Telecommunication Fuzzy Rules for Multi Services Access Nodes Locations using Artificial Bee Colony

Abstract

In the presence of high competition market, planning the infrastructures of Telecommunication Access Network (TAN) is one of the most important tasks facing telecommunication companies especially after the trend of using optical fiber cables. This infrastructure is controlled by a list of barriers which affect selecting the locations of the most widely used technology Multi Services Access Nodes (MSAN). Therefore, the importance of determining the appropriate location of MSANs is appeared. This paper presents the capabilities of the Artificial Bee Colony (ABC) to find the fuzzy classifications rules for the telecommunication MSANs locations based on a set of MSAN’s planning barriers. This system starts by preparing the training data set using the benefits of Geographic Information System (GIS) for generating digital maps. The system helps in analyzing spatial data of existing TAN and the barriers which affect planning TAN. Afterwards, the system fuzzifies the MSAN’s planning barriers using Particle Swarm Optimization and Total Entropy as fitness function (PSO-TE). Then, the ABC capabilities, correlation function and confidence rate as a fitness function and the mamdani inference system are utilized to find the appropriate telecommunication fuzzy rules with respect of training data. The system ends by evaluating the generated telecommunication fuzzy rules for MSAN locations via comparing the result of proposed model with a number of classification algorithms found in literature based on the test data set. The total classification accuracy of the TFRML-ABC model is 97.8%. Hence, the proposed TFRML-ABC model is concluded to be efficient in classifying the MSAN’s features taking into consideration the misclassification rates.

Keywords

Artificial bee colony (ABC)correlation Min-Max mamdani inference system particle swarm optimization-total entropy (PSO-TE)telecommunication access network (TAN)geographic information system (GIS)multi services access node (MSAN)

1. Introduction

Nowadays, Telecommunication services providers face many challenges especially after the high and rapid growth in data communications usage. In highly competitive markets, the increment of demands lead telecommunications companies to enhance and upgrade their technologies to meet the requirements of their customers, attract new customers and keep current customers.

The technology upgrade process includes total or partial rehabilitation of current telecommunicationnetwork with the most up to date technologies. Telecommunication Access Network (TAN) rehabilitation may include replacing the current network components with new improved components or adding new components which will give the network its ability to introduce the required qualitative and stable services.

In many developing countries, planning the infrastructure of a typical Telecommunication Access Network (TAN) is a challenging problem due to the implied high level of uncertainty and ambiguity. The Multi Services Access Node (MSAN) is considered the new solution and recent technology for fixed telecommunication services. MSAN becomes an important technology which meets an enormous demand for new business and residential telephone service. Locating the MSAN is a complex problem as there are many barriers and obstacles which face the decision of choosing MSAN location. Obstacles in determining the best location of MSAN include continuous growth of residential and business locations. Hence, the quality of service (QoS) is affected. Therefore, it is a must to supply the necessary equipment at the right time and place to reach an acceptable grade of service with the minimum number of MSANs especially in the direction of CAPEX (Capital Expenditure) control and the ideal utilization of resources [1].

Fuzzy rules could be employed to empower the decision of locating new MSANs according to the vague barriers and obstacles found in the environment under consideration. Fuzzy rules [2] play a very important role in making a fuzzy decision during determining the location of MSANs. Generating appropriate fuzzy rules is one of the most challenging issues in fuzzy systems’ design.

Building or designing location fuzzy rules basing on the accuracy of human being’s knowledge or experience, based on the existing planning regions, could be biased and time consuming. Automatic generation of these location fuzzy rules increases the performance of decision making and enhances the infrastructure of the telecommunication network. Thus, there is a need for using meta-heuristic search mechanism to generate location fuzzy rules. The success of developing a paramount fuzzy profile and the fuzzy rule base relies on efficient membership function and fuzzy rule base used [2].

This paper presents a new model of TFRML-ABC [2] (Telecommunication Fuzzy Rules for MSANs Locations using Artificial Bee Colony) for constructing the MSAN’s planning rules. The MSAN’s features (barriers) extracted from environment are used for classifying two classes of MSAN installation decisions (acceptable place or not acceptable). The model is composed of four consequent phases. During the preprocessing phase, a geographic information system prepares training dataset by dividing area under study into small regions called grids, analyze each region and determine existing barriers such as telecommunication access network components, buildings, and other utilities. Afterwards, the membership degrees of each MSAN’s features (barriers) will be evaluated and used as input in the next stage. This procedure is accomplished automatically via generating the membership function parameters using a meta-heuristic search mechanism and the information theory measures as a fitness function to adjust particles in Particle Swarm Optimization with Total Entropy (PSO-TE) [3]. Then, the location fuzzy rules designing phase combines the Artificial Bee Colony(ABC) [4] capabilities, correlation function and confidence level [5] as a fitness function and the mamdani inference system [6] to select appropriate rules with respect to the training data. The test phase evaluates the generated location fuzzy rules via applying new regions barriers to the system, calculating the system actual decision and comparing the results with the target. The classification results are used for evaluating the TFRML-ABC model. The total classification accuracy of the TFRML-ABC model is 97.8%. Therefore, the proposed TFRML-ABC model is concluded to be efficient in classifying the MSAN’s features (barriers) taking into consideration the misclassification rates.

The rest of this paper is organized as follows: Section 2 represents a survey in literature for designing the fuzzy rules. Section 3 sets the preliminaries such as fuzzy systems. Artificial Bee Colony and correlation function. Section 4 gives an overview of the input data which is the telecommunication network barriers, the whole system, and its modules. Then the classification accuracy value of the whole system is calculated. Experimental results and conclusion will appear in Sections 5 and 6 respectively.

2. Motivation and related work

Decision making process is a critically important task because decision makers face various difficulties when they deal with uncertainty issues [7]. Hence, fuzzy inference system is appeared to handle such problems. The Fuzzy inference system [2] uses fuzzy logic to map the actual process from given input to an output depending on its design. The operation of designing a fuzzy inference system [2] depends on generating accurate membership function, fuzzy logic, and if-then rules.

Many types of researches are interested in fuzzy if-then rules generated from numerical data. For example, one of these researches introduced hybrid model which generates membership function using Self-Organized Features Maps then introduced Fuzzy Rules from ANT-Inspired Computation – Simultaneous Rule Learning (FRANTIC-SRL) model to build fuzzy classification rule using credible variables[8].

A new two-phase framework is proposed by [6] for player selection and team formation in soccer to help coaches in determining the collection of individual players in forming an effective team. In this paper, the first issue used the fuzzy ranking method and choose the top performers for inserting it on the team. The second issue selected the best combinations for soccer’s team players using Fuzzy Inference System (FIS). Therefore, the model’s efficiency depends heavily on the cognitive capabilities of the coaches.

Many researchers are very interested in Artificial Bee colony like [4, 9] for generating fuzzy rules and picked the best rules from the given population of rules. These researches proved the ability of ABC to be a suitable candidate for classification tasks. Another research is interested in the epilepsy risk level of the (Electroencephalogram (EEG) signals) signals in two levels, the first one is using hybrid PSO and ABC algorithms to make optimization. Further, the second level used Minimum Relative Entropy (MRE) as a post classifier to optimize it [10, 11].

Other papers used the correlation based fuzzy logic control method was proposed for the voltage [11] injection and current injection schemes for Unified Power Quality Conditioner (UPQC) to improve power quality in [12]. Another research introduced a new hybrid method which has been presented by [13] to detect intruders using Artificial Bee Colony with Correlation-Based Feature Selection. This research found a solution for the recurring security challenges. It proved that the proposed algorithm is adaptable and flexible in finding the intruders effectively. Furthermore, a new paper introduced hybrid methods called Correlation-based feature selection method and Artificial Bee Colony algorithm (Co-ABC) for classification of gene expression profile accurately [11]. Another paper used Genetic Algorithms to build an efficient classification rules [5].

In the telecommunication sector, many researches care about how to plan telecommunication access network. One of them presents a new algorithm called M-PAM (Modified-Partitioning around Medoids) to address the problems of antenna placement or the cell planning for mobile networks. This algorithm satisfies customer demands and obstacles of planning mobile network infrastructure [14]. Another research introduced clustering algorithm called COD-DBSCAN (Clustering with Obstructed Distance - Density-Based Spatial Clustering of Applications with Noise) to plan MSANs [15]. This research used scanned images (raster maps) and drew streets with coordinates of beginning, ending and intersection nodes on these maps as a first step, then it used a clustering algorithm to solve the problem of network planning using COD-DBSCAN as a second step to determine the suitable location of MSANs bearing in mind obstacle distance and network constraints (streets). Also, Marcel T. Kalsch, KatrinTschirpke [16] proposed a mathematical optimization model to select the suitable location of MSANs and the connection between main distribution point and classical node. Thus, optimization model minimized the cost of planning by minimizing the number of nodes and connections between hub and nods. These researches focused on how to select appropriate MSAN’s location taking on the considerations obstacles of distance. All these researches focused on density and distance barriers, but they ignored the other barriers which are needed for planning MSANs and reduce the cost of planning such as environmental barriers, MSAN’s planning barriers got from telecommunication company standard and other obstacles got from experiences of planning engineers.

3. Preliminaries

3.1. Fuzzy system

Fuzzy system deals with vague and ambiguous terms (parameters or variables) to simulate human thinking in evaluating variables’ values (labels, words, and linguistic terms) instead of ordinary exact values. Each fuzzy variable has fuzzy values which partially belongs to a set of fuzzy subsets. Fuzzy membership degree could be defined as the degree of an item exists in a fuzzy subset. Fuzzy membership function can describe the degree of membership [8]. $μ_{A} (U) : U \to [0, 1]$ (1)

Where

U symbolizes the universe of discourse and A is a fuzzy subset of U.

The membership values represent real values between [0, 1], where the value 0 means that the element doesn’t belong to subset A, while the value 1 means that the element belongs to the subset A. The fuzzy variables are the foundation stones in a knowledge based system that helps decision making in uncertain situations. Uncertain knowledge could be expressed in various forms. One of these forms is the fuzzy IF-THEN rules. A famous example is Zadeh-Mamdani’s fuzzy rule in which both conditions and decisions consist of fuzzy variables that belong to some fuzzy sets with some degree of membership. Finding an accurate, efficient and good set of rules are the core of any knowledge-based system. Automating the process of designing fuzzy IF-THEN rules is a tricky problem [8]. $IF x is A, THEN y is B$

Where (x is A) and (y is B) are two fuzzy assumptions; x and y are fuzzy variables defined over universes of discourse U, and A, and B are fuzzy sets defined by their fuzzy membership functions [8]. $μ_{A} (U) : U \to [0, 1] and μ_{B} (V) : V \to [0, 1]$ (2)

Fuzzy Inference System is considered as one of the most famous methodologies which is used in fuzzy logic and fuzzy sets theory. It could be helpful in many fields such as, science, economic, engineering and geographic applications. It has the ability to analyze human’s experience, capture the environment’s changing as expert knowledge and integrate with fuzzy systems easily.

3.2. Artificial bee colony

The artificial bee colony is an intelligent optimization algorithm which was proposed by Karaboga [9] to deal with numerical data. There are three groups of bees in artificial bee colony: employed bees, onlookers, and scouts. Employed bees investigate the food sources and determine their nectar amounts; meanwhile, the employed bees share the position information of these food sources with onlooker bees. Then food sources with high profitability being chased by onlooker bees using greedy selection. Scout bees appear when employed bee whose food sources are abandoned by the bees and search for new food sources the structure of ABC algorithm consists of two equivalent halves of the swarms (employed bees and onlookers bees). ABC algorithm generates the possible solution for the optimization problem by defining the food source position. The fitness of the associated solution are generated by the nectar amount of that food source [9].

The ABC algorithm consists of four phases: initialization phase, employed phase, onlookers phase and scout phase. In the initialization phase, The ABC algorithm will produce random solutions for employed bees using Equation (3). For the telecommunication planning problem, the initial solutions will be a vector of barriers and rule class. $X_{ij} = X_{j}^{min} + rand (1, RL) (X_{j}^{min} - X_{j}^{min})$ (3)

Where

Each solution of x_i (i=1,2,….) have a D-dimensional vector of optimization parameters,x_ij is jth dimension of ith employed bees, RL is a Rank Limit, rand (1,RL) is a random barrier rank within the rang [1, 3] and [1, 2] for class rank, $x_{j}^{min}$ is lower bound and $x_{j}^{max}$ is upper bound of jth prameters

In the second phase of ABC algorithm, a new candidate position of the food source are generated by the employed bees and neighboring food sources (TAN’s rules (barriers’ and classes’ ranks)) are found using the following Equation (4): [9] $v_{ij} = x_{ij} + φ_{ij} (x_{ij} - x_{kj})$ (4)

Where

v_ij is jth dimension of ith solution, x_ij is jth dimension of ith employed bee, x_kj is jth dimension of kth employed bee, φ is a random number between [–1, 1] and i, k ∈ {1, 2, . . . , SN} with i ≠ K and j ∈ {1, 2, . . . , D}. φ is a random number between [–1, 1] and i, k ∈ {1, 2, . . . , SN} with i ≠ K and j ∈ {1, 2, . . . , D}. The fitness value, which is the output of correlation and confidence functions, evaluates the old and the updated food sources (TAN’s rules) position by the employed bees. Information about the position and the quality of these rules are shared with the onlooker bees.

The third phase is called onlooker which gets, evaluates and selects valuable information from the employed phase about food sources (TAN’s rules) according to its probability value which is calculated by Equation (5) [9] $p_{i} = \frac{{fit}_{i}}{\sum_{i = 1}^{SN} {fit}_{i}}$ (5)

Where

fit_i Represents the fitness of ith solution in the population.

Whenever the fitness value of a food source (TAN’s rules) increases, its probability will be increased. Hence this food source will be selected by onlooker bees. In onlooker phase, the same mechanism which applied in Equation (4) will be repeated to produce a modification on the position of that site. Also new TAN’s rules with high confidence level are memorized using greedy selection.

the last phase is called scout. During this phase, the scout bees search on any solutions neglected through a predefined number of generation and replace it with a new position that is randomly determined by Equation (3) [9]. The following Fig. 1 shows the ABC mechanism in this paper.

Fig.1

ABC mechanism.

4. The proposed telecommunication fuzzy rules for MSANs locations using artificial bee colony (TFRML-ABC)

This paper builds Telecommunication Fuzzy Rules for MSANs Locations using Artificial Bee Colony (TFRML-ABC). These location fuzzy rules for MSAN are simple if-then rules with fuzzy variables. These fuzzy rules will be built in four phases. The first phase prepares the GIS training data. The second phase generates the appropriate membership function for the subsets of the fuzzy variables. The GIS data are input to the system for generating membership function using an integrated hybrid of particle swarm optimization and the total entropy as a fitness function for generating fuzzy membership function for the GIS variables [3]. Once the fuzzy membership functions for GIS variables are defined, the system’s third phase continues to find the optimal fuzzy rules for locating the MSAN using ABC with the correlation coefficient and confidence level as a fitness function. Whereas, the fourth phase compares the results of the proposed algorithm with the results of other algorithms to prove its ability to design suitable location fuzzy rules. This research used access network infrastructure represented by Geographic Information System [17] as a case study. The framework of TFRML-ABC for generating MSAN location fuzzy rules from the GIS data is represented in Fig. 2.

Fig.2

The framework of proposed TFRML-ABC system.

The main components of the TFRML-ABC system are summarized as follows:

Data preprocessing phase: the Geographic Information System capabilities are used in preparing training dataset by dividing area under study into small regions called Grid to analyze each region and determine existing barriers such as telecommunication access network components, buildings, and other utilities.

Fuzzification phase: Generating appropriate membership function for fuzzy variables using an integrated hybrid model (PSO-TE) which used a meta-heuristic search algorithm for choosing the best parameters of subsets. Then, drawing trapezoid and triangle membership function for each network barrier. This hybrid algorithm is introduced before in a previous work by [3].

Fuzzy rules phase: Generating fuzzy rules using ABC and determining the fired rule for each region using Min-Max Mamdani inference mechanism using correlation and confidence values as fitness function for finding the best fuzzy rule base.

Calculating the whole system accuracy level: Determined through the absolute error rate in finding the correct classes resulted from testing the system on the unseen instances or regions.

4.1. Preparing training data set using GIS

Geographic data could be captured, stored, queried, analyzed and displayed to build an intelligent system that helps decision makers. Spatial data is a critical part of Geographic Information System (GIS) because it represents the spatial location and the attributive information [17].

In this preprocessing phase, all related barriers of planning TAN infrastructure from telecom Egypt planning standards [18] and the experts of planning engineers are collected. The TAN barriers are categorized into more than one category such as environmental barriers, topography, access network barriers and utilities barriers [3]. Then these barriers are located on geographic maps (vector map) defined by their coordinates in the area under the study using ArcGIS10.3 [3]. After that, the area under study is divided into small regions called Grids using Grid tools. The grid size for each region is 100*100 meters. The distances between the center of each grid and the network barriers (drains, monumental areas sewer network, manhole and copper cabinet) are calculated using a model builder tool in ArcGIS. Both existing and future planned regions are taken within consideration [3]. Each Grid has a unique number and it may contain MSAN or not depending on existing access network. Figure 3 shows 100*100 grids on area under the study.

Fig.3

Area under the study.

Each region (Grid) is further divided into small elements of 5*5 meters size. The centroid of each 5*5 region (Grid) could be considered as probable location of MSAN, The proposed TFRML-ABC system will predict the most suitable region (Grid) of locating MSAN. ARCGIS10.3 is used as an analysis tool to calculate the distance between each point (centroid) and barriers within the 100*100 grid taking in the consideration all types of barriers [3].

All centroids that intersect with any barriers were neglected and removed because of lack of possibility to install MSAN over a building.

The following Table 1 shows a sample of preprocessed data for seven barriers and two l00*100 regions. The data represent the distance between the center point of the grid and each barrier namely (sewer network, manhole, copper cabinet, gas pipes network, water network, and street and population area, monumental area). The class value is 1 or 2 indicating whether this location is suitable for MSAN location or not.

Table 1

Telecommunication Infrastructure Planning Barriers

Regions ID	NEAR Sewer	NEAR Manhole	NEAR copper cabinet	NEAR gas pipes	NEAR water network	NEAR population area	Near monumental area	Class
ID1446	17.14448	NULL	45.82903	19.14448	15.14448	0.376742	Null	2
ID1447	26.78866	39.59837	49.66674	28.78866	24.78866	11.06466	Null	1

The barriers collected are used as training data set to the next phase which is fuzzy membership generating for GIS variables.

4.2. Generating membership function for fuzzy variables

Generating appropriate membership function is divided into two integrated sub-modules: the first module uses the meta-heuristic search algorithm particle swarm optimization to find the best three parameters for each subset within each network variable to draw membership function. The second module evaluates the location of each generated parameters using the total entropy (entropy and mutual information) as a fitness function. This work was published in a previous paper [3]. The following Table 2 shows membe ship degrees generated by PSO-TE for three network barriers (near Copper Cabinet, near Water Network and near Population Area). The membership function for each network barrier along with the training data are used as an input for the next phase to generate the fuzzy MSAN location rules.

Table 2
Membership Degrees for two samples of barrier

Regions NEAR copper cabinet NEAR water network

ID

M1 M2 M3 M1 M2 M3

ID1446 0 0.061109 0.938891 0.019896 0.980104 0

ID1447 0.789955 0.210045 0 0.685425 0.314575 0

Regions	NEAR copper cabinet	NEAR water network
	M1	M2	M3	M1	M2	M3
ID1446	0	0.061109	0.938891	0.019896	0.980104	0
ID1447	0.789955	0.210045	0	0.685425	0.314575	0

4.3. Generating fuzzy rules by (TFRML-ABC)

In this stage, a set of fuzzy rules is built for locating the MSANs in the telecommunication company infrastructure. This is accomplished through two integrated modules; the first module is implemented via applying Artificial Bee Colony for generating random populations of fuzzy rules. Each fuzzy rule will be composed of all telecommunication barriers under study and a decision class. The second module is interested in evaluating the performance of the generated populations through the fitness function. Generating fuzzy rules by ABC algorithm and the used fitness function are illustrated in the following sections.

4.3.1. Artificial bee colony algorithm

One of the popular swarm intelligence algorithms that used meta-heuristic search is Artificial Bee Colony. This paper used the strengths of ABC such as high flexibility and adjustments, fast convergence, fewer setting parameters and strong robustness [10] in generating feasible fuzzy rules. The ABC algorithm uses appropriate barriers’ ranks with class rank designing for designing fuzzy if-then rules for MSAN location planning in three phases. Through the first phase, new solutions are generated for the employed bees using Equation (3) and evaluated for each barrier and class severally using correlation fitness function. Then greedy selection is applied to keep the best solution. After that, the employed bees share the position information of these food sources (barriers’ rank and class’s rank) with onlooker bees.

In the second phase, onlooker bees produce the new solutions using Equation (4) and evaluate them using Equation (5). Food sources (barriers’ rank) with high profitability being chased by onlooker bees are selected using greedy selection.

Finally, in the third phase, scout bees appear where employed bees whose food source (barriers’ rank) were abandoned and search for new food source (barriers’ rank). These food sources are replaced by a new randomly produced solution for the scout according to Equation (3). After a predefined number of iterations.

The algorithm displays the best solutions (location fuzzy rules). The algorithm of the integrated framework is illustrated in Fig. 4. The next section describes how the performance of the food sources (fuzzy if-then rules of barriers and class) is evaluated using the correlation coefficient between the conditional and decision attributes and confidence degree as a fitness function. The fit individuals selected should be positively correlated with high confidence values exceeding a predetermined threshold.

Fig.4

Algorithm for building fuzzy rules by using (TFRML-ABC).

4.3.2. Fit performance of ABC using fuzzy MIN-MAX inference with correlation analysis

MIN-MAX Mamdani inference system

Mamdani inference [6] is the most popular method for capturing expert knowledge. It is able to describe the expertise in more conjectural and human-like manner. Inference in fuzzy set theory maps inputs (features) to outputs (classes in the case of fuzzy classification). It uses fuzzy implication relations, fuzzy composition operators and an operator to link the fuzzy rules. The results of Mamdani inference process, which inferring new facts, are based on fuzzy rules and the input data supplied. Fuzzy rules have different reasoning strategies. Most of them use the generalized modus ponens rule in which the inference law is applied over a simple fuzzy rule. Simple fuzzy rule can be expressed as follows: (IF x is A, THEN y is B) and (x is A’), then (y is B’) should be inferred. The generalized modus ponens law is implemented by the compositional rule of inference. It is represented as follows:[5] $B' = A^{'\circ} A \to B = A^{'\circ} R_{ab}$ (6)

Where

° symbolizes a compositional operator

R_ab symbolizes a fuzzy relational matrix representing the implication relation between the fuzzy concepts A and B.

R_{ab} = {Min}_{x \in A & y \in B} {Max (μ_{A} x, μ_{B} y)}

(7)

Where (x is A) and (y is B) are two fuzzy propositions; x and y are fuzzy variables defined over universes of discourse U; and A and B are fuzzy sets defined by their fuzzy membership functions.

The results B_i for the output fuzzy variable y inferred by all the fuzzy rules for a given set of input facts are combined by fuzzy inference method. All the fuzzy rules are fired at every cycle in a fuzzy production system, which performs cycles of inference, and they all contribute to the final result. Some of the main links between fuzzy rules are OR-link (max operator) & AND-link (min operator) [5].

This research considers each population generated by the ABC algorithm an inference fuzzy rule set. The min-max inference is applied to choose the fired rule for each region from the generated rule set according to actual data. Through mamdani inference system, all the generated features’ rank of ABC’s population is applied on each region to get the fired rule. The procedure calculates the membership degree for each feature belongs to the subset’s rank generated by ABC algorithm, then get the maximum degree for each rule. Afterwards the procedure captures the rule which have the minimum degree. So, this is the fired rule for specific region. The procedure compares the fired rule (conditional and decision parts) for each region with the input stream (actual data) to calculate fitness function using correlation coefficient.

4.3.3. Finding appropriate fitness function

Choosing appropriate fitness function to measure the confidence of the generated fuzzy rules is a very important step. Confidence [19] is the statistics of probability that sub sequent events occur under the condition of occurrence of the precursor events in trading data sets. It is used to measure their liability of the rules using the following Equations (8)–(11). $confidence = prob (x | y) = \frac{sup (x \land y)}{sup (x)}$ (8) $sup (x \land y) = \frac{sup (x \land y)}{| N |}$ (9) $sup (x) = \frac{| x |}{| N |}$ (10) $sup (y) = \frac{| y |}{| N |}$ (11)

Where

x represents the conditional attributes (barriers’ rank) in rule R and y represents the decision attribute (class rank),

sup(x ∩ y) represents the number of data records containing both x & y divided by the total number of data records,

sup(x) represents the number of data records containing x divided by the total number of data records.

sup(y) represents number of data records containing y divided by the total number of data records.

The previous equations measure the repetition of the conditional and decision parts within the data which implies that the rule represent the data. But the rate of implication between x and y is important and should be taken in consideration. The correlation analysis [20] is concerned by measuring the implication between the conditional attributes (x) and thedecision classes attribute (y). The fit rule should have high confidence more than a certain predefined threshold [8] while classified as positively correlated. The algorithm of proposed TFRML-ABC system for generating MSAN location fuzzy rules is illustrated in Fig. 4. Therefore, the importance of the correlation analysis appears. Equation (12) measures the correlation between x and y. $corr (x, y) = \frac{pr (x, y)}{pr (x) * pr (y)}$ (12)

IF corr (x, y) <1 → x and y are negatively correlated, corr (x, y) >1 → x and y are positively correlated, corr (x, y) =1 → x and y are independent.

During the ABC algorithm, the rules with high confidence values and correlation that exceed 1 are taken only in consideration as the fittest rules.

The ABC fitness procedure for evaluating the fuzzy rules is represented by getting the fired rules for each region calculated by min-max mamdani method illustrated in the previous section. Then procedure calculates the probabilities for (x ∩ y), (x) and (y) using Equations (9)–(11) respectively. Afterwards, itmeasures the correlation using Equation (12). Finally, it returns the confidence value level of positively correlated rules as the most fit rules.

4.4. Proposed hybrid (TFRML-ABC) accuracy measure

The accuracy of the proposed hybrid model (TFRML-ABC) should be measured accurately to prove the ability of the proposed hybrid model in classification. The computation of the accuracy rate is measured by the complement of the absolute error rate Equation [21]. $Accuracy = 1 - \frac{N_{E}}{N}$ (13)

Where N_E the number of badly classified test instances and N is the total number of the testing data instances.

5. Experiments and results

Planning the infrastructure of a typical Telecommunication Access Network (TAN) is a challenging problem. Many problems appear in designing accurate telecommunication fuzzy rules for locating MSANs. This research handles these problems by GIS tools and two artificial intelligent algorithms. The proposed fuzzy inference system is composed of four sequential phases. The first module prepares the GIS training data set and defines the barriers in the different regions under study. This is implemented via collecting and inserting all barriers (features)which effect on selecting suitable MSANs Locations on digital maps (vector maps). These barriers represented in environmental barriers, Access network barriers, topographic barriers, utilities barriers and other miscellaneous barriers [3]. The researchers divided the region under the study into 100*100 grid by using geographic analysis tools of ARCGIS 10.3 to analyze each region to determine the appropriate grid for locating MSANs, after this step, the researchers calculated the distance automatically between the center point of the 100*100 grid and existing barrier individually. Moreover, each 100*100 grid divided into smaller regions 5*5 grid and gut the centroid point of each 5*5 grid to determine the suitable point (site) for MSAN. The researchers neglected all points overlaying on any barriers such as buildings, manholes, copper cabinets, then calculating the distance between each point (centroid) and barriers within the 100*100 grid taking in the consideration all types of barriers [3]. The second module is responsible for generating fuzzy membership functions for the barriers’ subsets. This is achieved through generating the degree of membership of the barriers’ values in their identical subsets. This procedure is implemented automatically for telecommunication network barriers using PSO-TE [3]. PSO uses meta-heuristic search to find the best parameters for drawing a triangle and trapezoid membership function for each network barrier. The maximization of total entropy function (entropy and mutual information) is worked as a fitness function of the PSO. This module is presented before in a previous work [3].

The third phase uses the generated membership degrees from the second phase and the set of training data to generate fuzzy rules via applying the capabilities of ABC. The procedure builds the fuzzy rule set in the initial subpopulations randomly. Then it chooses the fired rule for each region according to the actual training data basing on the mamdani Min-Max inference system. The procedure continues through all iterations of ABC to find the preferable rules representing the training data set whereby the fitness function which maximizes the rules correlation and confidence rates. The final subpopulations represent the final fuzzy rule set so they are just combined without repetition. The fourth phase measures the accuracy of the whole system that is calculated in the complement of absolute error rate of the proposed system. The data sets used in this research to test proposed (TFRML-ABC) are taken from GIS analysis tools namely (extract, overlay and proximity) and their properties are illustrated in Section 4.1.

In experiments, the PSO-TE trained with seven telecommunication barriers. Figure 5 (b1, b2) are examples of the membership function generated by the PSO-TE for telecommunication barriers namely (near Copper Cabinet and near manhole). Figure 5 (a1, a2) shows the PSO-TE convergence rate for converting the same two telecommunication barriers.

Fig.5

Membership functions of the spatial input data using the PSO_TE process.

TFRML-ABC is simulated by MATLAB r2015a software. The simulation is accomplished on an Intel Core i7-4510 U CPU processor, 6GB of RAM, and 1tera hard drive. After a number of trials the best parameters of ABC (No of iterations, No of populations (colony size), No of employed bees and No of Onlookers bees) shown on the following Table 3.

Table 3

ABC Parameters

Variable	Description	Value
MaxItr	No of iterations	50
nVars	No of barriers (decision variables)	7
VarMax	Maximum barriers’ rank	3
VarMin	Minimum barriers’ rank	1
ClassRank	Decision variables	1 or 2
Npop	No of population (colony size)	552
NEmloyedBees	No of employed bees	276
NOnlookerBees	No of Onlookers bees	276
L	An abandonment Limit Parameter	L=round(0.5(nVar+1)Npop)
a	An acceleration coefficient upper bound	1

Table 4 shows the accuracy level of the TFRML-ABC model and rule sets generated by C4.5, decision tree, JRip (Java RIPPER), Naïve Bayes, k-nearest neighbors(K-NN), Random Forest, Multilayer perceptron(ANN), function SMO (SVM), meta bagging, Multilayer perceptron &hoeffding tree(ANN &Hoeffding tree), function SMO & K-nearest neighbors (SVM & K-NN) using weka data miner tool [22]. Figure 6 shows the same comparison in graphical mode. These comparisons show that TFRML-ABC model gave better accuracy level than the other classification algorithms in WEKA data miner tool. An average accuracy of the proposed (TFRML-ABC) model is around 97.8161%.

Table 4

The comparison between the accuracy of proposed model and the accuracy of other algorithms

Algorithm name	Correctly classified instances	Incorrectly classified instances
C4.5	91.8478%	8.1522%
Decision Table	92.5725%	7.4275%
JRipper	94.2029%	5.7971%
Naïve Bayes	86.0507%	13.9493%
k-nearest neighbors	92.3913%	7.6087%
Random Forest	90.9574%	9.0426%
Multilayer perceptron	91.8478%	8.1522%
SMO	90.942%	9.058%
bagging	84.4203%	15.5797%
Multilayer perceptron&hoeffding tree	91.1232%	8.8768%
SMO&K-nearest neighbors	90.942%	9.058%
(TFRML-ABC)	97.8161%	2.1839%

Fig.6

The comparison between the time of proposed model and the time of other algorithms in graphical mode.

Table 5 and Fig. 7 show the time taken in generating fuzzy rules sets by TFRML-ABC model and the same algorithms illustrated in previous section.

Fig.7

The comparison between the time of proposed model and the time of other algorithms in graphical mode.

Table 5

The comparison between the time of proposed model and the time of other algorithms

Algorithm Name	Time by sec
C4.5	0.31
Decision Table	0.34
JRipper	0.28
Naïve Bayes	0.27
k-nearest neighbors	0.01
Random Forest	0.01
Multilayer perceptron	325.89
SMO	0.33
bagging	0.06
Multilayer perceptron &hoeffding tree	234.65
SMO &K-nearest neighbors	0.05
(TFRML-ABC)	0.56

Because the barriers values are combined with the membership degrees during processing, the time complexity shows that the TFRML-ABC takes longer than other algorithms. Although the proposed system takes longer time, it handles uncertainty in the telecommunication environment better than the other algorithms.

6. Conclusion

Nowadays, Telecommunication Access Network (TAN) is a vital issue in human lives. Planning the infrastructure of a typical Telecommunication Access Network (TAN) is a challenging problem. This is because the implied high level of both uncertainty and ambiguity of GIS data represented in locating MSANs in the appropriate site. In this paper, a proposed model called TFRML-ABC (Telecommunication Fuzzy Rules for MSANs Locations using Artificial Bee Colony) is presented to classify the MSAN’s locations. This model utilizes the ABC as a meta-heuristic search algorithm to generate appropriate barriers-class rules for planning telecommunication accessinfrastructure. The correlation and confidence functions work as the fitness function. It evaluates the locating MSAN rules’ according to the training data using min-max mamdani inference system. The experimental results proved the ability of proposed TFRML-ABC model to classify the MSAN’s features (barriers) taking into consideration the misclassification. The total classification accuracy of the TFRML-ABCmodel is 97.8% rates.

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Telecommunication Fuzzy Rules for Multi Services Access Nodes Locations using Artificial Bee Colony

Abstract

Keywords

1. Introduction

2. Motivation and related work

3. Preliminaries

3.1. Fuzzy system

Table 2 Membership Degrees for two samples of barrier Regions NEAR copper cabinet NEAR water network ID M1 M2 M3 M1 M2 M3 ID1446 0 0.061109 0.938891 0.019896 0.980104 0 ID1447 0.789955 0.210045 0 0.685425 0.314575 0

4.3.1. Artificial bee colony algorithm

References

Table 2
Membership Degrees for two samples of barrier

Regions NEAR copper cabinet NEAR water network

ID

M1 M2 M3 M1 M2 M3

ID1446 0 0.061109 0.938891 0.019896 0.980104 0

ID1447 0.789955 0.210045 0 0.685425 0.314575 0