A multi-objective evolutionary scheme for control points deployment in intelligent transportation systems

Martin Luther Mfenjou1, Ado Adamou Abba Ari2, Arouna Ndam Njoya3, Kolyang4, Wahabou Abdou5, Abdelhak Mourad Gueroui6 LaRI Lab, University of Maroua, Maroua, Cameroon, Afrika LI-PaRAD Lab, Université Paris Saclay, University of Versailles Saint-Quentin-en-Yvelines, Versailles cedex, France Department of Apply Mathematics and Computer Science, LASE Lab, University of Ngaoundéré, Ngaoundere, Cameroon LE2I Lab UMR CNRS 6306, University of Burgundy, Dijon cedex, France

INTRODUCTION Today, monitoring activities through road transport networks remain a serious problem for both developed and developing countries since road accidents cause huge losses. Shoukrallah and Rifaat [1] noted that around the world, we have about 1.2 million people killed on the road in 2008 at an estimated total cost of $ 518 billion, and 50 million people are injured in road accident. Moreover Jadaan Khair [2] in their work on a comparative analysis of road safety in developed and developing countries showed that 90% of deadly accidents are caused in developing countries while these countries only have 54% of the global vehicle rate. The emergence of intelligent transportation systems (ITS) together with the new generation of mobile networks contribute to a serious reduction of the death rate on the roads [3][4][5][6]. These systems exploit technological advances of telecommunications to facilitate communication among users, precisely monitor activities in road network [7]. The implementation of such concepts and systems become necessary for developing countries.
In the case of the developing countries, more work are aimed at laying the groundwork for road Ì ISSN: 2088-8708 networks oversight models for inter-urban transport. For instance, based on some factors such as smart parking, city-wide traffic monitoring, as well as public transportation information services, Gohar et al. [8] proposed a big data analytics architecture for ITS. Moreover, Silva et al. [9] studied smart cities in the context of ITS while reviewing their features and characteristics as well as some challenges and opportunities. Furthermore, sustainable smart city schemes and framework have been developed in order to enhance ITS users mobility in some cities of developing countries [10,11]. However, these models should consider the infrastructural realities of these countries. Thus, Mfenjou et al. [4] proposed a methodology that aims at contextualizing an ITS by taking into account the infrastructural realities. In [12], the authors proposed a monitoring communication architecture for developing countries' inter-urban road networks based on control points. They then introduced a deployment model for these control points according to the following criteria: minimizing the installation cost of these points, maximizing network coverage and considering areas where accidents are frequently occurring in developing countries' inter-urban road network. This deployment has been performed by the Non-Dominated sorting genetic algorithm II (NSGA-II). For the experimented scenarios, authors end up at the pareto front that helps decision-makers to take appropriate decisions.
Several works focus on the issues of monitoring and regulation transport systems of developing countries. For the reduction of traffic violation such as speed violation, Tarapiah et al. [13] used GPS/GPRS to propose a smart on-board transportation management system that can be attached to a vehicle. This system can help to track a vehicle depending on their position using Google map. This system offers innovations in terms of vehicle tracking in developing countries. No information is sent between the decision-making and the road users in relation to the dissemination of information on road traffic.
Moreover, the proposed works in [14] exploited smartphone sensors to classify the paved and unpaved road as well as road anomaly detection. This solution can only be used to detect obstacles across the road transport network. It may have an impact incidents that occur on the roads, but without communicating obstacles to other users. On the another hand, Patel et al. [15], propose a survey on ITS using the internet of things (IoT). It presents the advantages and inconvenient of proposed approaches in the use of the IoT for ITS. Therefore, in the context of developing countries, technologies used on the IoT could be exploited for the regulation or monitoring of activities through inter-urban road networks. Likewise, the work of Mfenjou et al. [12] focuses on monitoring activities through an inter-urban road network by setting up an architecture of communication based on control points in order to enhance the regulation of inter-urban road networks in developing countries. The proposed deployment was done using an optimization method: NSGA-II. It would be interesting to use several optimization methods to see which one could give better solutions. The following section provides a literature review of some optimization methods.
The purpose of this work is to perform the deployment of the control points using some optimization methods including the Non dominated sorting genetic algorithm-II (NSGA-II), the multi-objective particle swarm optimization (MOPSO), the strength pareto evolutionary algorithm -II (SPEA-II), and the pareto envelope based selection algorithm-II (PESA-II). Indeed, the use of several optimization method's leads to an evaluation of it thanks to the performance indicators. For comparison purpose, among the performance indicators available in the literature, we adopted the hypervolume, inverted generational distance (IGD) and spread.
The rest of the paper is organized as follows: In Section 2, we review some optimization methods based on evolutionary algorithms and their applications in the context of nodes or control points deployment. As for section 3, we propose a methodology to be adopted to carry out the deployments of the controls points and to analyze the obtained results. Concerning the section 4, we present the results of the pareto front of the non dominated solutions resulting from the used methods of optimization. Then, we evaluate these optimization methods thanks to some performance indicators. Finally, section 5 summarizes, concludes and introduce the future work.

2.
OVERVIEW OF SOME OPTIMIZATION METHODS 2.1. Multi-objective genetics algorithms Introduced by John Holland [16], genetics algorithms are among other the most used evolutionary algorithms. Whether in the context of single objective problems or multi objective problems, they are based on: − Selection [18,19]: At this level of genetic algorithm, it finds the best individuals for the mating process in such a way that the offsprings produced are better than in the previous population. Depending on how the best individual is sought, several methods of selection exist, but the most known are: the roulette wheel selection, the linear rank selection, the exponential rank selection, the tournament, the truncation selection.
− Crossover [20,21]: Here, the operation consists in merging two parents in order to generate a third new individual. There are also many variants of crossover: single point crossover, uniform crossover, N point crossover, three parent crossover, and arithmetic crossover.
− Mutation [22,23]: Here, the algorithm must generate solutions that are overall likely solutions. We also have several types of mutations: inversion mutation, insert mutation, scramble mutation, flip mutation, swap mutation, interchanging mutation, reversing mutation, uniform mutation, creep mutation.
− Evaluation [16]: To check whether the individual (if he optimizes function), the objective function is used. Otherwise, we go back to the selection.
− Replacement [22][23][24][25]: To become the best individual, it would reflect the related problem posed initially in the reality. There are many types of replacement: generational replacement, steady state replacement, elitism, delete n-last, delete n, weak parent replacement, both parents replacement, random replacement.
We are interested in problem solving by multi-objective algorithms. They are grouped into three classes [26]; aggregating function, population-based approaches, and pareto-based approaches. In this work, we are specially interested on nondominated sorting genetic algorithm II (NSGA-II), strength pareto evolutionary algorithm-II (SPEA-II), and pareto envelope based selection algorithm-II (PESA-II).

Nondominated sorting genetic algorithm II (NSGA-II)
This is one of the most used optimization methods. Its efficiency is recognized since compared to some optimization methods its complexity is O(mN 2 ). It is based on a classification of individuals in several levels [27]; it uses the elitist approach that gives it the ability to save the best solutions found from previous generations; it uses a calculation function of the crowding distance. This calculation makes it possible to choose the best solutions in a pareto front. This ensures a uniform dispersion of solutions on the pareto front.

Strength pareto evolutionary algorithm II (SPEA-II)
The SPEA-II [28] is an evolutionary multi objective algorithm that has an improved fitness assignment scheme that takes into account for each individual how many individuals it dominates and how many individuals it is dominated by. Moreover, the SEPA-II has a nearest neighbor density estimation scheme that allows a more precise guidance of the search process. Also, this evolutionary algorithm has an archive truncation scheme that guarantees the preservation of boundary solutions.

Pareto envolope based selection algorithm II (PESA-II)
It is also another optimization method based on evolutionary multi-objective algorithms. It uses a better technique for selecting individuals. Here, instead of associating an individual with a selective fitness, a selective fitness will be assigned to the hyperboxes in which the space is currently occupied by individuals in the approximation of the pareto frontier [29]. This method is more sensitive to ensure a better spread along the pareto frontier than methods based on individual selection.

Particle swarm optimization (PSO)
Particle swarm optimization (PSO) is developed by Kennedy and Eberthart [30]. The swarm of particles are possible solutions, optimization consists of browsing the space of search to find the global optimum. Eberhart and Shi [31] proposed the global version of the PSO. In their proposal, every particle of the swarm keeps tracks of its coordinates in the problem space that are associated with the best solution it achieved: this solution is known as pbest. The best solution value of all the swarm particle is called gbest. The aims of PSO is therefore to improve the gbest value. In fact, it consists at each time step, in updating the velocity. Each particle toward its pbest and gbest locations. This algorithm is based on the social behavior of animals that evolve swarm like schools of fish and flights of birds groups. It is a dynamic that springs from the local information, rules and memory of each individual that forms the basis of their movement while maintaining Ì ISSN: 2088-8708 cohesion with the rest of the animals in the group. From this information and rules, we quote: "stay close to the other individual", "go in the same direction", "go at the same speed as the others". The movement of a particle is therefore influenced by the component of inertia, the cognitive component and the social component.
Concerning the component of inertia, the particle tends to follow the current direction. About the cognitive component, a particle tends to move towards the best site by which he already passed. Finally, as for the social component, a particle tends to rely on the experience of its neighbors. The swarm is then composed of a set of particles each of which has a position (solution vector) and a speed. Any particle also has a memory allowing him to remember his best performance and that of his neighbors. The swarm of particles are possible solutions, optimization consists of browsing the search space to find the global optimum. PSO has been improved either by the modification of certain parameters, have the confinement of particles [32], the constriction factor [33], the inertia weight [34], the neighborhood topology [30]. Among the improved versions, we have fully informed particle swarm (FIPS) [35], 5TRIBES algorithm [36], PSO and hybridization [37][38][39] and Cooperative PSO [40]. Hence, this section allowed us to review the optimization methods that we used in the rest of this work. The following section proposes the approach we consider for the evaluation of the deployment of control points.

Problem formulation and design goal
The architecture presented in Figure 1 adapts to the technological and infrastructural context of these countries. It is based on control points. Two types have been defined: the treatment control points (TrCP) and the relay control points (RCP). The treatment control point (TrCP) have to main goal of processing the information collected by Relay Control Point. The information concern the behavior of vehicles traveling and disturbances in the inter-urban transport network.
As done in [12], the implementation of control points is based on two objectives: to minimize installation costs and to maximize the coverage in the inter-urban road network. The multi objective formulation given as shown in (5) associated with this type of control point according the objectives F 1 and Z 1 as shown in (1) and (2) as well as constraints C 1 and C 2 given in (3) and (4).
− F 1 : the objective function that represents the deployment cost of TrCPS.
− Z 1 allows the maximization of the coverage in the inter-urban roadway network. Indeed, Z 1 guarantees that all vehicles passing through the road network is visible and registered by at least one TrCP.
where m i,j is a boolean variable that is equal to 1 if there is an edge starting from i to j and 0 otherwise.
The corresponding constraints C 1 and C 2 are given as shown in (3) and (4). The used notations in the modeling of the optimization problem of TrCPs are given in Table 1.  Furthermore, according to the RCPs that used to collect information through the inter-urban road network, their deployment are done by ensuring a coverage of the network, minimizing the cost of installation and give the priority to road areas where accidents are mostly caused by the road users. As result, the multiobjective reformulation given as shawn in (12) is then based on three functions F 2 , Z 2 and Z 3 as shown in (6), (7) and (8) as well as constraints C 3 , C 4 and C 5 as shown in (9), (10) and (11). Now, let us define m u,v as a boolean variable that is equal to 1 if there is an edge starting from u to v and 0 otherwise; m u,v as a boolean variable that is equal to 1 if there is a way starting from u to v and 0 otherwise; and a u,v that is the number of registered accidents on an edge starting from u to v. − F 2 : the objective function that represents the deployment cost of TrCPs; − Z 2 allows to prioritize the RCPs where most accidents occur in a given road section; − Z 3 guarantees all vehicles passing through the road network is visible and registered by at least one RCP.
The constraints C 3 , C 4 and C 5 of the optimization problem are derived as shown in (9), (10) and (11).
Ì ISSN: 2088-8708 Table 2 presents the notations used in the modeling of the optimization problem given as shown in (12). Concerning the design Figure 2 illustrates the adopted approach to choose one (or more) method(s) according to the evaluation criteria we chose. For each selected scenario, as basic input parameters, we use:  Then we use the previously defined methods that will lead to the development of the pareto front. The pareto front allows to highlight for each method, non-dominated solutions. Finally, the chosen performance indicators offer the user the opportunity to select a method in relation to their priorities.

Framework
Here the binary encoding has been used as it can be seen in Figure. 3. Indeed, the objective here is to find the best positions according to the different types of control points. This is in order to minimize the costs of installations by maximizing the coverage of the areas to be monitored and to subserve areas with a high accident rate (case of relay points). Thus, for each chosen scenario, we have an M × N matrix where M represents the number of control point types and N represents the number of possible positions. The other optimization parameters are given in Table 3.

PERFORMANCE EVALUATION
In this section, we present the different results of the deployments of both types of control points. It is for all optimization methods. Then, we present the performance evaluation following the selected criteria. Before we get there, the used experimental values are given in Table 4. The experiments have been conducted in Matlab by considering three scenarios including: five, ten and fifteen admissible positions. Given the obtained curves, it would be important to use the tools for evaluating the performance of optimization methods. The evaluation criteria then allow the user to have a logical orientation on the choice to be made. Certainly, there are several performance metrics. The last make it possible to evaluate and compare the quality of the pareto front of the multi objective optimization methods. The work in [41] identified 54 metrics. In addition, according to Okabe et al. [42], these metrics take into account three aspects of the solution set including: the number of solution; the diversify (it is the distribution as well as spread); the convergence (this is the closeness of the theoretical pareto optimal front). Among these performance indicators, we choose the spread, the inverted generational distance and the hypervolume.
− Spread. According to [43,44], the spread is the metric that gives us a good evaluations results of the approximation. In fact, the spread uses the minimum distance between two successive solutions to the assessment of the distribution of the solution on a given search space. About the comparison of many multi-objective evolutionary algorithms, the lowest value of spread is associated to the best algorithm. Its formula is given as shown in (13).
P is the set of the pareto Solution.
− Inverted generational distance (IGD. It is used to measure the proximity between the evaluated solutions and the optimal pareto front P * [45]. Among many multi-objective evolutionary algorithms, the best algorithm is the one which has the lowest value of IGD. It is defined as given as shown in (14).
− → x * j )) 2 and − → x i and − → x j are solutions that belong respectively to P * and P − Hypervolume: It calculate the volume covered by the solutions in a given objective space. It measures both the diversity and convergence as shown in (15). A bigger hypervolume indicator define a better algorithm.
The curves obtained from the optimization methods previously mentioned namely: NSGA-II, PESA-II, SPEA-II and MOPSO. Moreover, the previously mentioned scenarios used namely: five eligible positions, ten eligible positions and fifteen eligible positions. Figures 4a, 4b, and 4c shows the obtained pareto fronts results for TrCP. Furthermore, Figures 5a, 5b, 5c, and 5d shows the pareto fronts results of the RCP with 05 admissible positions. Figures 6a, 6b, 6c, and 6d shows the pareto fronts results of the RCP with 10 admissible positions. Figures 7a, 7b, 7c, and 7d shows the pareto fronts results of the RCP with 15 admissible positions.   Tables 5, 6, and 7 present the IGD, spread, and hypervolume evaluations respectively of the optimization methods applied to the deployment scenarios of TrCP. Concerning the RCP, the IGD, Spread and  Hypervolume are shown in Tables 8, 9, and 10, respectively. With respect to the TrCPs, the comparison of the IGDs shows that for the 05 and 10 admissible points, the PESA-II method is the most appropriate. SPEA-II is best for 15 admissible points. Compared to Spread, the PESA-II method is the best for the deployment for all scenarios. As for the hypervolume, the NSGA-II method is the best. Moreover, with respect to relay checkpoints, the comparison of the IGDs indicates that the SPEA-II is the most appropriate. It is also the best for comparing Spread. As for the hypervolume, the NSGA-II method is the best. Performance indicators have provided more specific orientations to users. Given the large number (i.e., 54) of these indicators, [41], have classified these according to their uses in optimization work. Also, in most of the works in the literature, it appears that Hypervolume is the best criterion of evaluation. This leads us to conclude that the NSGA-II method is the most suitable for the deployment of control points.   1.65e+00 1.03e+00 1.87e+00 1.27e+00 2.77e+00 1.72e+00 9.36e-01 7.61e-01 10 2.54e+00 1.91e+00 5.30e+00 4.04e+00 3.57e+00 3.30e+00 1.99e+00 1.82e+00 15 2.60e+00 1.65e+00 4.41e+00 3.62e+00 2.13e+00 1.18e+00 1.77e+00 1.24e+00

CONCLUSION
Considering the description of our proposed scheme, it appears that ITS can contribute to the regulation of activities in inter-urban road networks in developing countries. The control points are then defined for the collection, RCP and the TrCP of information in this context. We used the multi-objective formulation proposed in previous work for the deployment of control points. We then use the NSGA-II, MOPSO, SPEA-II, PESA-II methods to search among them, the one that would be best indicated for these deployments. Thus, we build the pareto front for these deployments according to three scenarios: 05, 10 and 15 admissible points. We used three performance indicators namely hypervolume, IGD and spread. We noted that the NSGA-II is the preferred method for deploying these control points. Indeed, for all types of control points and for all scenarios, it offers the best results. The future works will consist in proposing an ontology of disturbances that occur in inter-urban road networks.