and • Future studies could further expand on this work by also considering scenarios in which the installation of the enforcement equipment occur in a gradual manner, which more closely re lects the way that real systems are gradually installed over time. This would allow for observations regarding which locations should be prioritized, for example.